HomeSpirograph mathCalculating the Number of Points in a Spirograph Pattern


Calculating the Number of Points in a Spirograph Pattern — 10 Comments

  1. There were two Super Spirograph arrangements with a very awkward gearing – the trapezoid and the open-end arrangement, with 268 points. As a result, all the rpatterns obtained were very dense, and none had fewer than 67 points.

  2. Other (inside) points numbers for Super Spirograph arrangements: Large square and diamond, 320; large triangle, 264; cloverleaf, 336; rectangle (4 x ‘E’ + 2 x ‘F’), 288.

  3. What is the point (no pun intended) of using the least common multiple? I am trying to do a math honors project and I would love some help…

    • Check out this post:

      There are 4 wheels that give a LCM of 7 when used in ring 105. If you have a Spirograph, draw the patterns and feel the difference between them; if not, trace them with your eyes and you’ll see that they follow different paths to arrive at a 7-pointed figure. If Spirograph had a 15-toothed wheel (it would be too tiny), it would trace a heptagon with no lines crossing. Wheel 30 (the outer green lines) skips one point as it goes around. Wheel 45 (the blue lines) skips two points. Wheel 60 (red) skips over 3 points and Wheel 75 (inner green) skips over 4 – or maybe you could say it goes -2 in the other direction. If we had a 90-tooth wheel, it would make a tightly looped pattern, rather like wheel 84 in the other ring of 144/96, except with 7 points.

  4. Another way of calculating the points in the pattern is to treat the ratio of (moving : fixed) as a fraction. Wheel 60 in ring 96 would give 60/96. Cancel the fraction down to lowest terms and you get 5/8. The bottom line of the reduced fraction will be the number of points in the pattern. So 52/105 cannot cancel, which is why that combo has the full 105 points.

    • Thanks for sharing this method of using the ratio of moving:fixed to calculate points. It is fun AND useful! Brings back all my grade school math skills! Way easier and quicker than figuring out the LCD. I’m fashioning my own chart but it’s sloppy. I need to check to see if Heather has any other ready-made charts I can print. Thanks again!

    • That is a big mystery which has not been solved yet, to my knowledge, nor Aaron Bleakley’s, from what I’ve read on the site.

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