Comments on: Calculating the Number of Points in a Spirograph Pattern

By: Heather

Heather — Thu, 06 May 2021 16:22:12 +0000

So I did a bit of exploring the variations of this, explained in this article and video:
https://spirographicart.com/2021/03/02/wheel-within-a-wheel-exploration-with-wild-gears/

By: MonaMarieRosemary

MonaMarieRosemary — Sun, 09 Feb 2020 00:23:49 +0000

In reply to Mark. 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!

By: Heather

Heather — Sat, 30 Nov 2019 21:33:44 +0000

In reply to Phenacite. 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 WildGears.com site.

By: Phenacite

Phenacite — Mon, 17 Jun 2019 04:38:09 +0000

How would you find the points for wild gears’ gear in a gear in a wheel?

By: Heather

Heather — Wed, 26 Apr 2017 23:53:13 +0000

In reply to Mark. Well that's a lot easier. I'll try that.

By: Mark

Mark — Wed, 26 Apr 2017 23:30:02 +0000

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.

By: Heather

Heather — Fri, 27 May 2016 15:09:16 +0000

In reply to Grace.

Check out this post: https://spirographicart.com/2013/12/11/seven-pointed-spirograph-designs/

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.

By: Grace

Grace — Fri, 27 May 2016 02:30:52 +0000

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…

By: Heather Holm

Heather Holm — Sun, 03 Aug 2014 23:41:10 +0000

Thanks Mark, you’re a step ahead of me, and this saves me some calculating. I plan to make a chart for the Super Spirograph arrangements with point numbers, like this one: https://spirographicart.com/table-spirograph-points/ but with illustrations.

By: Mark

Mark — Sun, 03 Aug 2014 22:52:40 +0000

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.