' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]LF L}BBL] X  ` 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?   1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!H(+ "@H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   LDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^Lõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- ( B  Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(` d ֠z# u`a DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2 :"PRESS RETURN WHEN READY TO CONTINUE.";X$\ <Y$(4):Y$;"RUN APR.87:PG.288- SHUFFLE - 4"] DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2:"PRESS RETURN WHEN READY TO CONTINUE.";X$a <Y$(4):Y$;"RUN MAR.87:PG.229- PERMUTATIONS - 1"Eb DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2:4:"FOR DETAILS, CONSULT:">8:"THE MATHEMATICS TEACHER"X13:"FEBRUARY, 1987"l16:"PAGE 127"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dX:237F5210:I421:I:2:J237:" ";:J:" ":I=PlZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$rx|p5040z5:3-ENTER SHORT DESCRIPTION"PROGRAM TO PLOT PERIODIC PICTURES.":3:"DESCRIPTION FOLLOWS IN THE PROGRAM."16Y"-- AUTHOR'S NAME39:13:"RAY S. NOWAK"G14:17:"FROM"m16:8:"THE MATHEMATICS TEACHER"---ENTER VOL. NO.11:"VOLUME 80 NUMBER 2"11:"(C) COPYRIGHT 1987"23(5210--- GO TO DESCRIPTION.60002<4"D$(4):D$"RUN SYSTEM MENU"*:45090:B:k:I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:"*":5040-- ARTICLE TITLE5:11:"PERIODIC PICTURES"7:18:"B216D(K2)pKBz22:"DO YOU WANT TO PLOT ANOTHER PERIODIC"a"PICTURE? (YES OR NO)";A$v(A$,1)"Y"210(A$,1)"N"890:~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$Y$"Y"?""('YES' OR 'NO')";G$1(G$,1)"N"830F(G$,1)"Y"760O700V2gGY815216x GX025228GX,GY GX*GY4 PLOTTING>:3HD(I1)D(J)RD(I2)D(J1)\KJI f28D(K),15216D(K1)28D(K1),15TURE";G$D!N X AND Y AXES+X:23Pb"DO YOU WANT 'X' AND 'Y' AXES?"jl"('YES' OR 'NO')";G$v(G$,1)"Y"660(G$,1)"N"70060020,80,1520,152252,152 GRID POINTS:23"DO YOU WANT GRID POINTS80 J I 210:  PERIODIC LENGTH AND DIGITSG LPIJ1O : "THE DIGITS IN THE PERIOD OF ";X"/";Y;" ARE:"  KJI D(K); K &: 0"THE LENGTH OF THE PERIOD IS: "LP:24:"PRESS RETURN TO PLOT PERIODIC PICx>px?p 0?0`x3x>p?p F?p1?xxc0xL 0C@@03CLa@0>p~p>`8p<`~~>?p`>@>p>xx>p?p?px>pG?p f03c0f`@L ~3CyO@03|CqOa@0>p~p>@?p~@>@?px?>~`>`|~>p?p?px>pG?p f00C1f`` F X AND Y":"MUST BOTH BE POSITIVE.":":GO TO 230J , DIVISION ALGORITHM] 6NY1:Y2N2n @R(25),D(50)v JRX TI1N ^R0D(I)0:480 hR(I)R rR10R |Z(RY) D(I)Z RRZY  CHECK FOR PERIOD J1I RR(J)4THAN ONE FOR THIS PROGRAM."J "THE MAXIMUM VALUE FOR 'Y' IS ABOUT 424."R :d "ENTER X ";Xj | ""ENTER Y ";Y %X0Y0ĺ:"THE VALUES OF X AND Y":"MUST BOTH BE POSITIVE."::230 'XY0XY1ĺ::2301 *X0Y0ĺ:"THE VALUES O " 1 2 2 3 N-1 N N 1"M :"PLOT EACH OF THESE POINTS AND JOIN"g "THEM SEQUENTIALLY." 24:"PRESS RETURN TO ENTER FRACTION 'X/Y' ";G$ PAGE TWO :: : "THE FRACTION 'X/Y' MUST BE GREATER THAN" "ZERO AND LESS ' BE ANY RATIONAL NUMBER FROM"I d"(0,1). REPRESENT PERIODIC DIGITS IN"s n"DECIMAL FORM OF 'X/Y' BY 'AA...A'." x" 12 N" :"FORM ORDERED PAIRS, SEQUENTIALLY AS" "FOLLOWS:" :"(A,A),(A,A), ... (A,A),(A,A)"! 5000" INTRO PAGE/:::298192c(4)"** PERIODIC PICTURES PROGRAM **"29)"NOWAK-FRIEDRICH 1982"::<"THIS PROGRAM PLOTS PERIODIC PICTURES"F"CREATED BY CLAIRE ZELLER IN THE"P"FOLLOWING WAY:" Z:"LET 'X/Y          LS, CONSULT:"/8:"THE MATHEMATICS TEACHER"I12:"DECEMBER, 1986"]16:"PAGE 734"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dIx>pw=?p|0C``0x>p?pp?||1pGpG|aCqpG|~>p@?p~s>pp~>pp@A|aC@A|q|?>~?`>p?pxx>px?p0c0``0x>p?pL 30C@@a03CLa@a0~>p?p~p>pp?x~p>~?p>p>p|>?`(5)N$(28):A$(6)N$(29):M6:8240 x#MX$"PROBABILITY & STATISTICS":A$(1)N$(10):A$(2)N$(11):A$(3)N$(12):A$(4)N$(14):A$(5)N$(38):A$(6)N$(39) y#A$(7)N$(40):A$(8)N$(41):A$(9)N$(49):A$(10)N$(50):A$(11)N$(51):M11:8240F:"PRESS RETURN WHEN READY TO CONTINUE.";X$` <Y$(4):Y$;"RUN MAY.87:PG.404- PERMUTE/COMBINE"INATIONS" a DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"PRESS RETURN WHEN READY TO CONTINUE.";X$\ <Y$(4):Y$;"RUN APR.87:PG.287- SHUFFLE - 3"A] DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"PRESS RETURN WHEN READY TO CONTINUE.";X$^ <Y$(4):Y$;"RUN MAR.87:PG.212- LN(X) PROGRAM"~>ppG>p `a03g`a03?p>@x>pA~_ DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 216:4:"FOR DETAILS, CONSULT:"A8:"THE MATHEMATICS TEACHER"\12:"SEPTEMBER, 1986"p16:"PAGE 472"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dI:I:2:J237:" ";:J:" ":I%PTZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$Zxdp5040nz5:3-ENTER SHORT DESCRIPTION"PROGRAM TO GENERATE MAGIC SQUARES ":3:"OF SIZE N. YOU ENTER A VALUE OF N "3:"BETWEEN 1 AND 20."9:13:"ANTONIO PIZARRO"/14:17:"FROM"U16:8:"THE MATHEMATICS TEACHER"l---ENTER VOL. NO.11:"VOLUME 79 NUMBER 6"11:"(C) COPYRIGHT 1986"23(5210--- GO TO DESCRIPTION.60002<:23F5210:I421 5090:B:I13:I:J138:"*";:J:"*":IfI421:I:1:"*";:39:"*":II138:"*";:I:"*":5040-- ARTICLE TITLE5:5:"COMPUTER-GENERATED MAGIC SQUARES"7:18:"BY"-- AUTHOR'S NAME PRINTS AUXILIARY SQUARES'I1N2J1NF5J);AU(I,J);QJ::XI^fy:~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$Y$"Y"ė:120D$(4):D$"RUN SYSTEM MENU":30 X1:X1N:740) XN:X1N(N1)K NU0NUX1NUX(NUX)790V H1Ig NUC(H)790n Hw 800 FL1  > AUXILIARY SQUARES HIABC RJDE \AU(I,J)AU(IK,JK) fJ pAU(I,PL)AU(IK,QL) zI TO ";(N1)N;" IN ANY ORDER"' DI1N/ NNU8 X690G bFL1650 l"THAT NUMBER IS ALREADY IN OR IS NOT A PROPER INTEGER" v590 C(I)NU C(I)MPI I   CHECK FOR EQUAL NUMBERS AND IMPROPER ENTRIES FL0 T720,7 I SUM.5N(NN1)@ :3);"THE MAGIC SUM IS ";SUMP 5210:4985z  USER PICKS THE ORDER OF THE NUMBERS I1N:C(I)1:I T550,570 &"ENTER THE NUMBERS 1 TO ";N;" IN ANY ORDER" 0580 :"ENTER MULTIPLES OF ";N;" FROM 0 J)AU(I,J) ^J hI, r PRINT SQUARESO |3);"AUXILIARY SQUARE #";T:X 910_ Tr  MAGIC SQUARE :"MAGIC SQUARE WITH ";N;" ROWS AND ";N;" COLUMNS": I1N J1N AU(I,J)F(I,J)S(NI1,J) 5J);AU(I,J); J::T2MME 520 J1N/ AU(P,J)C(J)6 JC PN280m AP1:BN:C1:D2:EN:K1:PL1:QLNv 830 P1300 AP1:B1:C1:D1:EN1:K1:PLN:QL1 "830 ,I1N 6J1N @T330,340 JF(I,J)AU(I,J):350 TS(I, 5000%d MAGIC SQUARESLnF(30,30),S(30,30),AU(30,30),C(30)ox"HOW MANY ROWS OR COLUMNS ";NN2(N2)0150"ONLY ODD NUMBERS ACCEPTED":120M1.5(N1):ME.5N(N1)T12"GET SQUARE #";T:T1MM1      40 z5:3* -ENTER SHORT DESCRIPTIONs "PROGRAM TO SOLVE THE EQUATION: ":7:"X^3 -X^2 -X -1 =0 " 3:"BY THE BINARY SEARCH (BISECTION)":3:"METHOD. YOU ENTER THE END POINTS OF" 3:"THE ORIGINAL INTERVAL." 16:4:"FOR DETAIR VOL. NO.( 11:"VOLUME 79 NUMBER 9"F 11:"(C) COPYRIGHT 1986"N 23X (5210r --- GO TO DESCRIPTION| .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p50 I138:"*";:I:"*":" , 5040B -- ARTICLE TITLEn 5:6:"POLYNOMIAL EQUATIONS REVISITED" 7:18:"BY" -- AUTHOR'S NAME 9:10:"JULIAN C. F. SULLIVAN" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTE ENDd ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$r Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":IP d"Q=";Q;15);"P(Q) =";P1:"R=";R;15);"P(R)= ";P2:"H= ";H;15);"P(H)= ";P3V el n(P3).00005170} xP1P30150 QH 40 RH 40 "THE APPROXIMATE SOLUTION IS=";H 4990 "THERE IS NO SOLUTION IN THE INTERVAL"  5000I SOLUTION OF EQUATION BY BINARY SEARCH (BISECTION)x"BOUNDARIES OF THE STARTING INTERVAL ARE""ENTER ENDPOINTS Q,R=";Q,R(2P1QQQQQQ1<P2RRRRRR1FP1P20190PH(QR)2 ZP3HHHHHH1SHIONS UNTIL IT DROPS INTO":3:"ONE OF THE CORNER POCKETS."`#16:4:"FOR DETAILS, CONSULT:"#8:"THE MATHEMATICS TEACHER"#12:"SEPTEMBER, 1986"#16:"PAGE 457"#24:5:"PRESS ANY KEY TO CONTINUE.";:R$#dIM TO SIMULATE THE PATH OF A":3:"BILLIARD BALL. THE PROBLEM ASSUMES":3:"A POOL BALL STARTS OUT AT THE LOWEST""3:"LEFT OF A TABLE AND TRAVELS AT A 45":3:"DEGREE ANGLE TO THE HORIZON. THE"<#3:"BALL CONTINUES TO CAROM OFF THE ":3:"VARIOUS CUCOPYRIGHT 1986"!23!!(5210;!--- GO TO DESCRIPTIONE!.6000K!2U!<:23!F5210:I421:I:2:J237:" ";:J:" ":I!P!Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$!x!p5040!z5:3!-ENTER SHORT DESCRIPTIONp""PROGRACLE TITLE/ 5:8:"WHERE IS THE BALL GOING?"@ 7:18:"BY"V -- AUTHOR'S NAME 9:5:"JACK A. OTT & ANTHONY CONTENTO" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 79 NUMBER 6"!11:"(C) TER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$9Y$"Y"4ZD$(4):D$"RUN SYSTEM MENU"b:l5090rz::I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:"*":5040 -- ARTI2060$ RESP$"NO"RESP$"N"ī3020* J "PLEASE ANSWER YES OR NO."T 2960^ 4985 CHANGE THE COLOR OF THE PATH AFTER EACH CAROM WW1 W4W8WW1 W16W0 y:+~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENh CRNERHITĺLr CRNERHITĺ"YOU DIDN'T GUESS CORRECTLY. IT'S NOT THE";| CRNERHITĺSPOT$(CRNER)" CORNER YOU PICKED." LNGTH" BY "WDTH" GIVES THE "SPOT$(HIT)" CORNER." "WOULD YOU LIKE TO TRY AGAIN ==> ";RESP$ RESP$"YES"RESP$"Y"īDX:30402 CALCULATE NEW POSITION FOR THE BALLE" XXDX:YYDYg, GO BACK AND REPEAT THE LOOPq6 2550@ COLOR IN THE CORNER WHERE THE BALL DROPSJ 11T X,Y:X,YDY:XDX,Y:XDX,YDY^ CRNERHITĺ"YOU GUESSED THE CORRECT CORNER."IKING PATTERN% CHECK TOP CUSHIONH Y6DY1YYDY:DYDY:3040c CHECK BOTTOM CUSHION YLNGTH5DY1YYDY:DYDY:3040 CHECK RIGHT CUSHION XWDTH5DX1XXDX:DXDX:3040 CHECK LEFT CUSHION X6DX1XXDX:DX>p ?