What's this? +Xah Lee made this picture, and I explain it on my blog,

http://blogs.ams.org/visualinsight/2013/11/15/astroid-as-catacaustic-of-deltoid/

After you read it you can tackle this:

#geometry

*Visual Insight*:http://blogs.ams.org/visualinsight/2013/11/15/astroid-as-catacaustic-of-deltoid/

After you read it you can tackle this:

**Puzzle:**what's the catacaustic of an astroid?#geometry

View 8 previous comments

- +Xah Lee - I never proved that the catacaustic of a deltoid is an astroid, but Greg Egan has a page explaining how to compute catacaustics of curves:

http://gregegan.customer.netspace.net.au/SCIENCE/Catacaustics/Catacaustics.htmlNov 16, 2013 - I posed this puzzle:
*what's the catacaustic of an astroid?*

Greg Egan put a picture of the answer here:

http://gregegan.customer.netspace.net.au/SCIENCE/Catacaustics/CatAstroid.png

and he wrote:**For a source at (-infinity,0) and an astroid with cusps on the coordinate axes, up to a choice of scale, a curve with parametric form:****(cos(3t) + 3 (4 cos(t)+cos(5t)), 2 sin(2t) (cos(t)-9 cos(3t)) - 4 cos(2t) (sin(t)-3 sin(3t))))****This is a six-cusped curve, but it not a hypocycloid.**

In other words: unlike the deltoid and astroid, it's not formed by rolling a circle in a circle!Nov 16, 2013 - Nov 16, 2013
- +John Baez I googled the answer since I was to lazy to find my ruler. Wolfram had a different perspective on it but it seems they construct the catacaustic differently.

http://mathworld.wolfram.com/AstroidCatacaustic.html

(Edited: Reason, didn't see at first glance Wolfram uses a generalized definition for the catacaustic so my original post didn't make much sense.)Nov 17, 2013 - Thanks for your answer +John Baez! No, i meant linking to your g+ posts. Nevermind. Your links do lead to interesting material and that's cool, too. (no irony, that paper really is a nice supplement) I also
*do*like the crisp format. Just wondering...

Not sure of you asked this but i'll tell anyways. I'd very much like to contribute! I know, i'm invited to send an email as everyone else. But it'd be more exciting for me if i could go for something you might consider special fun. You've been a great inspiration for me and i'd be thrilled to give back.

So if you see something i did, please feel invited to use any stuff you find interesting! I won't start mailing you half my posts, that'd be wasting all sides. But in case i get the message, i might even invest and see if i can do a custom picture myself. Now you know.Nov 17, 2013 - +Refurio Anachro - I'll check out your posts, thanks! I'm looking for images that are very beautiful and illustrate serious mathematical ideas.Nov 17, 2013

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