Home » CEEFAX disks » telesoftware17.adl » 25-08-89/T\Curio
25-08-89/T\Curio
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » CEEFAX disks » telesoftware17.adl |
| Filename: | 25-08-89/T\Curio |
| Read OK: | ✔ |
| File size: | 0814 bytes |
| Load address: | 0000 |
| Exec address: | FFFFFFFF |
File contents
A CURIOSITY. A pointless, but interesting program from Ray Elder. A few weeks ago my eldest brought home a piece of work related to her coursework for the new GCSE exam. As I was bored at the time and also felt that I should show a parental interest, I asked her what she was doing. This program is a result of that coursework. THE TASK: The subject was maths (not my most favourite) and the work was as follows: Take any multiplication table and calculate each step. If the result is greater than 9 (ie.two or more digits) then add the digits together. Repeat until the product is a single digit. For example: 5 x 1 = 5 ... Product = 5 5 x 2 = 10 .. Product = 1+0 = 1 5 x 3 = 15 .. Product = 1+5 = 6 ...etc. 5 times 23= 115 . Product = 1+1+5 = 7 ...etc. Using graph paper, draw a line vertically up for the length of the first product, then for each other product draw a line at 90 degrees clockwise to the end of the previous line of length equal to the product. So for our 5 times table example the first line is 5 units upwards, the next line 1 unit long going to the right, followed by a line of 6 units downwards followed by a line of 2 units going to the left ... and so on. How many different patterns can be formed? There is no limit to the number of tables to be used and at first sight I thought she had a piece of work that would take a life time. I could imagine her at 60 still working out 23897 times 1, 23897 times 2. So I thought that a program to do the calculations would be useful, as even using a calculator would mean entering each sum one at a time. So I took on the task of utilising the computers graphics facilities and produced this program, with surprising results. Try it yourself, curious isn't it! Due to the computer screen pixels not being square there may be some slight distortion of the patterns. This is best seen when processing the 9 times table. The result should be a perfect square. The program is written to allow the easy addition of any refinements of your own, such as screen print routines and so on.
00000000 41 20 43 55 52 49 4f 53 49 54 59 2e 0d 0d 41 20 |A CURIOSITY...A | 00000010 70 6f 69 6e 74 6c 65 73 73 2c 20 62 75 74 20 69 |pointless, but i| 00000020 6e 74 65 72 65 73 74 69 6e 67 20 70 72 6f 67 72 |nteresting progr| 00000030 61 6d 20 66 72 6f 6d 20 52 61 79 20 45 6c 64 65 |am from Ray Elde| 00000040 72 2e 0d 0d 41 20 66 65 77 20 77 65 65 6b 73 20 |r...A few weeks | 00000050 61 67 6f 20 6d 79 20 65 6c 64 65 73 74 20 62 72 |ago my eldest br| 00000060 6f 75 67 68 74 20 68 6f 6d 65 20 61 20 70 69 65 |ought home a pie| 00000070 63 65 20 6f 66 20 77 6f 72 6b 20 72 65 6c 61 74 |ce of work relat| 00000080 65 64 20 74 6f 20 68 65 72 0d 63 6f 75 72 73 65 |ed to her.course| 00000090 77 6f 72 6b 20 66 6f 72 20 74 68 65 20 6e 65 77 |work for the new| 000000a0 20 47 43 53 45 20 65 78 61 6d 2e 20 41 73 20 49 | GCSE exam. As I| 000000b0 20 77 61 73 20 62 6f 72 65 64 20 61 74 20 74 68 | was bored at th| 000000c0 65 20 74 69 6d 65 20 61 6e 64 20 61 6c 73 6f 0d |e time and also.