Explaining Spirographs

[mrgreenankle]

Hi!

I am supposed to write a report on how spirographs work. I know some trigonometry (we just covered the unit circle so I understand that), and I can understand the formulas defining the shape of a spirograph decently. However, I have now idea what to write in my report. I'm not sure if I could just paste the equation and explain it, because it is supposed to take the shape of an investigation.

Does anyone have any suggestions about how one might do this?

Would appreciate any help immensely!

 

[Ishuda]

Hi mrgreenankle,

Assuming you mean the toy, why don't you read
http://en.wikipedia.org/wiki/Spirograph
or something similar. In fact, it wouldn't be a bad idea to go to several sites because that might help your understanding. Depending on just what is wanted exactly, write up the explanation in your own words. It might be a good idea to reference those pages. You don't have to do all of those formulas but you should try to get the concept across.

I found it interesting that, while looking around, there may be a connection between the toy and The Ptolemaic System, do a Google search for
Worldviews The Ptolemaic System "Chapter 13, 14" Richard Dewitt
to read a copy.

-Ishuda

 

[mrgreenankle]

Hi mrgreenankle,

Assuming you mean the toy, why don't you read
http://en.wikipedia.org/wiki/Spirograph
or something similar. In fact, it wouldn't be a bad idea to go to several sites because that might help your understanding. Depending on just what is wanted exactly, write up the explanation in your own words. It might be a good idea to reference those pages. You don't have to do all of those formulas but you should try to get the concept across.

I found it interesting that, while looking around, there may be a connection between the toy and The Ptolemaic System, do a Google search for
Worldviews The Ptolemaic System "Chapter 13, 14" Richard Dewitt
to read a copy.

-Ishuda

Thank you for the reply! I have read about them on wikipedia and all other sites that emerge when you google it, but most of them are too complex for me to understand to the degree that I should explain it using my own words.

What I understand from the wikipedia explanation, for example, is the equations defining the position of the pencil at a certain instant. However, I do not understand how you would make such an equation explain the entirety of the shape created.

Is there a simpler explanation that could be made? I would appreciate if you found any while you were looking, or if you could try to write a simple explanation yourself if you understood it well!

 

[Ishuda]

Try the Spirograph demonstrations
https://www.youtube.com/channel/UC12vaoAfL5sqKbj0I6fvn5Q

Describe the basic way it is done - a smaller circle revolving inside another circle, the smaller circle always tangent to the larger fixed circle. Try to visualize and describe what a single design ('one' time around to close the loop) if the pencil were at the center of the small circle (a circle results) and what would happen if it were out at the edge (a hypocycloid results). How are different patterns made (by moving the pencil and drawing either the same offset pattern or maybe a new pattern. Pick one of the demonstrations above and describe it.

Don't forget to give credit to the sites.