~>p`?p~~>pp>p?|c|q pG?@a03[qGa@a0 ~>|@~p>~?pxpx>pg?p 00C1 ``0>>p `~>p`?p~>pp>ppa03pa0A>p~>p~@x>pw=?plF~pC9xc0`0>| `~>p@?p HIT0ī2890M CHECK TO SEE IF THE BALL IS ABOUT TO CAROM OFF A CUSHION IF SO, REPOSITION THE BALL FOR THE CORRECT REBOUND AND ALTER DX OR DY TO CHANGE ITS DIRECTION AFTER THE REBOUND  ALSO CHANGE THE PATH COLOR TO PRODUCE A MORE STRLUDED FOR COMPLETENESS IN CASE A REVISIONUZ INCLUDES ANGLES OTHER THAN 45 DEGREESyd X6YLNGTH5DX1DY1HIT2n CHECK TOP LEFT CORNERx X6Y6DX1DY1HIT4 CHECK BOTTOM RIGHT CORNER XWDTH5YLNGTH5DX1DY1HIT3AY:INDEXE CHECK TO SEE IF THE BALL IS ABOUT TO GO INTO A POCKETP HIT0m( CHECK TOP RIGHT CORNER2 XWDTH5Y6DX1DY1HIT1< CHECK BOTTOM LEFT CORNERF THIS CASE SHOULD BE IMPOSSIBLE WITH ONLY 45 DEGREE ANGLES.)P IT IS INCGTH65 5,WDTH65- 5,WDTH6LNGTH6C 5,LNGTH6WDTH6a COLORS IN TABLE SURFACEh 4y Y6LNGTH5 6,WDTH5Y Y INITIALIZE VARIABLES X6:YLNGTH5:DX1:DY1:W15 DRAW BALL W X,Y  INDEX14DL) TO 255(SLOW) ==> ";DLAY6 DLAY0DLAY255ī2350Z "INCORRECT CHOICE; TRY AGAIN."d$ 2300j. 8 CLEAR THE TEXT PART OF SCREENB 24L :::V 22` "YOUR TABLE IS "LNGTH" BY "WDTH"."j DRAWS TABLE BOUNDARIESt 8~ 5,LN" 2) LOWER LEFT"2" 3) LOWER RIGHT"K" 4) UPPER LEFT"Qv"CHOOSE 1,2,3 OR 4 ==> ";CRNER(CR1)(CR2)(CR3)(CR4)0ĺ"INCORRECT CHOICE; TRY AGAIN":2200"PICK A SPEED FOR THE ROLLING BALL." "USE 0(FASTRN' KEY."P255USIO YOU WANT TO USE?"0p"USE 3 TO 33 ==> ";WDTHBzWDTH3ī2150UWDTH33ī2150SPOT$(1)"UPPER RIGHT":SPOT$(2)"LOWER LEFT":SPOT$(3)"LOWER RIGHT":SPOT$(4)"UPPER LEFT""WHICH CORNER WILL THE BALL DROP INTO"" 1) UPPER RIGHT" STROBEA$ : 255M "THE LENGTH IS THE VERTICAL DIMENSION."t*"WHAT LENGTH DO YOU WANT TO USE?"4"USE 5 TO 33 ==> ";LNGTH>LNGTH5ī2090HLNGTH33ī2090R\"THE WIDTH IS THE HORIZONTAL DIMENSION."f"WHAT WIDTH DAY BE ABLE TO OBSERVE SOME"!O"PATTERN TO THE SIZE THAT WILL HELP YOU"U"PREDICT INTO WHICH CORNER THE BALL""WILL FALL."::::"HIT ANY KEY WHEN READY TO START."::49168,0: CLEAR KEYBOARDLx>pg?p F?0C1xc `0>`3"WILL ALSO COMMENT ON HOW ACCURATE YOUR"9&T0"ORIGINAL GUESS WAS."^:::D"HIT ANY KEY WHEN READY TO GO ON."N49168,0: CLEAR KEYBOARD STROBEXA$bl"BY CHECKING OVER THE RESULTS OF SEVERAL"v"RUNS, YOU M4"WISH TO USE. NEXT, YOU WILL BE ASKED TO":g"GUESS WHICH CORNER THE BALL WILL DROP"m"INTO. FINALLY, THE COMPUTER WILL DRAW""OUT THE BALL'S PATH ON THE TABLE UNTIL""IT DROPS INTO A POCKET. THE MACHINE" WHICH J8T"CORNER THE POOL BALL WILL DROP INTO."B^::jh"HIT ANY KEY WHEN READY TO GO ON."r49168,0: CLEAR KEYBOARD STROBE|A$"YOU WILL HAVE A CHANCE TO SPECIFY THE""DIMENSIONS (SIZE) OF THE POOL TABLE YOU" IT DROP"9"INTO THE SAME CORNER, OR MAYBE THE"?i"UPPER RIGHT, OR POSSIBLY THE UPPER"o"LEFT OR LOWER RIGHT? CLEARLY, YOU HAVE"","FOUR (4) CHOICES. THE SIZE OF THE TABLE"6@"PROBABLY HAS SOMETHING TO DO WITH READY TO GO ON."6 49168,0: CLEAR KEYBOARD STROBE> A$D q "THE OBJECT OF THIS EXERCISE IS TO TRY"w  "AND GUESS WHICH CORNER THE POOL BALL"  "WILL DROP INTO. IT ALWAYS STARTS OUT IN"  "THE LOWER LEFT CORNER. WILL"Y"ī1300  1250 ) 100T ("THIS PROGRAM WORKS MUCH BETTER ON A"Z 2 <"COLOR TELEVISION. OTHERWISE, SOME OF" F P"THE PATHS DISPLAYED ARE HARD TO FOLLOW" Z d"ON A BLACK & WHITE SET." n:: x"HIT ANY KEY WHEN ALWAYS TRAVELS AT 45 DEGREES TO THE HORIZON.3 9 A :j "DO YOU WISH INFORMATION ABOUT AND"p  "DIRECTIONS FOR THIS PROGRAM?"  "PLEASE ANSWER YES OR NO ==> ";REPLY$ REPLY$"NO"REPLY$"N"ī2060 REPLY$"YES"REPLY$TABLE AND TRAVELS AT A 45 DEGREE ANGLE TO THE HORIZON.w t THE BALL CONTINUES TO CAROM OFF THE VARIOUS CUSHIONS UNTIL ~ IT FINALLY DROPS INTO ONE OF THE CORNER POCKETS.  THERE ARE NO SIDE POCKETS AND NO SPIN OR 'ENGLISH' ON THE-  BALL, SO ITD BALL PROBLEM- 8 (HERE CALLED POOL TABLE)m B DESCRIBED IN THE TEXTBOOK, MATHEMATICS, A HUMAN ENDEAVOR, L WRITTEN BY HAROLD JACOBS AND PUBLISHED BY FREEMAN & CO. V ` THE PROBLEM ASSUMES A POOL BALL STARTS OUT AT THE LOWER LEFT6 j OF A  5000< AUTHORS: ANTHONY CONTENTO & JACK OTTf WEST HEMPSTEAD HIGH SCHOOL 400 NASSAU BOULEVARD WEST HEMPSTEAD, NY 11552 516-489-7620$ . THIS PROGRAM DUPLICATES THE BILLIAR                  :"PRESS RETURN WHEN READY TO CONTINUE.";X$b <Y$(4):Y$;"RUN MAR.87:PG.210- ARCTAN(X) PROGRAM"Xc DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  ERIOR OF THE UNIT CIRCLE.">16:4:"FOR DETAILS, CONSULT:"`8:"THE MATHEMATICS TEACHER"z12:"DECEMBER, 1986"16:"PAGE 729"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dIION"A SIMULATION TO CALCULATE THE ":3:"FREQUENCY OF AB<1, WHERE A AND B":3:"ARE POINTS IN THE INTERIOR OF THE":3:"UNIT CIRCLE. PROGRAM ALSO CALCULATES"3:"THE FREQUENCY THAT THE DISK WITH ":3:"DIAMETER, AB, LIES WITHIN THE":3:"INT"11:"(C) COPYRIGHT 1986"'231(5210K--- GO TO DESCRIPTIONU.6000[2e<:23F5210:I421:I:2:J237:" ";:J:" ":IPZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$xp5040z5:3-ENTER SHORT DESCRIPTAT ILLUSTRATE THE":4:"TECHNIQUES OF COMPUTER SIMULATION"K7:18:"BY"a-- AUTHOR'S NAME9:3:"JOSEPH E. CHANCE & PEARL W. BRAZIER"14:17:"FROM"16:8:"THE MATHEMATICS TEACHER"---ENTER VOL. NO.11:"VOLUME 79 NUMBER 9" ";Y$Y$"Y"45D$(4):D$"RUN SYSTEM MENU"=:G5090MU:~:I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:"*":5040-- ARTICLE TITLE:5:4:"TWO PROBLEMS THILURE?FAILFAIL1:V2:H2:"*":H2H21:H240H211:V2V21_FAIL300(FAIL300)ī560r CLEAR SCREEN13:10:958&16:1:FAIL:V213:H2110~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:E FREQUENCY OF DISK IN CIRCLE IS ";DSKN2 J4990E  PLOT SUCCESSs V1:H1:"*":H1H11:H140H111:V1V11 SUC300(SUC300)ī460  CLEAR SCREEN & PRINT SUBTOTAL V1110:10:V1:868: 4:1:SUC:V11:H111  PLOT FAAB2P  COUNT DISK IN CIRCLE IF DISTANCE BETWEEN CENTERS + RADIUS OF DISK < 1p (XM2YM2)R1DSKDSK1w "I '20:(7);(7);"PRESS RETURN FOR SUMMARY";:A$: ,"FOR ";N;" TRIALS" 1 6"THE FREQUENCY OF AB<1 IS ";SUCN ;( @"THOINT B=(X,Y)A CALCULATE DISTANCE AB AND COUNT SUCCESS IF < 1] AB((X1X)2(Y1Y)2){ AB1SUCSUC1:400:250 500: PLOT FAILURE CALCULATE MIDPOINT OF AB,(XM,YM) AND RADIUS, R OF DISK WITH DIAMETER AB XM(X1X)2:YM(Y1Y)2:RIL0U V11:H111:V213:H211: INITIAL SCREEN LOCATIONS FOR SUCCESSES AND FAILURESr "NUMBER OF TRIALS = ";N :1:1:"SUCCESS":13:"FAILURE" I1N 50: GET POINT A SAVE POINT A=(X1,Y1) X1X:Y1Y 50: GET POINT B PE. 90c ( ** SUBROUTINE TO GENERATE A RANDOM POINT (X,Y) IN THE INTERIOR OF THE UNIT CIRCLEt 2X(1.0)21 <Y(1.0)21 FX2Y2150 P Z MAIN PROGRAM d SUC. COUNTS AB<1 n DSK..COUNTS DISK WITHIN CIRCLE xSUC0:DSK0:FA 5000 A SIMULATION TO CALCULATE THE FREQUENCY OF AB<1, WHERE A AND B ARE POINTS IN THE INTERIOR OF THE UNIT CIRCLE.  THE PROGRAM ALSO CALCULATES THE FREQUENCY THAT THE DISK WITH DIAMETER, AB, LIES WITHIN THE INTERIOR OF THE UNIT CIRCL       xp5040z5:37-ENTER SHORT DESCRIPTION"PROGRAM TO FIND THE ZEROS OF A":3:"POLYNOMIAL BY SYNTHETIC DIVISION."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"OCTOBER, 1986"16:"PAGE 558"&24---ENTER VOL. NO.511:"VOLUME 79 NUMBER 7"S11:"(C) COPYRIGHT 1986"[23e(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J237:" ";:J:" ":IPZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$:5040(-- ARTICLE TITLE~5:5:"USING THE MICROCOMPUTER TO FIND":4:"THE ZEROS OF A POLYNOMIAL FUNCTION"7:18:"BY"-- AUTHOR'S NAME9:11:"CHARLES D. FRIESEN"14:17:"FROM"16:8:"THE MATHEMATICS TEACHER" THE NUMBER OF YOUR CHOICE"9"AND PRESS 'RETURN':";OPJ OP1ė:230X*OP2120yD$(4):D$"RUN SYSTEM MENU":5090::I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:"*"NUE")"OR PRESS 'P' FOR A PRINT OUT."SA$::A$"P"PTR1:(4);"PR#1":270Y|"SELECT ONE OF THESE OPTIONS"::"1. SAME POLYNOMIAL, DIFFERENT INTERVAL":"2. DIFFERENT POLYNOMIAL":"3. EXIT FROM THE PROGRAM":: "TYPE:"PRESS RETURN WHEN READY TO CONTINUE.";X$c <Y$(4):Y$;"RUN MAY.87:PG.408- BINOMIAL PROB. - 3"d DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"PRESS RETURN WHEN READY TO CONTINUE.";X$\ <Y$(4):Y$;"RUN APR.87:PG.286- SHUFFLE - 2"A] DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2 157"3 24:5:"PRESS ANY KEY TO CONTINUE.";:R$9 dINUE. ";:R$ x p5040% z5:3C -ENTER SHORT DESCRIPTION "PROGRAM TO APPROXIMATE PI BY FINDING":3:"THE PERIMETER OF AN N-GON." 16:4:"FOR DETAILS, CONSULT:" 8:"THE MATHEMATICS TEACHER" 13:"FEBRUARY, 1987" 16:"PAGEICS TEACHER"# ---ENTER VOL. NO.A 11:"VOLUME 80 NUMBER 2"_ 11:"(C) COPYRIGHT 1987"g 23q (5210 --- GO TO DESCRIPTION .