| 000000d0 66 65 6c 74 20 74 68 61 74 20 49 20 73 68 6f 75 |felt that I shou| 000000e0 6c 64 20 73 68 6f 77 20 61 20 70 61 72 65 6e 74 |ld show a parent| 000000f0 61 6c 20 69 6e 74 65 72 65 73 74 2c 20 49 20 61 |al interest, I a| 00000100 73 6b 65 64 20 68 65 72 20 77 68 61 74 20 73 68 |sked her what sh| 00000110 65 20 77 61 73 0d 64 6f 69 6e 67 2e 20 54 68 69 |e was.doing. Thi| 00000120 73 20 70 72 6f 67 72 61 6d 20 69 73 20 61 20 72 |s program is a r| 00000130 65 73 75 6c 74 20 6f 66 20 74 68 61 74 20 63 6f |esult of that co| 00000140 75 72 73 65 77 6f 72 6b 2e 0d 0d 54 48 45 20 54 |ursework...THE T| 00000150 41 53 4b 3a 0d 0d 54 68 65 20 73 75 62 6a 65 63 |ASK:..The subjec| 00000160 74 20 77 61 73 20 6d 61 74 68 73 20 28 6e 6f 74 |t was maths (not| 00000170 20 6d 79 20 6d 6f 73 74 20 66 61 76 6f 75 72 69 | my most favouri| 00000180 74 65 29 20 61 6e 64 20 74 68 65 20 77 6f 72 6b |te) and the work| 00000190 20 77 61 73 20 61 73 0d 66 6f 6c 6c 6f 77 73 3a | was as.follows:| 000001a0 0d 0d 54 61 6b 65 20 61 6e 79 20 6d 75 6c 74 69 |..Take any multi| 000001b0 70 6c 69 63 61 74 69 6f 6e 20 74 61 62 6c 65 20 |plication table | 000001c0 61 6e 64 20 63 61 6c 63 75 6c 61 74 65 20 65 61 |and calculate ea| 000001d0 63 68 20 73 74 65 70 2e 20 49 66 20 74 68 65 20 |ch step. If the | 000001e0 72 65 73 75 6c 74 20 69 73 0d 67 72 65 61 74 65 |result is.greate| 000001f0 72 20 74 68 61 6e 20 39 20 28 69 65 2e 74 77 6f |r than 9 (ie.two| 00000200 20 6f 72 20 6d 6f 72 65 20 64 69 67 69 74 73 29 | or more digits)| 00000210 20 74 68 65 6e 20 61 64 64 20 74 68 65 20 64 69 | then add the di| 00000220 67 69 74 73 20 74 6f 67 65 74 68 65 72 2e 0d 52 |gits together..R| 00000230 65 70 65 61 74 20 75 6e 74 69 6c 20 74 68 65 20 |epeat until the | 00000240 70 72 6f 64 75 63 74 20 69 73 20 61 20 73 69 6e |product is a sin| 00000250 67 6c 65 20 64 69 67 69 74 2e 20 46 6f 72 20 65 |gle digit. For e| 00000260 78 61 6d 70 6c 65 3a 0d 0d 20 35 20 78 20 31 20 |xample:.. 5 x 1 | 00000270 3d 20 35 20 2e 2e 2e 20 50 72 6f 64 75 63 74 20 |= 5 ... Product | 00000280 3d 20 35 0d 20 35 20 78 20 32 20 3d 20 31 30 20 |= 5. 5 x 2 = 10 | 00000290 2e 2e 20 50 72 6f 64 75 63 74 20 3d 20 31 2b 30 |.. Product = 1+0| 000002a0 20 3d 20 31 0d 20 35 20 78 20 33 20 3d 20 31 35 | = 1. 5 x 3 = 15| 000002b0 20 2e 2e 20 50 72 6f 64 75 63 74 20 3d 20 31 2b | .. Product = 1+| 000002c0 35 20 3d 20 36 20 20 2e 2e 2e 65 74 63 2e 0d 0d |5 = 6 ...etc...| 000002d0 20 35 20 74 69 6d 65 73 20 32 33 3d 20 31 31 35 | 5 times 23= 115| 000002e0 20 2e 20 50 72 6f 64 75 63 74 20 3d 20 31 2b 31 | . Product = 1+1| 000002f0 2b 35 20 3d 20 37 20 20 2e 2e 2e 65 74 63 2e 0d |+5 = 7 ...etc..