# Geometric name for Spyrograph patterns?
**URL:** https://boards.straightdope.com/t/geometric-name-for-spyrograph-patterns/545016
**Category:** Factual Questions
**Created:** [June 30, 2010, 1:30am UTC](https://boards.straightdope.com/t/geometric-name-for-spyrograph-patterns/545016 "2010-06-30T01:30:00Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Jinx](https://boards.straightdope.com/u/Jinx)
#### Post date: [June 30, 2010, 1:30am UTC](https://boards.straightdope.com/t/geometric-name-for-spyrograph-patterns/545016/1 "2010-06-30T01:30:00Z")
I was wondering if there is a geometric name for patterns of circles and loops created by a Spryrograph toy where one wheel rolls either over or inside the circumference of another circle?
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### Author:  [@minor7flat5](https://boards.straightdope.com/u/minor7flat5)
#### Post date: [June 30, 2010, 1:34am UTC](https://boards.straightdope.com/t/geometric-name-for-spyrograph-patterns/545016/2 "2010-06-30T01:34:30Z")
How about an [Epicycloid](http://en.wikipedia.org/wiki/Epicycloid)?
The general term for curves that roll on curves without slipping would be [Roulette](http://en.wikipedia.org/wiki/Roulette_(curve)).
(and that’s something new I learned today from Wikipedia!)
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### Author:  [@BrotherCadfael](https://boards.straightdope.com/u/BrotherCadfael)
#### Post date: [June 30, 2010, 1:36am UTC](https://boards.straightdope.com/t/geometric-name-for-spyrograph-patterns/545016/3 "2010-06-30T01:36:26Z")
According to [this](http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node34.html), they are called “Roulettes”.
I know nothing about the mathematics of roulettes, I just Googled “spirograph geometry”, and this was the first result.
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### Author:  [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)
#### Post date: [June 30, 2010, 3:46am UTC](https://boards.straightdope.com/t/geometric-name-for-spyrograph-patterns/545016/4 "2010-06-30T03:46:36Z")
Also noted on [this Wikipedia page](http://en.wikipedia.org/wiki/Hypotrochoid) (among others):
The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.
It looks to me like an epicycloid is a special case of an epitrochoid, where the tracing point is exactly on the perimeter of the moving circle.
Similarly, the hypotrochoid covers the general case where the moving circle rolls along the _inside_ of the fixed circle. Then, a hypocycloid is the special case where the tracing point is on the perimeter.
All four of these curves have Wikipedia pages, incidentally.