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTI*";:39:"*":I+ I138:"*";:I:"*":1 ; 5040Q -- ARTICLE TITLE 5:10:"LESSONS LEARNED WHILE":12:"APPROXIMATING PI" 7:18:"BY" -- AUTHOR'S NAME 9:11:"JAMES E. BEAMER" 14:17:"FROM" 16:8:"THE MATHEMAT :"SIN A =";SAs ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I I421:I:1:" ; 5000&Z APPROXIMATE PI,_Sd"N";:36,10:"PI";:36,25:"SINE"YianN6lxSA0.5r}~SA0210S2SAPNS2CA(1SASA)N;:36,10:P;:36,25:SASA((1CA)2)NN2126 END LOOP  "*";:J:"*":I3I421:I:1:"*";:39:"*":IOI138:"*";:I:"*":U_5040u-- ARTICLE TITLE5:7:"STUDYING DECIMAL FRACTIONS":10:"WITH MICROCOMPUTERS"7:18:"BY"-- AUTHOR'S NAME9:4:"RUTH ANN MEYER AND J:"PRESS RETURN WHEN READY TO CONTINUE.";X$c <Y$(4):Y$;"RUN MAY.87:PG.407- BINOMIAL PROB. - 2"d DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"OCTOBER, 1985"% 16:"PAGE 549"S 24:5:"PRESS ANY KEY TO CONTINUE.";:R$Y dI5040 z5:3, -ENTER SHORT DESCRIPTIONu "PROGRAM TO COMPUTE SIMPLE INTEREST":3:"USING THE FORMULA I=PRT." 3:"YOU ENTER THE PRINCIPAL, RATE," 3:"AND TIME." 16:4:"FOR DETAILS, CONSULT:" 8:"THE MATHEMATICS TEACHER" 13TER VOL. NO.* 11:"VOLUME 78 NUMBER 7"H 11:"(C) COPYRIGHT 1985"P 23Z (5210t --- GO TO DESCRIPTION~ .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p:39:"*":I( I138:"*";:I:"*":. 8 5040N -- ARTICLE TITLEu 5:7:"FROM SIMPLE INTEREST TO E" 7:18:"BY" -- AUTHOR'S NAME 9:11:"CLARK KIMBERLING" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---EN[ 5000p~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$~Y$"Y"4D$(4):D$"RUN SYSTEM MENU":5090::I13:I:J138:"*";:J:"*":I I421:I:1:"*";   :"PRESS RETURN WHEN READY TO CONTINUE.";X$c <Y$(4):Y$;"RUN MAY.87:PG.402- FUNCTION ITERATION"1d DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2 12)N$(48):M12:8240F#MX$"ANALYTIC GEOM./TRIG.":A$(1)N$(6):A$(2)N$(13):A$(3)N$(14):A$(4)N$(17):A$(5)N$(18):A$(6)N$(19)G#A$(7)N$(30):A$(8)N$(36):A$(9)N$(37):A$(10)N$(46):A$(11)N$(48):M11:8240'P#MX$"APPLICATIONS":A$(1)N$(1):A$(2)N$(713"224:5:"PRESS ANY KEY TO CONTINUE.";:R$8dI;:R$ xp5040z5:3=-ENTER SHORT DESCRIPTION"PROGRAM TO GRAPH QUADRATIC FUNCTIONS":3:"AS PART OF A WORKSHEET ACTIVITY."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"12:"DECEMBER, 1986"16:"PAGE ACHER"---ENTER VOL. NO.;11:"VOLUME 79 NUMBER 9"Y11:"(C) COPYRIGHT 1986"a23k(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J237:" ";:J:" ":IPZ24:7:"PRESS ANY KEY TO CONTINUE. "8:"*";:I:"*":!50407-- ARTICLE TITLEs5:7:"MICROCOMPUTER UNIT: GRAPHING ":15:"PARABOLAS"7:18:"BY"-- AUTHOR'S NAME9:3:"ELLEN H. HASTINGS AND BRIAN PETERMAN"14:17:"FROM"16:8:"THE MATHEMATICS TE:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$gY$"Y"4D$(4):D$"RUN SYSTEM MENU":5090::I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II13>ppGa 3CLa@A?|qCLa@A?|>p~p>?p`|~x>`8p@ ~>xx>p      XHI( &X11.58X11.58L0:6109 0D0L0580e :14012XL,809Y114012X,809Y:600z D14012X,809Y ND1:D11:L1:L11 XXLX bD1Y1Y lD0D11660 vR0R11L0L11660 II.0833 440 160 Y~11.58(K)8.77660 I0) XLH:XRH2 Y1K> JAIIH YKJe Y8.88Y8.77D0:610o XHI X11.58X11.58R0:540 D0R0510 14012XR,809Y114012X,809Y:530 14012X,809Y D1:D11:R1:R11 XRX140,0140,159 0,80279,80/ I827912> I,77I,83E "IT ,I81599e 6137,I143,Il @I J271,65277,71 T277,65271,71 ^147,0150,3153,0 h150,3150,6 r DRAW PARABOLA |HB(2A) K(4ACBB)(4A) (H)160+ ABB:SB$" + ":B0SB$" - ":ABBS ACC:SC$" + ":C0SC$" - ":ACC 21:" " 22:"Y = ";A;"X";:21:"2";:22:SB$;AB;"X";SC$;AC DRAW AXES  OT ENTER ZERO FOR A." x:? "TO QUIT, PRESS CTRL-RESET."n 23:"PRESS SPACE BAR TO CONTINUE ";:A$:u 3 23:" " 23:"TYPE A, B, AND C: (0,0,0 TO QUIT)";A,B,C A0B0C0ĉ::4990 A0: 5000 ?"TO GRAPH AN EQUATION OF THE FORM"ET(" 2"2"Y = AX + BX + C, ENTER YOUR VALUES FOR"<:F"A, B, AND C, SEPARATED BY COMMAS."P:Z"IF A = 0, THE EQUATION IS NOT QUADRATIC,"d n"SO DO N           ITS DIGITS, THEN DO THE SAME"|5:"THING WITH THE SUM, YOU WILL":5:"EVENTUALLY REACH A SUM THAT IS":5:"PALINDROMIC."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"15:"MAY, 1986"16:"PAGE 377"5210dINY KEY TO CONTINUE. ";:R$ x*p50404z5:3R-ENTER SHORT DESCRIPTION"PROGRAM THAT APPLIES THE FOLLOWING":3:"RULE TO PRODUCE PALINDROMES:":3:5:"IF YOU ADD ANY POSITIVE INTEGER":5:"TO THE NUMBER OBTAINED BY REVERS-":5:"ING THEORY":A$(1)N$(2):A$(2)N$(8):A$(3)N$(9):A$(4)N$(24):A$(5)N$(25):A$(6)N$(26):A$(7)N$(32)e#:A$(8)N$(33):A$(9)N$(34):A$(10)N$(35):A$(11)N$(44):A$(12)N$(45):M12:8240! n#MX$"PREALGEBRA":A$(1)N$(24):A$(2)N$(25):A$(3)N$(26):A$(4)N$(27):A$FOR DETAILS, CONSULT:"88:"THE MATHEMATICS TEACHER"R13:"FEBRUARY, 1987"f16:"PAGE 106"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dY237:" ";:J:" ":IPJZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$PxZp5040dz5:3-ENTER SHORT DESCRIPTION"PROGRAM TO GENERATE A TABLE OF ":3:"PRIMITIVE PYTHAGOREAN TRIPLES USING"3:"HALL'S ALGORITHM."16:4:""PHYLLIS LEFTON"%14:17:"FROM"K16:8:"THE MATHEMATICS TEACHER"b---ENTER VOL. NO.11:"VOLUME 80 NUMBER 2"11:"(C) COPYRIGHT 1987"23(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J:I13:I:J138:"*";:J:"*":IGI421:I:1:"*";:39:"*":IcI138:"*";:I:"*":is5040-- ARTICLE TITLE5:6:"MATRIX METHOD FOR GENERATING":9:"PYTHAGOREAN TRIPLES"7:18:"BY"-- AUTHOR'S NAME9:12:KY1X1EY113:10Y19);M1(1,Y1);:Y1::~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$Y$"Y"Ľ::100D$(4):D$"RUN SYSTEM MENU":5090:# &( Y13:10Y9);T(1,Y);:Y::D Y13:S(1,Y)T(1,Y):Y:t X113:Y113:R(X1,Y1)D(X1,Y1):Y1:X1:X113:Y113:R(X1,Y1)A(X1,Y1):Y1:X1:X111Y113M1(X1,Y1)0K13M1(X1,Y1)M1(X1,Y1)S(X1,K)M(K,Y1)4X113:Y113:M(X1,Y1)U(X1,Y1):Y1:X1:]X113:Y113:M(X1,Y1)A(X1,Y1):Y1:X1:X113:Y113:M(X1,Y1)D(X1,Y1):Y1:X1: X111 Y113 T(X1,Y1)0 K13 T(X1,Y1)T(X1,Y1)S(X1,K)R(K,Y1) K Y1 X1:"PRESS RETURN WHEN READY TO CONTINUE.";X$^ <Y$(4):Y$;"RUN MAY.87:PG.373- OCTAL SQUARES""_ DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"PRESS RETURN WHEN READY TO CONTINUE.";X$\ <Y$(4):Y$;"RUN APR.87:PG.285- SHUFFLE - 1"A] DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2660"224:5:"PRESS ANY KEY TO CONTINUE.";:R$8dI5040z5:3--ENTER SHORT DESCRIPTION"THIRD OF THREE PROGRAMS THAT ":3:"COMPUTE THE PROBABILITY OF A":3:"BINOMIAL EXPERIMENT."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"12:"NOVEMBER, 1986"16:"PAGE NTER VOL. NO.+11:"VOLUME 79 NUMBER 8"I11:"(C) COPYRIGHT 1986"Q23[(5210u--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J237:" ";:J:" ":IPZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$xp"*": 5040+-- ARTICLE TITLEv5:3:"THE MICROCOMPUTER AS AN ALTERNATIVE":12:"TO BINOMIAL TABLES"7:18:"BY"-- AUTHOR'S NAME9:11:"CLARK KIMBERLING"14:17:"FROM"16:8:"THE MATHEMATICS TEACHER" ---EO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$[Y$"Y"ė:30|D$(4):D$"RUN SYSTEM MENU":5090::I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:C(B)):870 V$:701*WR(C(B)C(A1)):870=4V$:70C>[H::"N,P = ";N","PgR:H$:m\fW0V$"0":920pW.999999V$"1":920zW$(WE)(W$)E1W$(10(E11))V$"."O$(E1(W$))W$I~:"DO YOU WISH TQ TO QUIT"Z(16384))16368,09Z69ĺ:80IZ85ĺ:50VZ8190_650e}"INPUT A,B = ";A,BA(A):B(.5B)"P[ A <= X <= B ] = ";ABANB0ĺ0:70A0A0BNBN:C(N)1 A0810 WR($;WR(D):870"36,30:V$/XN560J&X0X16(X16)590\0:36,20:R$;q:A$:XNė::70zD840NXX1:430Xb:X0:16368,0l"TAP E TO EVALUATE P[ A <= X <= B ]"v"TAP U TO INPUT ANOTHER N,P" "TAP  P0P1380, N0N300N(N)3805 840; f YX(P)(NX)(1P)L(N)L(X)L(NX)t P(X)(Y) X0C(0)P(0):D1C(0):470 C(X)C(X1)P(X):D1C(X) X; WR(P(X)):870 36,5:V$; WR(C(X)):87036,17:V YOU'LL SEE ALL THE INDIVIDUAL "Q 6" AND CUMULATIVE PROBABILITIES. THEN " @" INPUT A,B AND SEE P[ A <= X <= B]. " JS$:::"WAIT FOR PROMPT: "; T ^K1300:L(K)L(K1)(K):K h36,20:R$;:A$:: r |"INPUT N,P = ";N,POF X AS THE NUMBER OF HEADS "P " WHEN N COINS ARE TOSSED, EACH HAVING " " PROBABILITY P OF FALLING 'HEAD'. " S$ " YOU MAY INPUT ANY N FROM 0 TO 300 " " AND ANY P FROM 0 TO 1. " "S$::S$" ," FIRST "E I19:O$(I)O$(I1)"0":IK W ::S$ " THIS PROGRAM EVALUATES BINOMIAL PRO- " " BABILITIES; THAT IS, VALUES OF A " " BINOMIAL RANDOM VARIABLE X. " S$::S$! " THINK LUES F610: PRINT MENUL P720: INPUT A,B AND PRINT P[ A <= X <= B ]V Z ENDb _:4990| dC(300),L(300),P(300) nE16:E10(E1) xR(T)E(.5TE) H$"x P[X = x] P[X <= x] P[X >= x] " R$"PRESS 'RETURN' ..."% S$" : 5000* SAM'S SUMS H BINOMIAL PROBABILITIESr100: INITIALIZE VALUES AND STRINGS180: EXPLAIN PROGRAM(350: FILL ARRAY L (SUMS OF LOGS)2380: INPUT AND CHECK N,P <430: COMPUTE AND PRINT BINOMIAL VA     BROUTINE TO INITIALIZE STARTING TRIPLE,`9jS(1,1)3FtS(1,2)4S~S(1,3)5Y_w DATA FOR MATRICES} 1,2,2,-2,-1,-2,2,2,3 1,2,2, 2, 1, 2,2,2,3-1,-2,-2,2,1,2,2,2,3X113:Y113:R(X1,Y1)U(X1,Y1):Y1:X1:-"S(1,1)X(J1)%S(1,2)Y(J1)7S(1,3)Z(J1)>JD^ OPTION TO RUN AGAINd"DO YOU WANT TO LIST MORE TRIPLES?""PLEASE ENTER 'Y' OR 'N': ";A$:A$(A$,1)$A$"Y"ė:::190.A$"N"ė:4990B1050L&V SURI13\I1İ2100&^I2İ22005`I3İ2300Qf4500: MAT M1 = S * Mkp4600:MAT PRINT M1,wzPI3JP10001040X(P)M1(1,1)Y(P)M1(1,2)Z(P)M1(1,3)IX(P)2Z(P)ĺ"....END OF GENERATION";Y(P)41;"..."PLEASE ENTER AN INTEGER 1 OR GREATER"1NF(N)NN0740TN6790] 820fN6 "YOU ASKED FOR TOO MANY TRIPLES!"*"THIS WILL NOW LIST 1000 TRIPLES ONLY."4K(3N3)2>1100: INITIALIZE STARTING TRIPLEHJ0KS*R (2600: MAT PRINT T,=2700:MAT S = TDIv1020: GIVE USER OPTION TO RUN PROGRAM AGAIN| LIST GENERATIONS OF TRIPLESM1(1,3),M(3,3)X(1000),Y(1000),Z(1000)"HOW MANY GENERATIONS DO YOU WANT?"