| 00000300 0d 55 73 69 6e 67 20 67 72 61 70 68 20 70 61 70 |.Using graph pap| 00000310 65 72 2c 20 64 72 61 77 20 61 20 6c 69 6e 65 20 |er, draw a line | 00000320 76 65 72 74 69 63 61 6c 6c 79 20 75 70 20 66 6f |vertically up fo| 00000330 72 20 74 68 65 20 6c 65 6e 67 74 68 20 6f 66 20 |r the length of | 00000340 74 68 65 20 66 69 72 73 74 0d 70 72 6f 64 75 63 |the first.produc| 00000350 74 2c 20 74 68 65 6e 20 66 6f 72 20 65 61 63 68 |t, then for each| 00000360 20 6f 74 68 65 72 20 70 72 6f 64 75 63 74 20 64 | other product d| 00000370 72 61 77 20 61 20 6c 69 6e 65 20 61 74 20 39 30 |raw a line at 90| 00000380 20 64 65 67 72 65 65 73 20 63 6c 6f 63 6b 77 69 | degrees clockwi| 00000390 73 65 0d 74 6f 20 74 68 65 20 65 6e 64 20 6f 66 |se.to the end of| 000003a0 20 74 68 65 20 70 72 65 76 69 6f 75 73 20 6c 69 | the previous li| 000003b0 6e 65 20 6f 66 20 6c 65 6e 67 74 68 20 65 71 75 |ne of length equ| 000003c0 61 6c 20 74 6f 20 74 68 65 20 70 72 6f 64 75 63 |al to the produc| 000003d0 74 2e 0d 0d 53 6f 20 66 6f 72 20 6f 75 72 20 35 |t...So for our 5| 000003e0 20 74 69 6d 65 73 20 74 61 62 6c 65 20 65 78 61 | times table exa| 000003f0 6d 70 6c 65 20 74 68 65 20 66 69 72 73 74 20 6c |mple the first l| 00000400 69 6e 65 20 69 73 20 35 20 75 6e 69 74 73 20 75 |ine is 5 units u| 00000410 70 77 61 72 64 73 2c 20 74 68 65 0d 6e 65 78 74 |pwards, the.next| 00000420 20 6c 69 6e 65 20 31 20 75 6e 69 74 20 6c 6f 6e | line 1 unit lon| 00000430 67 20 67 6f 69 6e 67 20 74 6f 20 74 68 65 20 72 |g going to the r| 00000440 69 67 68 74 2c 20 66 6f 6c 6c 6f 77 65 64 20 62 |ight, followed b| 00000450 79 20 61 20 6c 69 6e 65 20 6f 66 20 36 20 75 6e |y a line of 6 un| 00000460 69 74 73 0d 64 6f 77 6e 77 61 72 64 73 20 66 6f |its.downwards fo| 00000470 6c 6c 6f 77 65 64 20 62 79 20 61 20 6c 69 6e 65 |llowed by a line| 00000480 20 6f 66 20 32 20 75 6e 69 74 73 20 67 6f 69 6e | of 2 units goin| 00000490 67 20 74 6f 20 74 68 65 20 6c 65 66 74 20 2e 2e |g to the left ..| 000004a0 2e 20 61 6e 64 20 73 6f 20 6f 6e 2e 0d 0d 48 6f |. and so on...Ho| 000004b0 77 20 6d 61 6e 79 20 64 69 66 66 65 72 65 6e 74 |w many different| 000004c0 20 70 61 74 74 65 72 6e 73 20 63 61 6e 20 62 65 | patterns can be| 000004d0 20 66 6f 72 6d 65 64 3f 0d 0d 54 68 65 72 65 20 | formed?..There | 000004e0 69 73 20 6e 6f 20 6c 69 6d 69 74 20 74 6f 20 74 |is no limit to t| 000004f0 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 74 61 62 |he number of tab| 00000500 6c 65 73 20 74 6f 20 62 65 20 75 73 65 64 20 61 |les to be used a| 00000510 6e 64 20 61 74 20 66 69 72 73 74 20 73 69 67 68 |nd at first sigh| 00000520 74 20 49 0d 74 68 6f 75 67 68 74 20 73 68 65 20 |t I.thought she | 00000530 68 61 64 20 61 20 70 69 65 63 65 20 6f 66 20 77 |had a piece of w| 00000540 6f 72 6b 20 74 68 61 74 20 77 6f 75 6c 64 20 74 |ork that would t| 00000550 61 6b 65 20 61 20 6c 69 66 65 20 74 69 6d 65 2e |ake a life time.| 00000560 20 49 20 63 6f 75 6c 64 0d 69 6d 61 67 69 6e 65 | I could.imagine| 00000570 20 68 65 72 20 61 74 20 36 30 20 73 74 69 6c 6c | her at 60 still| 00000580 20 77 6f 72 6b 69 6e 67 20 6f 75 74 20 32 33 38 | working out 238| 00000590 39 37 20 74 69 6d 65 73 20 31 2c 20 32 33 38 39 |97 times 1, 2389| 000005a0 37 20 74 69 6d 65 73 20 32 2e 20 53 6f 20 49 0d |7 times 2. So I.