*5:"PRESS ANY KEY TO CONTINUE.";:R$+dI4:7:"PRESS ANY KEY TO CONTINUE. ";:R$.x8p5040Bz5:3`-ENTER SHORT DESCRIPTION"PROGRAM DESCRIPTION FOLLOWS."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"JANUARY, 1987"16:"PAGE 66"%24:OM")16:8:"THE MATHEMATICS TEACHER"@---ENTER VOL. NO.^11:"VOLUME 80 NUMBER 1"|11:"(C) COPYRIGHT 1987"23(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J237:" ";:J:" ":IP(Z2:I:J138:"*";:J:"*":I@I421:I:1:"*";:39:"*":I\I138:"*";:I:"*":bl5040-- ARTICLE TITLE5:8:"POWERS OF COMPLEX NUMBERS"7:18:"BY"-- AUTHOR'S NAME9:11:"CLARK KIMBERLING"14:17:"FRUT (0,0), WITH" "RADIUS "V? :"READY FOR ANOTHER RUN?"E  ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  ::I13 + ("D$")*I"" K1;:36,5:C$) K/ = B0470^ :"IMPORTANT OBSERVATIONS:" :"FOR EACH ROOT X+Y*I HAVING Y<>0," "THE CONJUGATE X-Y*I IS ALSO A ROOT." :"YOUR "N" ROOTS LIE EQUALLY SPACED ALONG" "A CIRCLE CENTERED ABOTP "VR(1N) ,A 6:"THERE ARE "N" COMPLEX NUMBERS Z "b @"SATISFYING Z^"N" = ";P$:} JK0N1:U(T2KP)N TCV(U):SV(U) ^I(C)EC(.5C) hI(S)ES(.5S) rC$(C):D$(S) |C0C$D$"*I":400 S0C$C$"UST NOT = 0." 130* P$(A):Q$(B)J B0P$P$" + ("Q$")*I"^ "INPUT N = ";Nq N0N(N)80 "SORRY, BUT N MUST BE A POS. INTEGER." 200 R(AABB):A0T(BA) A0B0TP2 A0B0T3P2 A0TN( P250: COMPUTE RADIUS R, ANGLE TK Z310: COMPUTE THE N NUMBERSg d430: PRINT ANALYSISo n70u x "INPUT A('Q' TO QUIT)= ";A$:A(A$) (A$,1)"Q"ė:4990 "INPUT B = ";B A0B0180 "SORRY, BUT ONE OF A AND B M- 50003 FRACTIONAL POWERS OF A+B*ia:"THIS PROGRAM COMPUTES (A+B*I)^(1/N),""WHERE A+B*I IS ANY NONZERO COMPLEX"("NUMBER AND N IS ANY POSITIVE INTEGER."2I(X)(X(.5X))<P4(1):E11024: F130: INPUT A,B,     z#ٮǮ̠® ٮǮ̠® ٮǮ̠®ҮǮΠ ҮǮΠҮǮƭǠ ٮǮ̠Ӡ ٮǮΠٮǮش ٮǮůҮǮԠ ҮǮҠӠ ҮǮҠҮǮŠ ҮǮŠҮǮŠҮǮŠ Ҡ®ǮĠƠ ®ǮŠɠҮǮΨة͠ҮǮӠҮǮӠҮǮӠ ήǮؠӠ ®ǮΠ !ήǮؠӠ"ήǮؠӠ ήǮؠӠ!®ǮΠ®ǮĠ  îǮ͠Ӡ îǮΠ îǮΠ ήǮŠӠ ήǮŠӠ ήǮŠӠ®Ǯà ֮ǮȠƠǠ ֮Ǯ٠Ӡ ҮǮΨة îǮǠ ֮Ǯ̠!֮Ǯ̠֮Ǯ̠ ЮǮ̠ŠЮǮàӠ ԮǮůŠ ԮǮӠƠٮԮǮҠ ԭؠ֮Ǯ͠Ϡ͠ՠ Ĵ"Ϡ ĠƠҠΠ Š ֮Ǯ٠ӠTION .6000 2 <:23O F5210:I421:I:2:J237:" ";:J:" ":IU P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p5040 z5:3 -ENTER SHORT DESCRIPTION"PROGRAM TO EXPRESS A RATIONAL NUMBER":3:"AS A DECIMAL WITH :"BY" -- AUTHOR'S NAMEK 9:4:"RUTH ANN MEYER AND JAMES E. RILEY"_ 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 80 NUMBER 2" 11:"(C) COPYRIGHT 1987" 23 (5210 --- GO TO DESCRIPNU" : 5090 # :L :I13:I:J138:"*";:J:"*":Ip I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE 5:7:"STUDYING DECIMAL FRACTIONS":10:"WITH MICROCOMPUTERS" 7:18"ANOTHER FRACTION(Y OR N)? ";A$% : (A$,1)"Y"500` "THANKS FOR USING THIS PROGRAM."f l u 255 ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM ME :( "WHAT IS THE NUMERATOR? ";N0 :S "WHAT IS THE DENOMINATOR? ";D[ &: 0"HOW MANY PLACES IN EXPANSION? ";P D::: NQ(ND) XN;"/";D;"="Q;"."; bI1P lN10(NDQ) vQ(ND) Q; I ::: $ 5000125 2Jd"THIS PROGRAM WILL GIVE THE DECIMAL"P|"EXPANSION OF ANY POSITIVE FRACTIONAL","NUMBER 'N/D' TO ANY NUMBER OF DECIMAL"^"PLACES 'P'.":"THINK OF A FRACTION YOU WANT TO EXPAND."N."' 16:4:"FOR DETAILS, CONSULT:"I 8:"THE MATHEMATICS TEACHER"c 12:"DECEMBER, 1986"w 16:"PAGE 736" 24:5:"PRESS ANY KEY TO CONTINUE.";:R$ dIRESS ANY KEY TO CONTINUE. ";:R$& x0 p5040: z5:3X -ENTER SHORT DESCRIPTION "PROGRAM TO SOLVE THE EQUATION: ":7:"X^3 -X^2 -X -1 =0 " 3:"BY THE METHOD OF ITERATION.":3:"YOU ENTER A FIRST ESTIMATE" 3:"OF THE SOLUTIO16:8:"THE MATHEMATICS TEACHER"8 ---ENTER VOL. NO.V 11:"VOLUME 79 NUMBER 9"t 11:"(C) COPYRIGHT 1986"| 23 (5210 --- GO TO DESCRIPTION .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PJ:"*":I. I421:I:1:"*";:39:"*":IJ I138:"*";:I:"*":P Z 5040p -- ARTICLE TITLE 5:6:"POLYNOMIAL EQUATIONS REVISITED" 7:18:"BY" -- AUTHOR'S NAME 9:10:"JULIAN C. F. SULLIVAN" 14:17:"FROM"! d"THE APPROXIMATE SOLUTION IS ";P) e3 n END ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";: 50009 SOLUTION OF EQUATION BY ITERATIONf"STARTING ESTIMATE FOR THE SOLUTION IS""ENTER ESTIMATE Q=";Q(P(QQQ1)(QQ)2P1QQQQQQ1<"ESTIMATE=";P:"EXPRESSION=";P1:F(PQ).00005100PQPZ40#     m -- DOS 3.3 HELLO  0::C$(4)Y(:16302,0:C$;"BLOAD HEAD4,A$4000"l<C$;"RUN LOGO" 2,0:N12500:N<C$;"RUN LOGO"NT OF Y IN INV  A20+ A11M17 A2A2AK A2A2M(A2M)Y A21600a A1g x  NO INVERSE~  "NO INVERSE" 900 X b FIND CONSTANT IN INVERSE l vB2A1B1 B10M1 B2B21 B2B2M(B2M)E 5000d4n PROGRAM FINDS INVERSESOx OF Y = AX +B (MOD M)Uy[y OBTAIN COEFFICIENTS AND MODULUS; CK FOR FLAG"LINEAR COEFFICIENTS (A,B)";A,B:A0B04990"MODULUS ";M  FIND COEFFICIE    OB. - 1"7N$(50)"MAY.87:PG.407- BINOMIAL PROB. - 2"fN$(51)"MAY.87:PG.408- BINOMIAL PROB. - 3"N$(52)"END OF COMPUTER SESSION"M52GG180002450:5:8:K1M:T3lK10T2T:K;". ";N$(K) K15(K15)İ2800:44)"APR.87:PG.312- SELF-CHECKING CODES"RN$(45)"MAY.87:PG.373- OCTAL SQUARES"N$(46)"MAY.87:PG.402- FUNCTION ITERATION"N$(47)"MAY.87:PG.404- PERMUTE/COMBINE"N$(48)"MAY.87:PG.405- 4X4 DETERMINANT"N$(49)"MAY.87:PG.406- BINOMIAL PR(N$(38)"APR.87:PG.285- SHUFFLE - 1"PN$(39)"APR.87:PG.286- SHUFFLE - 2"xN$(40)"APR.87:PG.287- SHUFFLE - 3"N$(41)"APR.87:PG.288- SHUFFLE - 4"N$(42)"APR.87:PG.291- INTEGRATION - 1"N$(43)"APR.87:PG.292- INTEGRATION - 2"(N$("MAR.87:PG.229- PERMUTATIONS - 1"NN$(33)"MAR.87:PG.230- PERMUTATIONS - 2"{N$(34)"MAR.87:PG.231- PERMUTATIONS - 3"N$(35)"MAR.87:PG.237- ABUNDANT NUMBERS"N$(36)"MAR.87:PG.247- POLAR GRAPHS"N$(37)"MAR.87:PG.249- POLAR INTERSECTION"- PERIODIC PICTURES"BN$(27)"FEB.87:PG.144- EXPAND A FRACTION"qN$(28)"FEB.87:PG.147- PERIOD OF FRACTION"N$(29)"FEB.87:PG.157- APPROXIMATE PI"N$(30)"MAR.87:PG.210- ARCTAN(X) PROGRAM"N$(31)"MAR.87:PG.212- LN(X) PROGRAM"!N$(32)(21)"JAN.87:PG. 64- COMPLEX POWERS - 2"WN$(22)"JAN.87:PG. 65- COMPLEX POWERS - 3"N$(23)"JAN.87:PG. 66- COMPLEX POWERS - 4"N$(24)"FEB.87:PG.103- PYTHAGOREAN 3'S - 1"N$(25)"FEB.87:PG.106- PYTHAGOREAN 3'S - 2"N$(26)"FEB.87:PG.127ISECTION METHOD"= N$(16)"DEC.86:PG.736- ITERATION METHOD"l N$(17)"JAN.87:PG. 19- CURVE ANALYSIS - 1" @N$(18)"JAN.87:PG. 24- CURVE ANALYSIS - 2" rN$(19)"JAN.87:PG. 26- CURVE ANALYSIS - 3" |N$(20)"JAN.87:PG. 63- COMPLEX POWERS - 1"(N$PY NUMBERS - 2"8 N$(10)"NOV.86:PG.659- BINOMIAL - 1"a N$(11)"NOV.86:PG.659- BINOMIAL - 2" FN$(12)"NOV.86:PG.660- BINOMIAL - 3" xN$(13)"DEC.86:PG.713- GRAPHING PARABOLAS" N$(14)"DEC.86:PG.729- RANDOM POINTS" N$(15)"DEC.86:PG.734- BR INVERSES"4 N$(4)"OCT.86:PG.552- ENCODE/DECODE"^ N$(5)"OCT.86:PG.558- ZEROS OF POLY." N$(6)"NOV.86:PG.599- MAXIMUM AREA" LN$(7)"NOV.86:PG.616- MATH OF WRONG TURNS" ~N$(8)"NOV.86:PG.618- HAPPY NUMBERS - 1" N$(9)"NOV.86:PG.619- HAPTHE DESIRED NUMBER: ";P$:P(P$)4 P1GG0:TAG1H P2GG1:TAG2a P800,800,7000,2775j 110 N$(1)"SEP.86:PG.457- POOL TABLE" !8:F$" THE MATHEMATICS TEACHER " RN$(2)"SEP.86:PG.472- MAGIC SQUARES" N$(3)"OCT.86:PG.550- MODULAL TOPIC:":11:"ALGEBRA, GEOMETRY, ETC.)"m 14:8:"3. MATHEMATICS TEACHER":11:"COURSEWARE REVIEW INDEX" 19:3:"NOTE: THE ARITHMETIC TEACHER PROGRAMS":9:"ARE ON SIDE 2 OF THIS DISK." 17:8:"4. END OF COMPUTER SESSION" 23:5:"ENTER d:N$(55),A$(20)i255AnF$" SELECT YOUR MENU ":TAG0Kx2450w5:8:"WHICH MENU DO YOU WISH TO USE?"7:8:"1. MATHEMATICS TEACHER"11:"(CHRONOLOGICALLY BY ISSUE)"10:8:"2. MATHEMATICS TEACHER") 11:"(BY MATHEMATICA       "PRESS ANY KEY TO CONTINUE.";:R$'dIS PROGRAM IS":5:"Y=X^4-2X^2.":3:"YOU CAN CHANGE THE EQUATION BY":3:"ALTERING STATEMENT 20:":5:"20 DEF FN Z(X)= equation " 16:4:"FOR DETAILS, CONSULT:" 8:"THE MATHEMATICS TEACHER" 13:"JANUARY, 1987" 16:"PAGE 19"!24:5:AS MANY PLACES AS"?3:"YOU WISH. YOU ENTER THE NUMERATOR,"z3:"DENOMINATOR, AND NUMBER OF DECIMAL":3:"PLACES."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"FEBRUARY, 1987"16:"PAGE 144"24:5:"PRESEY TO CONTINUE. ";:R$ x& p50400 z5:3N -ENTER SHORT DESCRIPTION "PROGRAM TO MAGNIFY THE GRAPH OF AN":3:"EQUATION. YOU ENTER THE MIDPOINT":3:"(ABSCISSA) OF AN INTERVAL AND THE":3:"INTERVAL'S WIDTH":3: 3:"THE EQUATION IN THIHE MATHEMATICS TEACHER". ---ENTER VOL. NO.L 11:"VOLUME 80 NUMBER 1"j 11:"(C) COPYRIGHT 1987"r 23| (5210 --- GO TO DESCRIPTION .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY K:1:"*";:39:"*":I1 I138:"*";:I:"*":7 A 5040W -- ARTICLE TITLE 5:5:"USE OF THE ZOOM IN THE ANALYSIS":14:"OF A CURVE" 7:18:"BY" -- AUTHOR'S NAME 9:11:"F. RUBIO MONTANER" 14:17:"FROM" 16:8:"T$"Y"10 END :y ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I I421:I) 50001 "ABSCISSA AND WIDTH";P,W:FZ(X)X42X2_Y(X)Z(XP)Z(P)p(H.87W::32XWWW200<M139X100W:N95Y(X)87HF(N8N182)90PM,191NZXd23:"DO YOU WANT ANOTHER?(Y/N)"nR$ xR16:"PAGE 550"=24:5:"PRESS ANY KEY TO CONTINUE.";:R$Cd-IONV"PROGRAM TO FIND THE INVERSES OF THE":3:"MODULAR FUNCTION Y=AX + B(MOD M)."3:"YOU ENTER THE COEFFICIENTS A,B AND"3:"THE MODULUS M."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"OCTOBER, 1986"" 11:"(C) COPYRIGHT 1986"' 231 (5210K --- GO TO DESCRIPTIONU .6000[ 2e <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p5040 z5:3-ENTER SHORT DESCRIPT+ 5:6:"GET THE MESSAGE? CRYTOGRAPHS,"P 7:"MATHEMATICS, AND COMPUTERS"a 7:18:"BY"w -- AUTHOR'S NAME 9:13:"JAMES REAGAN" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 79 NUMBER 7R 'N' THEN PRESS RETURN:";:" ";Y$0 Y$"Y"4Q D$(4):D$"RUN SYSTEM MENU"Y :c 5090i q : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE B20800 B1 -  NO INVERSE3 E "NO INVERSE"N 900T r * PRINT INVERSE STATEMENTx 4 >"Y="A"X+"B"(MOD"M") HAS INVERSE" H:"Y="A1"X+"; RB1"(MOD"M")"" ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' O-- ARTICLE TITLE> 5:6:"GET THE MESSAGE? CRYTOGRAPHS,"c 7:"MATHEMATICS, AND COMPUTERS"t 7:18:"BY" -- AUTHOR'S NAME 9:13:"JAMES REAGAN" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO.11:?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$C Y$"Y"Ľ:4d D$(4):D$"RUN SYSTEM MENU"l :v 5090|  : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 J DM(I)V DM(I);" ";1 *(I10)I10ĺ8 4I> [  CONVERT DECODED VALUES|  TO OBTAIN ORIGINAL MESSAGE  ::"O-MESSAGE:" I1L ME$(DM(I)) ME$; I:  2 ~:"DO YOU WISH TO RUN THE PROGRAM AGAINI1L &V1 0J136 :VVEM(I):VVM((VM))= DJI NEM(I)VY XEM(I);" ";m b(I10)I10ĺt lIz   DECODE MESSAGE  ::"D-MESSAGE:" I1L V1:DM(I)EM(I) J1(2M1)3 VVDM(I):VVM((VM))  M$(I)(M$,I,1) M$(I);% I+ ,K 6 CONVERT EACH CHARACTER TO^ @ ASCII VALUESd Jv T::"ASCII:" ^I1L hEM(I)(M$(I)) rEM(I);" "; |(I10)I10ĺ I   ENCODE ASCII VALUES  ::"E-MESSAGE:"  5000 9 ENCODING AND DECODING USINGM E(X)=X^3MOD Mi( D(X)=X^(2M-1)/3 MOD M<M$(50),EM(50),DM(50)FM149Pd"MESSAGE ";M$nx"MESSAGE:"; PUT MESSAGE IN ARRAY M$L(M$)I1L   ON OF SUCH A PROGRAM,"= 5:"PERFORM THE FOLLOWING STEPS:"F5:n8:"1. DEPRESS THE CONTROL (CTRL)"(11:"KEY AND STRIKE THE 'C' KEY."28:"2. TYPE THE MESSAGE:"75:<12:"RUN SYSTEM MENU"A5: F11:"THEN PRESS THE 'RETU16:2:" NOTE "#5:5J"SEVERAL OF THE PROGRAMS ON THIS"t5:"DISKETTE PERFORM A LARGE NUMBER"5:"OF COMPUTATIONS AND EXECUTE FOR"5:"A LONG PERIOD OF TIME."5:5:"IF YOU WISH TO TERMINATE THE"5:"EXECUTI 2:$ 3:"TO LIST A PROGRAM:"S $3:"1. SELECT THE PROGRAM FROM THE MENU," )3:"2. WHEN TITLE APPEARS, KEY CONTROL-C":6:"(CTRL-C) THEN PRESS 'RETURN'," .3:"3. TYPE THE COMMAND 'LIST', THEN":6:"PRESS 'RETURN'." 3255 8:25MAKE A"3 3:"COPY FOR EACH OF THEIR COMPUTERS."| 3:"PLEASE DO NOT ALLOW UNAUTHORIZED":3:"COPIES TO BE MADE.":3: 3:"'MATHDISK' PROGRAMS ARE IN 'AS IS'" 3:"FORM FROM NCTM JOURNALS. YOU ARE" 3:"ENCOURAGED TO LEARN FROM THEM."7:" ";:J:" ":I G 24:7:"PRESS ANY KEY TO CONTINUE. ";:R$M W :25 4:3:"NCTM 'MATHDISK' PROGRAMS ARE" 3:"PRODUCED FROM ARTICLES COPYRIGHTED" 3:"BY THE NCTM, BUT MAY BE COPIED FOR" 3:"PERSONAL USE. SCHOOLS MAY 0":2:9);"DONALD W. SCHEUER, JR." >16:6:"NATIONAL COUNCIL OF TEACHERS":13:"OF MATHEMATICS":9:"1906 ASSOCIATION DRIVE":12:"RESTON, VA 22091" ?11:"(C) COPYRIGHT 1987" A23 F255 P1000 :23 255:I421:I:2:J23MATHDISK' IV ":2:5:"PROGRAMS FROM THE MATHEMATICS TEACHER"` 38:"& THE ARITHMETIC TEACHER" 42:"-------------------------------------":2: 67:"SEPTEMBER 1986 - MAY 1987" 810:10:"COMPILED & EDITED BY":2:# <2:12);"JAMES M. RUBILLI12500:I:" 50, 1200N:10:11:"LOADING THE MENU"pD$(4):D$;"RUN SYSTEM MENU"x::I13:I:J138:"*";:J:"*":I#I421:I:1:"*";:39:"*":I(I138:"*";:I:"*":-= 225:2:10:" NCTM '     2250 400 G1250+ AMMNN8 B2MNG CMMNN COUNTCOUNT1:COUNT20(COUNT20)Ą"PRESS RETURN TO CONTINUE. ";A$::500 M;5);N;10);A;20)B;30);C N M   OPTION TO RUN PROGRAM AGAIN " ,& 6"PYTHAGOREAN TRIPLES USING DIOPHANTUS'":"ALGORITHM."Y d"ENTER MAXIMUM VALUE FOR M ";Ve eCOUNT0k n x LOOPS TO FIND AND PRINT PRIMITIVE TRIPLES "M";5);"N";10);"A"20);"B";30);"C" M1V N1M1 ((MN)2)(MN) 5000 = PROGRAM - DIOPHANTUS' ALGORITHMCu( THIS PROGRAM GENERATES A TABLE OF PRIMITIVE2 PYTHAGOREAN TRIPLES USING THE PARAMETRIZATION< A=M*M B=2*M*N C=M*M+N*NFP"THIS PROGRAM WILL LIST PRIMITIVE"5 Z4:5:"PRESS ANY KEY TO CONTINUE.";:R$/dICAN CHANGE THE EQUATION BY":3:"ALTERING STATEMENT 20:":5:"20 DEF FN R(T)= equation "| 16:4:"FOR DETAILS, CONSULT:" 8:"THE MATHEMATICS TEACHER" 13:"JANUARY, 1987" 16:"PAGE 24" 24:5:"PRESS ANY KEY TO CONTINUE.";:R$ d. ";:R$ x p5040" z5:3@ -ENTER SHORT DESCRIPTION "PROGRAM TO MAGNIFY THE GRAPH OF A ":3:"POLAR EQUATION. YOU ENTER THE NUMBER":3:"OF TURNS YOU WISH TO GRAPH."X 3:"THE EQUATION IN THIS PROGRAM IS":10:"R= 3*T ":3:"YOU TEACHER" ---ENTER VOL. NO.> 11:"VOLUME 80 NUMBER 1"\ 11:"(C) COPYRIGHT 1987"d 23n (5210 --- GO TO DESCRIPTION .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTINUE"*":I# I138:"*";:I:"*":) 3 5040I -- ARTICLE TITLE 5:5:"USE OF THE ZOOM IN THE ANALYSIS":14:"OF A CURVE" 7:18:"BY" -- AUTHOR'S NAME 9:11:"F. RUBIO MONTANER" 14:17:"FROM" 16:8:"THE MATHEMATICS END :k ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$y Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39: 5000, "NUMBER OF TURNS";N:;R(T)3TD:3`T0N6.2833.1416180t((R(T))80702X130R(T)(T):Y191(95R(T)(T))<X,YFTP23:"DO YOU WANT ANOTHER? (Y/N)"ZR$dR$"Y"10n END   :"THOSE IN THE ARTICLE."G3:"REASON-- APPLE VS. COMMODORE CODES."k16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"OCTOBER, 1986"16:"PAGE 552"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dINTER SHORT DESCRIPTIONw"PROGRAM TO ENCODE AND DECODE USING":3:"E(X)=X^3MOD M AND ":6:"D(X)= X^(2M-1)/3 MOD M."3:"YOU ENTER THE MESSAGE TO BE ENCODED."10:3:"NOTE: THE VALUES GENERATED BY THE":3:"E-MESSAGE WILL NOT CORRESPOND TO":3"VOLUME 79 NUMBER 7"211:"(C) COPYRIGHT 1986":23D(5210^--- GO TO DESCRIPTIONh.6000n2x<:23F5210:I421:I:2:J237:" ";:J:" ":IPZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$xp5040z5:3-E x:10=}"****************************************":l"REMOVE THE DISKETTE FROM THE DISK DRIVE":" AND TURN THE COMPUTER OFF !!!!!!":"****************************************" 1b DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2S ANY KEY TO CONTINUE.";:R$"dI THE NUMBER OF YOUR CHOICE"9"AND PRESS 'RETURN':";OPJ OP1ė:230X*OP2120yD$(4):D$"RUN SYSTEM MENU":5090::I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:"*"NUE")"OR PRESS 'P' FOR A PRINT OUT."SA$::A$"P"PTR1:(4);"PR#1":270Y|"SELECT ONE OF THESE OPTIONS"::"1. SAME POLYNOMIAL, DIFFERENT INTERVAL":"2. DIFFERENT POLYNOMIAL":"3. EXIT FROM THE PROGRAM":: "TYPEl(CR).000001ĺ"**":650Dv CONSECUTIVE REMAINDERS CHANGE SIGNkFIRSTD(PR)(CR)PR0ĺ"^^";:LOOPLOOP1:280LOOP0: IF THROUGH PRINTING, THEN TURN OFF PRINTERPTR1ĺ(4);"PR#0":PTR0"PRESS RETURN TO CONTID(R)(100C(R).5)1007&8((D(R1))));D(R);>0R_: PR IS 'PREVIOUS' REMAINDERD CR IS 'CURRENT' REMAINDER NPRCR:CRC(0)X A ZERO IS FOUNDb USE .000001 BECAUSE OF INEXACT COMPUTER COMPUTATIONS; MAY BE CHANGED BY USER.ER' COLUMNS. HOWEVER, USE C(0) FOR COMPUTATION PURPOSES IN STATEMENT 590 STATEMENTS 520, 540, AND 550 MAY NEED TO BE CHANGED DEPENDING UPON THE DEGREE OF PRECISION NEEDED FOR A PARTICULAR SOLUTION.D(K1)(1000D.5)1000:D(K1);RK01SOR COEFF. OF QUOT REM":4308"DIVISOR QUOT. REM"VM18(K1)7:"#";:M:t ****PRINT TOP LINE**** 8);:PK01A(P);8((A(P))));P: ***PRINT OTHER LINES***H ROUND D AND C( ) TO D( ) TO OBTAIN 'NARROWTATIONS ,DLASTINC2660+ 6C(K)A(K)F @ DIVIDE SYNTHETICALLYV JJK101h TB(J)C(J1)D{ ^C(J)B(J)A(J) hJ rLOOP1520 | PRINT HEADINGS :: K2ĺ"DIVISOR COEFF. OF QUOTIENT";8(K1)27);"REM":430K2ĺ"DIVITHE LAST NUMBER TO BE USED":"AS A DIVISOR:";:LASTz ::"ENTER THE DIFFERENCE BETWEEN":"CONSECUTIVE DIVISORS:";:INC PTR0: PRINTER IS OFF :LOOP1:CR0 DFIRST(LOOP1)INC " DONE? INC/2 USED TO COMPENSATE FOR INEXACT COMPUTER COMPUG COEFFICIENT."3 "A(0) IS THE CONSTANT TERM.":A QK01[ "A("Q")=";:" ";A(Q)b Q DIVIDE SYNTHETICALLY FROM FIRST TO LAST IN INCREMENTS OF INC :"ENTER THE FIRST NUMBER TO BE USED":"AS A DIVISOR:";:FIRST3 ::"ENTER % "ENTER DEGREE OF POLYNOMIAL:";K K20K1K(K)ĺ:"VALUE ENTERED MUST BE AN INTEGER":"GREATER THAN 0 AND LESS THAN 21!":X11000:::20:"PRESS 'RETURN' TO CONTINUE.";R$:120 :"NOW ENTER THE COEFFICIENTS." "A(";K;") IS THE LEADINLYNOMIALS OF DEGREE >20 CHANGE DIM BELOWE ZA(20),B(20),C(20),D(20) d:"THIS PROGRAM WILL ALLOW YOU TO"::"SYNTHETICALLY DIVIDE A POLYNOMIAL" n:"BY CONSECUTIVE TERMS OF AN"::"ARITHMETIC SEQUENCE.":::"PRESS 'RETURN' TO CONTINUE.";:A$ x.# CR IS 'CURRENT' REMAINDER -50003T SYNTHETIC DIVISION TO FINDv ZEROS OF POLYNOMIALS  WRITTEN BY CHUCK FRIESEN( LINCOLN PUBLIC SCHOOLS2 720 SOUTH 22ND< LINCOLN, NE 68510F OCTOBER, 1985( P FOR PO       :2450:5K42800$f1800*p:10:8:"LOADING THE PROGRAM INTO":9:"THE COMPUTER'S MEMORY."v. :10:5:"INCORRECT ENTRY - TRY AGAIN":J11500:J:240`  :: :I13:I:J038:"*";:J:"*":: :I420:I:"END POINTS(IN RADIANS). THE GRAPH" 3:"IN THIS PROGRAM IS THE ASTROID.":5:"X=(COS(T))^3 Y=(SIN(T))^3.":3:"CHANGE THE EQUATION- ALTER LINE 20:":3:"20 DEF FN X(T)= rule : DEF":7:"FN Y(T)=rule" 3::3:"INPUT? TRY 4,0,6.28"18:4:"F7:"PRESS ANY KEY TO CONTINUE. ";:R$+ x5 p5040? z5:3] -ENTER SHORT DESCRIPTION$ "PROGRAM TO MAGNIFY THE GRAPH OF A ":3:"RELATION DEFINED BY PARAMETRIC ":3:"EQUATIONS. YOU ENTER INCREMENT ":3:"WIDTH, THE INTERVAL'S START AND":3:& 16:8:"THE MATHEMATICS TEACHER"= ---ENTER VOL. NO.