| 000005b0 74 68 6f 75 67 68 74 20 74 68 61 74 20 61 20 70 |thought that a p| 000005c0 72 6f 67 72 61 6d 20 74 6f 20 64 6f 20 74 68 65 |rogram to do the| 000005d0 20 63 61 6c 63 75 6c 61 74 69 6f 6e 73 20 77 6f | calculations wo| 000005e0 75 6c 64 20 62 65 20 75 73 65 66 75 6c 2c 20 61 |uld be useful, a| 000005f0 73 20 65 76 65 6e 0d 75 73 69 6e 67 20 61 20 63 |s even.using a c| 00000600 61 6c 63 75 6c 61 74 6f 72 20 77 6f 75 6c 64 20 |alculator would | 00000610 6d 65 61 6e 20 65 6e 74 65 72 69 6e 67 20 65 61 |mean entering ea| 00000620 63 68 20 73 75 6d 20 6f 6e 65 20 61 74 20 61 20 |ch sum one at a | 00000630 74 69 6d 65 2e 0d 0d 53 6f 20 49 20 74 6f 6f 6b |time...So I took| 00000640 20 6f 6e 20 74 68 65 20 74 61 73 6b 20 6f 66 20 | on the task of | 00000650 75 74 69 6c 69 73 69 6e 67 20 74 68 65 20 63 6f |utilising the co| 00000660 6d 70 75 74 65 72 73 20 67 72 61 70 68 69 63 73 |mputers graphics| 00000670 20 66 61 63 69 6c 69 74 69 65 73 20 61 6e 64 0d | facilities and.| 00000680 70 72 6f 64 75 63 65 64 20 74 68 69 73 20 70 72 |produced this pr| 00000690 6f 67 72 61 6d 2c 20 77 69 74 68 20 73 75 72 70 |ogram, with surp| 000006a0 72 69 73 69 6e 67 20 72 65 73 75 6c 74 73 2e 20 |rising results. | 000006b0 54 72 79 20 69 74 20 79 6f 75 72 73 65 6c 66 2c |Try it yourself,| 000006c0 20 63 75 72 69 6f 75 73 0d 69 73 6e 27 74 20 69 | curious.isn't i| 000006d0 74 21 0d 0d 44 75 65 20 74 6f 20 74 68 65 20 63 |t!..Due to the c| 000006e0 6f 6d 70 75 74 65 72 20 73 63 72 65 65 6e 20 70 |omputer screen p| 000006f0 69 78 65 6c 73 20 6e 6f 74 20 62 65 69 6e 67 20 |ixels not being | 00000700 73 71 75 61 72 65 20 74 68 65 72 65 20 6d 61 79 |square there may| 00000710 20 62 65 20 73 6f 6d 65 0d 73 6c 69 67 68 74 20 | be some.slight | 00000720 64 69 73 74 6f 72 74 69 6f 6e 20 6f 66 20 74 68 |distortion of th| 00000730 65 20 70 61 74 74 65 72 6e 73 2e 20 54 68 69 73 |e patterns. This| 00000740 20 69 73 20 62 65 73 74 20 73 65 65 6e 20 77 68 | is best seen wh| 00000750 65 6e 20 70 72 6f 63 65 73 73 69 6e 67 0d 74 68 |en processing.th| 00000760 65 20 39 20 74 69 6d 65 73 20 74 61 62 6c 65 2e |e 9 times table.| 00000770 20 54 68 65 20 72 65 73 75 6c 74 20 73 68 6f 75 | The result shou| 00000780 6c 64 20 62 65 20 61 20 70 65 72 66 65 63 74 20 |ld be a perfect | 00000790 73 71 75 61 72 65 2e 0d 0d 54 68 65 20 70 72 6f |square...The pro| 000007a0 67 72 61 6d 20 69 73 20 77 72 69 74 74 65 6e 20 |gram is written | 000007b0 74 6f 20 61 6c 6c 6f 77 20 74 68 65 20 65 61 73 |to allow the eas| 000007c0 79 20 61 64 64 69 74 69 6f 6e 20 6f 66 20 61 6e |y addition of an| 000007d0 79 20 72 65 66 69 6e 65 6d 65 6e 74 73 20 6f 66 |y refinements of| 000007e0 0d 79 6f 75 72 20 6f 77 6e 2c 20 73 75 63 68 20 |.your own, such | 000007f0 61 73 20 73 63 72 65 65 6e 20 70 72 69 6e 74 20 |as screen print | 00000800 72 6f 75 74 69 6e 65 73 20 61 6e 64 20 73 6f 20 |routines and so | 00000810 6f 6e 2e 0d |on..| 00000814
25-08-89/T\Curio.m0
25-08-89/T\Curio.m1
25-08-89/T\Curio.m2
25-08-89/T\Curio.m4
25-08-89/T\Curio.m5
.