[ 11:"VOLUME 80 NUMBER 1"y 11:"(C) COPYRIGHT 1987" 23 (5210 --- GO TO DESCRIPTION .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P% Z24:$ I421:I:1:"*";:39:"*":I@ I138:"*";:I:"*":F P 5040f -- ARTICLE TITLE 5:5:"USE OF THE ZOOM IN THE ANALYSIS":14:"OF A CURVE" 7:18:"BY" -- AUTHOR'S NAME 9:11:"F. RUBIO MONTANER" 14:17:"FROM":"PRESS RETURN WHEN READY TO CONTINUE.";X$` <Y$(4):Y$;"RUN APR.87:PG.291- INTEGRATION - 1"a DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2:"PRESS RETURN WHEN READY TO CONTINUE.";X$a <Y$(4):Y$;"RUN MAR.87:PG.230- PERMUTATIONS - 2"dR$ nR$"Y"10! x END ) : ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I 50000 "WIDTH, INTERVAL";W,T1,T2TX(T)((T))3:Y(T)((T))3eH.87W::3~(TT1T2(T2T1)2002X139X(T)200W:Y95Y(T)87H<((X(T))W(Y(T))H)80FX,191YPTZ23:"DO YOU WANT ANOTHER?(Y/N)"   :5:"PRESS ANY KEY TO CONTINUE.";:R$,dIxp5040z5:37-ENTER SHORT DESCRIPTION"PROGRAM TO FIND THE ZEROS OF A":3:"POLYNOMIAL BY SYNTHETIC DIVISION."16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"OCTOBER, 1986"16:"PAGE 558"&24---ENTER VOL. NO.511:"VOLUME 79 NUMBER 7"S11:"(C) COPYRIGHT 1986"[23e(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J237:" ";:J:" ":IPZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$:5040(-- ARTICLE TITLE~5:5:"USING THE MICROCOMPUTER TO FIND":4:"THE ZEROS OF A POLYNOMIAL FUNCTION"7:18:"BY"-- AUTHOR'S NAME9:11:"CHARLES D. FRIESEN"14:17:"FROM"16:8:"THE MATHEMATICS TEACHER"  1108 D$(4)::D$"RUN END OF COMPUTER SESSION" 22:"ENTER THE DESIRED NUMBER, OR":"PRESS RETURN FOR THE NEXT SCREEN: ";P$:P(P$)" (P$)0KMıT (P$)0KM1ī2750 P(P) P1PMD$(4):2250:D$"RUN ";N$(P)P 22:"1:"*";:40:"*":I5( 21::I038:"*";:I:"*":DX TAG0Ė11XY TAG1TAG2Ė8cZ 2:F$i  :10:"THAT COMPLETES THE MENU."::"NO SELECTION MADE" 23:"DO YOU WISH TO RETURN TO THE MAIN MENU?":"ENTER 'Y' OR 'N': ";R$ R$"Y"ı:"FOR DETAILS, CONSULT:";8:"THE MATHEMATICS TEACHER"U13:"FEBRUARY, 1987"i16:"PAGE 103"24:5:"PRESS ANY KEY TO CONTINUE.";:R$d"PRESS ANY KEY TO CONTINUE. ";:R$)x3p5040=z5:3[-ENTER SHORT DESCRIPTION"PROGRAM TO GENERATE A TABLE OF ":3:"PRIMITIVE PYTHAGOREAN TRIPLES USING"3:"THE PARAMETRIZATION: A=M*M, B=2*M*N":3:"AND C= M*M + N*N."16:416:8:"THE MATHEMATICS TEACHER";---ENTER VOL. NO.Y11:"VOLUME 80 NUMBER 2"w11:"(C) COPYRIGHT 1987"23(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:2:J237:" ";:J:" ":IP#Z24:7:I421:I:1:"*";:39:"*":I< I138:"*";:I:"*":B L 5040b -- ARTICLE TITLE 5:6:"MATRIX METHOD FOR GENERATING":9:"PYTHAGOREAN TRIPLES" 7:18:"BY" -- AUTHOR'S NAME 9:12:"PHYLLIS LEFTON" 14:17:"FROM"$);"N";10);"A"20);"B";30);"C"%  ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I "DO YOU WANT ANOTHER LIST OF TRIPLES?"U @"PLEASE ENTER 'Y' OR 'N': ";A$:A$(A$,1)h JA$"Y"ė:100| TA$"N"ė:4990 ^320 M1M N1N TM1 M1N1 N1TN1(TN1) N10470 420 GM1   END "M";5OR DETAILS, CONSULT:"78:"THE MATHEMATICS TEACHER"P13:"JANUARY, 1987"c16:"PAGE 26"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dIATICS TEACHER"( 12:"NOVEMBER, 1986"< 16:"PAGE 599"j 24:5:"PRESS ANY KEY TO CONTINUE.";:R$p dIIS BEING ":3:"ENGRAVED ON 400 SQ. CM OF GOLD.":3:"THIS PROGRAM FINDS THE DIMENSIONS" 3:"OF THE RECTANGLE WITH MAXIMUM":3:"AREA, GIVEN A TOP BORDER OF 2 CM":3:"AND A SIDE BORDER OF 6 CM." 16:4:"FOR DETAILS, CONSULT:" 8:"THE MATHEM 23 (5210, --- GO TO DESCRIPTION6 .6000< 2F <:23w F5210:I421:I:2:J237:" ";:J:" ":I} P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p5040 z5:3 -ENTER SHORT DESCRIPTIONX "A RECTANGULAR PLAQUE OLVING TECHNIQUES":10:"WITH MICROCOMPUTERS"> 7:18:"BY"T -- AUTHOR'S NAMEs 9:12:"WILLIAM E. HAIGH" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 79 NUMBER 8" 11:"(C) COPYRIGHT 1986"N:";:" ";Y$ Y$"Y"4; D$(4):D$"RUN SYSTEM MENU"C :M 5090S [ : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE- 5:7:"PROBLEM Sr 50008 "WIDTH";10);"LENGTH";25);"AREA"GW61004SL400We(A(L4)(W6)z2W;10);L;25);A7(W2)80((W2)80)İ5210:<WF END ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETUR     RI13\I1İ2100&^I2İ22005`I3İ2300Qf4500: MAT M1 = S * Mkp4600:MAT PRINT M1,wzPI3JP10001040X(P)M1(1,1)Y(P)M1(1,2)Z(P)M1(1,3)IX(P)2Z(P)ĺ"....END OF GENERATION";Y(P)41;"..."PLEASE ENTER AN INTEGER 1 OR GREATER"1NF(N)NN0740TN6790] 820fN6 "YOU ASKED FOR TOO MANY TRIPLES!"*"THIS WILL NOW LIST 1000 TRIPLES ONLY."4K(3N3)2>1100: INITIALIZE STARTING TRIPLEHJ0K"ARITHMETIC":A$(1)N$(2):A$(2)N$(8):A$(3)N$(9):A$(4)N$(27):A$(5)N$(28):M5:8240<#MX$"ALGEBRA":A$(1)N$(3):A$(2)N$(4):A$(3)N$(5):A$(4)N$(13):A$(5)N$(15)=#A$(6)N$(16):A$(7)N$(20):A$(8)N$(21):A$(9)N$(22):A$(10)N$(23):A$(11)N$(31)>#A$( RETURN FOR THE NEXT SCREEN: ";P$:P(P$)9y"PM18100L"(P$)0KMıe"(P$)0KM1ī8750p"P(P)#P1PMD$(4):2250:D$"RUN ";A$(P) #22:"INCORRECT RESPONSE -TRY AGAIN":"PRESS RETURN TO CONTINUE: ";X$:KK15:T2#MX$;". RETURN TO SUBJECT MENU"%l 8800/v 8240l.":10:"THAT COMPLETES THE MENU."::"NO SELECTION MADE"8"23:"DO YOU WISH TO RETURN TO THE TOPIC MENU?":"ENTER 'Y' OR 'N': ";R$B"R$"Y"ıD"110)`"22:"ENTER THE DESIRED NUMBER, OR":"PRESSDESIRED NUMBER: ";R$:R(R$)T R9010,9020,9030,9040,9045,9050,9060,9070,9080,110^& 8100h0 24505 4:3:"TOPIC: ";MX$: 5:8:K1M:T3D K10T2N T:K;". ";A$(K)X K15(K15)İ8800::2450:5b Kg 3:M110Ė2h M1ALGEBRA"*8:"3. ANALYTIC GEOM./TRIG."D8:"4. APPLICATIONS"Z8:"5. CALCULUS"p8:"6. GEOMETRY"8:"7. NUMBER THEORY"8:"8. PREALGEBRA"8:"9. PROBABILITY & STATISTICS" 7:"10. RETURN TO MAIN MENU" 22:"ENTER THE INCORRECT RESPONSE -TRY AGAIN":"PRESS RETURN TO CONTINUE: ";X$:KK15:XD$(4)::10:8:"LOADING COURSEWARE INDEX"bD$"RUN MT-INDEX"@24505:3:"WHICH TOPIC DO YOU WISH TO EXAMINE?"7:8:"1. ARITHMETIC"8:"2. S*R (2600: MAT PRINT T,=2700:MAT S = TDIv1020: GIVE USER OPTION TO RUN PROGRAM AGAIN| LIST GENERATIONS OF TRIPLESM1(1,3),M(3,3)X(1000),Y(1000),Z(1000)"HOW MANY GENERATIONS DO YOU WANT?"*:"PRESS RETURN WHEN READY TO CONTINUE.";X$` <Y$(4):Y$;"RUN MAY.87:PG.405- 4X4 DETERMINANT":"PRESS RETURN WHEN READY TO CONTINUE.";X$` <Y$(4):Y$;"RUN APR.87:PG.292- INTEGRATION - 2"a DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"PRESS RETURN WHEN READY TO CONTINUE.";X$a <Y$(4):Y$;"RUN MAR.87:PG.231- PERMUTATIONS - 3"b DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2 AGAIN$:AGAIN$"N"AGAIN$"Y"17304 AGAIN$: @  ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"4 D$(4):D$"RUN SYSTEM MENU" : 5090  ::I13:I:K rJ |TWOFIVEĺ"IT WILL HAVE ";FIVE;" PLACES NOT REPEATING":1680y "IT WILL HAVE "TWO" DIGITS NOT REPEATING"  "IT WILL HAVE ";K;" DIGITS REPEATING"    DO AGAIN 20:1 "DO YOU WANT TO ENTER ANOTHER FRACTION";(MNUM5 1210  .  VALUE OF K6 K0F NUM11390S K1NUMc (C(10K1)| 2CNUM(CNUM)1390 <K n s @ OUTPUT J T12);TWO;16);FIVE ^DEN;8);"= "2;" X ";15)5;" X "NUM c h"VALUE OF K IS "; POWER OF TWO TWO01 NUM2(NUM2)1090? TWOTWO1M NUMNUM2W 1020] Bc Gv L INPUT NUMBER `"WHAT IS THE DENOMINATOR? ";DEN jNUMDEN    POWER OF 5 FIVE0 NUM5(NUM5)1290 FIVEFIVE1 NULACES < AGAIN$ = DO AGAIN?$ P* Z8 d PROGRAMD n INPUTN x1100_ POWER OF 2i 1000z POWER OF 5 1200 VALUE OF K 1300 RESULTS 1600 DO AGAIN? 1700 AGAIN$"Y"100 4990  FIND 5000; FINDING PERIOD OF REPEATING DECIMALM LEON ROLANDV125f VARIABLES# TWO = POWER OF TWO( FIVE = POWER OF FIVE- NUM = NUMBER VALUE IN CALCULATION2 DEN = DENOMINATOR 7 K = POWER OF 10 FOR REPEATING P8:"THE MATHEMATICS TEACHER"912:"NOVEMBER, 1986"M16:"PAGE 616"{24:5:"PRESS ANY KEY TO CONTINUE.";:R$dI" ";:J:" ":IPDZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$JxTp5040^z5:3|-ENTER SHORT DESCRIPTION"PROGRAM TO PERFORM WRONG-TURN ":3:"CALCULATIONS. SEE ARTICLE FOR":3:"DETAILS."16:4:"FOR DETAILS, CONSULT:"BERT WHITE" 14:17:"FROM"E 16:8:"THE MATHEMATICS TEACHER"\ ---ENTER VOL. NO.z 11:"VOLUME 79 NUMBER 8" 11:"(C) COPYRIGHT 1986" 23 (5210 --- GO TO DESCRIPTION .6000 2 <:23F5210:I421:I:2:J237:I13:I:J138:"*";:J:"*":IE I421:I:1:"*";:39:"*":Ia I138:"*";:I:"*":g q 5040 -- ARTICLE TITLE 5:5:"THE MATHEMATICS OF WRONG TURNS" 7:18:"BY" -- AUTHOR'S NAME 9:3:"DOUGLAS L. CASHING AND AL. ND2;10);R(1N)(1N);25);(ND2D1)R5 KE  10,100,55 ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"ė:120 D$(4):D$"RUN SYSTEM MENU" : 5090  :! :TS OF .01  0& 6K90993 @NK100a JND2;10);R(1N)(1N);25);(ND2D1)Rh TKt ^5210:z   THIS LOOP IS FOR VALUES  OF N FROM .991 TO .999 USING  INCREMENTS OF .001  K991999 NK1000 THIS LOOP IS FOR VALUES7 OF N FROM 0 TO .8 USINGN INCREMENTS OF .1T _ K08k NK10 ND2;10);R(1N)(1N);25);(ND2D1)R K 5210: , - THIS LOOP IS FOR VALUES . OF N FROM .90 TO .99 USING / INCREMEN 5000d7e D1 - DISTANCE FROM A TO BWf D2 - DISTANCE FROM B TO Dxg R - ORIGINAL SPEED h N - FROM BC = N * BDi K - LOOP COUNTER jnD1,D2,Rx"BC";10);"NEW SPEED";25);"TIME FOR A TO C"       STANDARD VERSION. APR. 1987,":" 317.""GREEN GLOBS AND GRAPHING EQUATIONS,":" APPLE II FAMILY, 48K, WITH 1 DISK ":" DRIVE. JAN. 1987, 68.""GUESS MY RULE, APPLE II FAMILY, 64K.":" OCT. 1986, 561."5"PC GRAPHICS, IBM PC AND PC":" COX . 23:"PRESS ANY KEY TO CONTINUE ";:Z$4 r P5000,6000,7000,8000,9000,10000,11000,12000,13000,14000 "ERROR": 3100 "EQUATIONS III, APPLE II FAMILY, 48K.":" OCT. 1986, 559."("FUNCTION GRAPHING, APPLE II FAMILY,":" 48K,D$(4), PMİ2250:D$;"RUN SYSTEM MENU" 22:"INCORRECT RESPONSE -TRY AGAIN":"PRESS RETURN TO CONTINUE: ";X$:KK15:  :"SUBJECT: ";N$(P) 0 D "REVIEW TITLE, ISSUE & PAGE NUMBER" N "-------------------------------------" AT COMPLETES THE MENU."::"NO SELECTION MADE":23:"PRESS RETURN TO CONTINUE";X$:: 22:"ENTER THE DESIRED NUMBER, OR":"PRESS RETURN FOR THE NEXT SCREEN: ";P$:P(P$) " (P$)0KMı T (P$)0KM1ī2750 P(P) P1PM14000 ." F . :10:5:"INCORRECT ENTRY - TRY AGAIN":J11500:J:240P ::y :I13:I:J038:"*";:J:"*":: :I420:I:1:"*";:40:"*":I ( 21::I038:"*";:I:"*": Z 2:7:" MT COURSEWARE REVIEW INDEX " U :10:"THPROCESSING", N$(11)"RETURN TO MAIN MENU"5 M11? 2450T :5:8:K1M:T3c lK10T2x T:K;". ";N$(K) K15(K15)İ2800::2450:5 K 42800 f1800  :10:8:"LOADING THE PROGRAM INTO":9:"THE COMPUTER'S MEMORY=d:N$(50):M=25)N$(1)"ALGEBRA"BN$(2)"APPLICATIONS"YN$(3)"ARITHMETIC"n,N$(4)"CALCULUS"EN$(5)"COMPUTER SCIENCE"JN$(6)"GAMES AND PUZZLES"^N$(7)"GEOMETRY"N$(8)"STATISTICS"N$(9)"TRIGONOMETRY" N$(10)"WORD      ILS, CONSULT:"08:"THE MATHEMATICS TEACHER"J12:"NOVEMBER, 1986"^16:"PAGE 618"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dIRAM TO FIND HAPPY NUMBERS. ":3:"EXAMPLE: 19 IS A HAPPY NUMBER":6:" 19 -- 1 X 1 + 9 X 9 = 82" 7:"82 -- 8 X 8 + 2 X 2 = 68":7:"68 -- 6 X 6 + 8 X 8 = 100":6:"100 -- 1 X 1 + 0 X 0 + 0 X 0 = 1":3:"CALCULATIONS END AT 1."16:4:"FOR DETA) COPYRIGHT 1986" 23# (5210= --- GO TO DESCRIPTIONG .6000M 2W <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p5040 z5:3 -ENTER SHORT DESCRIPTIONc "PROG 5040# -- ARTICLE TITLE? 5:14:"HAPPY NUMBERS"P 7:18:"BY"f -- AUTHOR'S NAME 9:13:"RITA L. PETROSA" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 79 NUMBER 8" 11:"(CN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$S Y$"Y"4t D$(4):D$"RUN SYSTEM MENU"| : 5090  : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"*";:I:"*": 0 ISOLATE THE DIGITS OF THE 3 DIGIT NUMBERS_ H(Z100):T(Z10)H10:UZ(H100T10)v ZHHTTUU:110 ISOLATE THE DIGITS OF THE 2 DIGIT NUMBERS T(Z10):UZT10 ZTTUU:110 END :::E ~:"DO YOU WISH TO RU 5000& "HAPPY NUMBERS",Z CHECK ALL NATURAL NUMBERS LESS THAN 100f(X199n2ZX< GENERATE SIX TERMSFN16PZ100170ZZ10200dZZZnNxCHECK FOR HAPPY NUMBERSZ1ĺX;" ";X 220     2:J237:" ";:J:" ":I POZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$Ux_p5040iz5:3-ENTER SHORT DESCRIPTION"PROGRAM TO FIND THE PERIOD OF ANY ":3:"RATIONAL NUMBER. YOU ENTER THE"3:"DENOMINATOR."16:4:"FOER AND JAMES E. RILEY"*14:17:"FROM"P16:8:"THE MATHEMATICS TEACHER"g---ENTER VOL. NO.11:"VOLUME 80 NUMBER 2"11:"(C) COPYRIGHT 1987"23(5210--- GO TO DESCRIPTION.60002<:23F5210:I421:I:J138:"*";:J:"*":I;I421:I:1:"*";:39:"*":IWI138:"*";:I:"*":]g5040}-- ARTICLE TITLE5:7:"STUDYING DECIMAL FRACTIONS":10:"WITH MICROCOMPUTERS"7:18:"BY"-- AUTHOR'S NAME9:4:"RUTH ANN MEYLE II FAMILY, 48K. SEPT.":" 1986, 477-78."<63200:1800MSTRUCTOR'S COMPUTERIZED TEST ":" GENERATOR TO ACCOMPANY BASIC COLLEGE":" MATHEMATICS: AN APPLIED APPROACH, 2ND":" ED. AND INSTRUCTOR'S COMPUTERIZED ":" TEST GENERATORS TO ACCOMPANY INTRO-",6" DUCTORY ALGEBRA AND INTERMEDIATE ":" ALGEBRA, APP00 23100~2"PROGRAMS FOR TRIGONOMETRY, APPLE II":" FAMILY, 48K (AVAILABLE IBM PC AND":" PC JR). DEC. 1986, 738-39."2"TRIGONOMETRY OF THE RIGHT TRIANGLE,":" APPLE II FAMILY, 48K. SEPT. 1986,":" 478-79."33200:1800631006"INILY, 64K.":" DEC. 1986, 739."/+3200:18009.3100."PLAIN VANILA STATISTICS, APPLE II ":" FAMILY, 64K, NOV. 1986, 665."."UNIX/STAT, IBM PC AND COMPATIBLES,":" MS-DOS 2.0-3.0, 96K (AVAILABLE UNIX).":" NOV. 1986, 666-67."/3200:18., 128K (AVAIL-":" ABLE APPLE, COMMODORE 64, AND ATARI).":" SEPT. 1986, 477." +"PERIMETER, AREA, AND VOLUME, APPLE II":" FAMILY, 48K (AVAILABLE TRS-80, MODELS":" III/4, AND COMMODORE 64). DEC. 1986,":" 738."*+"THE SUPER FACTORY, APPLE FAM0."] +"THE GEOMETRIC SUPPOSER: QUADRILATERALS,":" APPLE II FAMILY, 64K. OCT. 1986, 560."+"THE GEOMETRIC SUPPOSER: TRIANGLES,":" APPLE II FAMILY, 64K. OCT. 1986,":" 560-61."Q+"GEOMETRY VOLUME 1: BASIC GEOMETRICAL":" NOTIONS, IBM PC/PC JR (AVAILABLE TRS-80). SEPT.":" 1986, 478."$'"PLAYING TO LEARN: MATH/LOGIC GAMES,":" APPLE II FAMILY, 48K (AVAILABLE":" COMMODORE 64). NOV. 1986, 665-66."'3200:1800*3100+"EUCLID, IBM PC, DOS 2.1 OR LATER, 256K.":" OCT. 1986, 559-6986 - MAY 1987." r3200:1800*(#31002#"NO COURSEWARE REVIEWED IN THIS ":" CATEGORY DURING THE PERIOD ":" SEPT. 1986 - MAY 1987."#3200:1800'3100+'"MAGIC MATH PLUS, MSDOS, IBM ":" COMPATIBLES, SEMICOMPATIBLES, SANYO,":" ETC.,":" AND IIC (AVAILABLE IBM AND DIGITAL":" RAINBOW). OCT. 1986, 561-62."l"SCIENTIFIC NOTATION, APPLE II FAMILY,":" 48K. NOV. 1986, 666."3200:1800@3100J"NO COURSEWARE REVIEWED IN THIS ":" CATEGORY DURING THE PERIOD ":" SEPT. 1PPLE II ":" FAMILY, 32K, DOS 3.3 (AVAILABLE ":" TRS-80 MODELS 3 & 4). MAR. 1987, 252."g"MATHEMATICS:SOLVING STORY PROBLEMS,":" SKILL GROUP SETS (LEVELS 7-8): WHOLE":" NUMBERS, FRACTIONS, DECIMALS, AND"Kh" GEOMETRY MISCELLANEOUS, APPLE IIEM PC, TRS-80 MODEL 4":" AND COMMODORE 64). MAR. 1987, 252."GF3200Q1800[p3100z"NO COURSEWARE REVIEWED IN THIS ":" CATEGORY DURING THE PERIOD ":" SEPT. 1986 - MAY 1987."~32001800X3100Zb"MATHEMATICS FOR CONSUMERS, A RSC, AND TRS-80). JAN. 1987, 68."t"SOLVING FRACTIONAL EQUATIONS, APPLE II":" FAMILY, 48K. NOV. 1986, 666. "="THE DIG (DIAGNOSTIC INSTRUCTIONAL":" GAMING) MATH COMPUTER PROGRAM, APPLE":" II FAMILY, 64K, WITH 1 DISK DRIVE":" (AVAILABLE IBMPATIBLES, 128K, 1 DISK DRIVE. ":" APR. 1987, 317."p"POLYNOMIAL PAL, IBM PC, 128K. DEC. ":" 1986, 738."3200:3100#"PRIME FACTOR: PRACTICE WITH POLY-":" NOMIALS, APPLE II FAMILY, WITH 1 DISK":" DRIVE. (AVAILABLE COMMODORE, IBM, ":"d DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2:"PRESS RETURN WHEN READY TO CONTINUE.";X$d <Y$(4):Y$;"RUN APR.87:PG.312- SELF-CHECKING CODES"Ie DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2:"PRESS RETURN WHEN READY TO CONTINUE.";X$a <Y$(4):Y$;"RUN MAR.87:PG.237- ABUNDANT NUMBERS"b DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2R DETAILS, CONSULT:"68:"THE MATHEMATICS TEACHER"P13:"FEBRUARY, 1987"d16:"PAGE 147"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dTHE MATHEMATICS TEACHER"2 12:"NOVEMBER, 1986"F 16:"PAGE 619"t 24:5:"PRESS ANY KEY TO CONTINUE.";:R$z dIS. ":3:"EXAMPLE: 19 IS A HAPPY NUMBER":6:" 19 -- 1 X 1 + 9 X 9 = 82" 7:"82 -- 8 X 8 + 2 X 2 = 68":7:"68 -- 6 X 6 + 8 X 8 = 100":6:"100 -- 1 X 1 + 0 X 0 + 0 X 0 = 1":3:"CALCULATIONS END AT 1." 16:4:"FOR DETAILS, CONSULT:" 8:"-- GO TO DESCRIPTION .6000$ 2. <:23_ F5210:I421:I:2:J237:" ";:J:" ":Ie P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p5040 z5:3 -ENTER SHORT DESCRIPTIONK "STRUCTURED PROGRAM TO FIND":3:"HAPPY NUMBER5:14:"HAPPY NUMBERS"' 7:18:"BY"= -- AUTHOR'S NAME[ 9:13:"RITA L. PETROSA"o 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 79 NUMBER 8" 11:"(C) COPYRIGHT 1986" 23 (5210 -THEN PRESS RETURN:";:" ";Y$* Y$"Y"4K D$(4):D$"RUN SYSTEM MENU"S :] 5090c k : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE | 5000 X199%ZX0N15?(H(Z100)U2T((Z100H)10)h<UZ100H10TzFZHHTTUUPZ1ĺX;" IS A HAPPY NUMBER":N5ZNdXn END ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N'      DEC. 1985,":" 714-15."'6"MATHEMATICS WORKSHEET GENERATOR, APPLE":" II, II+, IIE, IIC, 48K, DOS 3.3":" (LICENSE FEES FOR NETWORKS ON":" REQUEST). OCT. 1985, 566."'6"PUZZLE MASTER, TRS-80, MODEL III, 4,":" 48K. JAN. 1986, 69."(63200:181800&23100&2"WEPCO ELECTRONIC STUDY GUIDE FOR ":" TRIGONOMETRY, DISKETTE 3: TRIG- ":" ONOMETRIC GRAPHING, APPLE II FAMILY.":" JAN. 1986, 70."&23200:1800&63100'6"EASYSEARCH: RESOURCES IN A NUTSHELL, ":" APPLE II, 64K, DISKS. ONAL":" FEE). DEC. 1985, 713."h% +"GEOMETRY WITH LOGO, APPLE II FAMILY, ":" 48K. APR. 1986, 301."%+"TRIANGLES, APPLE, DISK. NOV. 1985,":" 644-45."%+3200:1800%.3100%."STAT1 AND STAT2, IBM PCJR. APR. 1986, ":" 301-302."&/3200: MODEL III, DISKS":" (AVAIL. ATARI, NO. 1162-BC).":" MAY 1985, 392."X$'3200:1800b$*3100 %+"BEST (BASIC EDUCATIONAL SKILLS TUTOR)":" INSTRUCTIONAL MODULE: GEOMETRY, ":" APPLE II+, IIE, IIC, DISK (CAN BE":" USED ON A NETWORK FOR AN ADDITI FAMILY, 48K, ":" (AVAILABLE IBM PC, PCJR). JAN. 1986,":" 68-69."#.'"WHAT'S MY LOGIC?, APPLE II FAMILY, ":" 48K, DOS 3.3 (AVAIL. COMMODORE 64,":" COLOR VERSION ONLY). JAN. 1986, 70."H$~'"TARGETS: A NUMBER GAME, TRS-80, NO.":" 1235-BC, 48K,AL SYNTAX POSTERS, SET OF 18 ":" POSTERS. MAY 1986, 393.""Z#"SUPERCALC 3, IBM PC APPRENTICE SERIES,":" IBM PC, IBM PC/XT, IBM PORTABLE PC,":" 128K, DOS 1.1 OR HIGHER. FEB. 1986,":" 148-49.""#3200:1800"'3100F#$'"PRIME NUMBERS, APPLE II1: SIMPLE PROGRAMS AND":" LOOPS, PHOTOCOPY MASTERS COMBO. ":" INCLUDES 'LEARNING PASCAL' MASTERS":" AND MICROPASCAL DISKETTE (AVAILABLE"!G#" COMMODORE 64/PET, IBM PC/PCJR, AND":" TRS-80 MODELS III/4). MAY 1986, 393."!O#3200:3100;"P#"PASCCS TEACHER""14:"APRIL, 1986"616:"PAGE 280"@5210Fd':"PRESS RETURN WHEN READY TO CONTINUE.";X$c <Y$(4):Y$;"RUN MAY.87:PG.406- BINOMIAL PROB. - 1"4):A$(3)N$(6):A$(4)N$(7):A$(5)N$(38)jQ#:A$(6)N$(39):A$(7)N$(40):A$(8)N$(41):A$(9)N$(44):M9:8240U#MX$"CALCULUS":A$(1)N$(42):A$(2)N$(43):M2:8240Z#MX$"GEOMETRY":A$(1)N$(1):A$(2)N$(6):A$(3)N$(14):A$(4)N$(29):M4:8240`d#MX$"NUMBER:"PRESS RETURN WHEN READY TO CONTINUE.";X$] <Y$(4):Y$;"RUN MAR.87:PG.247- POLAR GRAPHS"M^ DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  :"PRESS RETURN WHEN READY TO CONTINUE.";X$b <Y$(4):Y$;"RUN FEB.87:PG.210- ARCTAN(X) PROGRAM"Wc DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2 :"PRESS RETURN WHEN READY TO CONTINUE.";X$c <Y$(4):Y$;"RUN MAR.87:PG.249- POLAR INTERSECTION"2d DIRECT TO SIDE 2p10:"THE PROGRAM YOU HAVE SELECTED IS":"STORED ON SIDE 2 OF THIS DISKETTE."(:"PLEASE REMOVE THE DISKETTE FROM THE":"DISK DRIVE, TURN IT OVER, RE-INSERT":"THE DISKETTE IN THE DRIVE, AND CLOSE ":"THE DOOR."+ 2  NTER A, B AND THE POWER N."? 16:4:"FOR DETAILS, CONSULT:"a 8:"THE MATHEMATICS TEACHER"z 13:"JANUARY, 1987" 16:"PAGE 62" 24:5:"PRESS ANY KEY TO CONTINUE.";:R$ dUE.";:R$ dI21:I:2:J237:" ";:J:" ":I' PV Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$\ xf p5040p z5:3 -ENTER SHORT DESCRIPTION "SHORT IN-CLASS PROGRAM TO RAISE":3:"THE COMPLEX NUMBER A + BI TO ANY":3:"INTEGER POWER." 3:"YOU E 9:11:"CLARK KIMBERLING"1 14:17:"FROM"W 16:8:"THE MATHEMATICS TEACHER"n ---ENTER VOL. NO. 11:"VOLUME 80 NUMBER 1" 11:"(C) COPYRIGHT 1987" 23 (5210 --- GO TO DESCRIPTION .6000 2 <:23! F5210:I4" : 5090 ! :J :I13:I:J138:"*";:J:"*":In I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE 5:8:"POWERS OF COMPLEX NUMBERS" 7:18:"BY" -- AUTHOR'S NAME 5000, "ENTER A,B,N: ";A,B,M=R(AABB)JT(BA)[((MT)RM;s2" + I*";(MT)RM~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$Y$"Y"4 D$(4):D$"RUN SYSTEM MENU     OF SUCCESS"/ 16:4:"FOR DETAILS, CONSULT:"Q 8:"THE MATHEMATICS TEACHER"k 12:"NOVEMBER, 1986" 16:"PAGE 659" 24:5:"PRESS ANY KEY TO CONTINUE.";:R$ dI p5040 z5:34 -ENTER SHORT DESCRIPTION "FIRST OF THREE PROGRAMS THAT COMPUTE":3:"THE PROBABILITY OF A BINOMIAL":3:"EXPERIMENT." 3:"YOU ENTER:":6:"X - THE NUMBER OF SUCCESSES":6:"N - THE NUMBER OF TRIALS":6:"P - THE PROB. ---ENTER VOL. NO.2 11:"VOLUME 79 NUMBER 8"P 11:"(C) COPYRIGHT 1986"X 23b (5210| --- GO TO DESCRIPTION .6000 2 <:23 F5210:I421:I:2:J237:" ";:J:" ":I P Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x";:I:"*":  50402 -- ARTICLE TITLE} 5:3:"THE MICROCOMPUTER AS AN ALTERNATIVE":12:"TO BINOMIAL TABLES" 7:18:"BY" -- AUTHOR'S NAME 9:11:"CLARK KIMBERLING" 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$b Y$"Y"ė:30 D$(4):D$"RUN SYSTEM MENU" : 5090  : :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"* 5000* GEORGE'S SIX LINER8 :L(300)V"WORKING -- PLEASE WAIT"wK1300:L(K)L(K1)(K):K}"INPUT X,N,P= ";X,N,P(YX(P)(NX)(1P)L(N)L(X)L(NX)2"P[X=";X"]="(Y)< PRINT : GOTO 30P ~:"DO YOU   5000"d Dn PROGRAM - HALL'S ALGORITHMJx THIS PROGRAM GENERATES A TABLE OF PRIMITIVE PYTHAGOREAN TRIPLES ORGANIZED AS A FAMILY ACCORDING TO HALL'S ALGORITHM DIMENSION AND READ THE MATRICES !"""""  HE ":3:"COMPLEX NUMBER A + BI."K 3:"YOU ENTER A, B AND THE POWER N."o 16:4:"FOR DETAILS, CONSULT:" 8:"THE MATHEMATICS TEACHER" 13:"JANUARY, 1987" 16:"PAGE 64" 24:5:"PRESS ANY KEY TO CONTINUE.";:R$ d .6000 2 <:23I F5210:I421:I:2:J237:" ";:J:" ":IO P~ Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$ x p5040 z5:3 -ENTER SHORT DESCRIPTION! "SHORT IN CLASS PROGRAM TO COMPUTE N":3:"DIFFERENT 1/N POWERS OF T 7:18:"BY"& -- AUTHOR'S NAMEE 9:11:"CLARK KIMBERLING"Y 14:17:"FROM" 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 80 NUMBER 1" 11:"(C) COPYRIGHT 1987" 23 (5210 --- GO TO DESCRIPTIONY$"Y"4) D$(4):D$"RUN SYSTEM MENU"1 :; 5090A I :r :I13:I:J138:"*";:J:"*":I I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE 5:8:"POWERS OF COMPLEX NUMBERS" 5000, "ENTER A,B,N: ";A,B,N=R(AABB)JT(BA)X(VR(1N)e2K0N1y<U(T6.283K)NFV(U);" + I*";V(U)PK~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ !!!!!DETAILS, CONSULT:"48:"THE MATHEMATICS TEACHER"N12:"NOVEMBER, 1986"b16:"PAGE 659"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dIEXPERIMENT. THIS PROGRAM ":3:"SUMS THE PROBABILITIES OF SEVERAL":3:"OUTCOMES." 3:"YOU ENTER:":6:"N - THE NUMBER OF TRIALS ":6:"P - THE PROB. OF SUCCESS":6:"A - START NUMBER OF SUCCESSES":6:"B - END NUMBER OF SUCCESSES"16:4:"FOR <:23; F5210:I421:I:2:J237:" ";:J:" ":IA Pp Z24:7:"PRESS ANY KEY TO CONTINUE. ";:R$v x p5040 z5:3 -ENTER SHORT DESCRIPTIONR "SECOND OF THREE PROGRAMS THAT ":3:"COMPUTE THE PROBABILITY OF A":3:"BINOMIAL Y" -- AUTHOR'S NAME7 9:11:"CLARK KIMBERLING"K 14:17:"FROM"q 16:8:"THE MATHEMATICS TEACHER" ---ENTER VOL. NO. 11:"VOLUME 79 NUMBER 8" 11:"(C) COPYRIGHT 1986" 23 (5210 --- GO TO DESCRIPTION .6000 2 5090  :@ :I13:I:J138:"*";:J:"*":Id I421:I:1:"*";:39:"*":I I138:"*";:I:"*":  5040 -- ARTICLE TITLE 5:3:"THE MICROCOMPUTER AS AN ALTERNATIVE":12:"TO BINOMIAL TABLES" 7:18:"B(X):X Z"P[A<=B] = ";Q$ dQ0:L n"ANOTHER? (0,0 TO QUIT) A,B =";A,B_ x(A0B0)80e ~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";:" ";Y$ Y$"Y"ė:30 D$(4):D$"RUN SYSTEM MENU" : 5000* SAM'S SUMS @ :L(300):P(300)^"WORKING -- PLEASE WAIT"K1300:L(K)L(K1)(K):K"INPUT N,P,A,B= ";N,P,A,B(X0N2YX(P)(NX)(1P)L(N)L(X)L(NX)<P(X)(Y)FX PXAB:QQP!! ! ! ! ! !TRIPLES DO YOU WANT"; "PLEASE ENTER A POSITIVE INTEGER"B &NW 0(N)NN0540h :N6L3590q D620z NN6 X"ONLY THE FIRST 6 OF THESE TRIPLES ARE" b"LISTED HERE. AFTER THAT THE TRIPLES":"ARE TOO BIG." lI1N v2500: MAT T= WITH C=B+1"1 "TYPE 2 FOR TRIPLES WITH C=A+2"V "TYPE 3 FOR TRIPLES WITH B=A+1"] Ll L1İ2000{ L2İ3000 L3İ4000 L1L2L3410   LIST SPECIAL TRIPLES  1110: INITIALIZE STARTING TRIPLE "HOW MANY + 6"TYPE S FOR SPECIAL LINES OF DESCENT"3 @A$C JA$"G"690S TA$"S"380u ^"PLEASE FOLLOW INSTRUCTIONS"~ h300 r | GIVE CHOICES FOR SPECIAL TRIPLES  "YOU HAVE A CHOICE OF 3 TYPES OF TRIPLES (A,B,C) "TYPE 1 FOR TRIPLES LIST GENERATIONS": "OF PRIMITIVE PYTHAGOREAN TRIPLES"` "ACCORDING TO HALL'S ALGORITHM."f  "DO YOU WANT TO LIST THE TRIPLES BY" ""GENERATIONS OR WOULD YOU LIKE TO LIST":"A SPECIAL LINE OF DESCENT?" ,"TYPE G FOR GENERATION LISTING" U(3,3),A(3,3),D(3,3)7 S(1,3),R(3,3),T(1,3)] X113:Y113:U(X1,Y1):Y1:X1 X113:Y113:A(X1,Y1):Y1:X1 X113:Y113:D(X1,Y1):Y1:X1 PRINT INSTRUCTIONS AND GIVE INITIAL CHOICES  "THIS PROGRAM WILLPLEX NUMBER A+BI."=3:"YOU ENTER A, B, AND THE POWER M."a16:4:"FOR DETAILS, CONSULT:"8:"THE MATHEMATICS TEACHER"13:"JANUARY, 1987"16:"PAGE 65"24:5:"PRESS ANY KEY TO CONTINUE.";:R$dI DESCRIPTION.60002&<:23WF5210:I421:I:2:J237:" ";:J:" ":I]PZ24:7:"PRESS ANY KEY TO CONTINUE. ";:R$xp5040z5:3-ENTER SHORT DESCRIPTION"PROGRAM TO COMPUTE ANY INTEGER":3:"POWER OF THE COMPLEX NUMBERS"7:18:"BY"4-- AUTHOR'S NAMES9:11:"CLARK KIMBERLING"g14:17:"FROM"16:8:"THE MATHEMATICS TEACHER"---ENTER VOL. NO.11:"VOLUME 80 NUMBER 1"11:"(C) COPYRIGHT 1987"23(5210 --- GO TO:" ";Y$Y$"Y"47D$(4):D$"RUN SYSTEM MENU"?:I5090OW::I13:I:J138:"*";:J:"*":II421:I:1:"*";:39:"*":II138:"*";:I:"*":5040-- ARTICLE TITLE 5:8:"POWERS OF COM "(R*COS T + I*SIN T))^M ") 36,1V &" = (R^M)*COS(M*T) + I*(R^M)*SIN(M*T)," 0"WHICH IS THE NUMBER UNDERLINED ABOVE." ::"READY FOR ANOTHER RUN?" D~:"DO YOU WISH TO RUN THE PROGRAM AGAIN?":"ENTER 'Y' OR 'N' THEN PRESS RETURN:";")*I" K039:"_";:K:K :"YOUR COMPLEX NUMBER A+B*I, WRITTEN IN"t "THE FORM R*(COS T + I*SIN T), HAS" F(R)ER(.5R) F(T)ET(.5T) 36,4 "R="R" AND T="T" RAD"  :"DeMOIVRE'S THEOREM STATES THAT " 36,4200  "R(AABB)- ,A0T(BA)@ 6A0B0TP2U @A0B0T3P2d JA0TTPz TC(MT):S(MT) ^CCRM:SSRM hF(C)EC(.5C) rF(S)ES(.5S) | :36,4 "("A"+"B"*I)^"M" = " 36,4 C" + ("S0: PRINT ANALYSIS 140# Y "INPUT A,B,M ON ONE LINE(0,0,0 TO QUIT): ";A,B,M_ w (A0B0M0)4990 A0B0280 "SORRY, BUT ONE OF A AND B MUST NOT = 0." 200 M(M)280 "SORRY, BUT M MUST BE AN INTEGER." ONAL PART OF X* Z P = 3.14159266 (PI)I d E = TOLERANCE LEVEL FORg n ROUNDING TO NEARBY x INTEGER (e.g., Line 360) 200: INPUT A,B,M 290: COMPUTE RADIUS R, ANGLE T 390: COMPUTE & PRINT Mth POWER 51 50002 INTEGER POWERS OF A+B*i\:"THIS PROGRAM COMPUTES (A+B*I)^M,""WHERE A+B*I IS ANY NONZERO COMPLEX"("NUMBER AND M IS ANY INTEGER."2F(X)(X(.5X))<P4(1):E11024:F P FNF(X) = SIZE OF FRACTI"" " " " " """"