Math Is Fun Forum

circlemaker

Member

Registered: 2011-04-03

Posts: 20

The Squarcle

What's a squarcle?  Why it's a circle and a square, at the same time!  It also appears to be a 3d rotating sine wave.

http://perspectiveinfinity.com/squarcle.html

PS. It's pretty lame that I can't post a proper link.  It worked the last time I was here.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Squarcle

Hi circlemaker;

I have edited your post to turn that into a link.

Nice site, offhand about that Squarcle, I have no idea what that is.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

circlemaker

Member

Registered: 2011-04-03

Posts: 20

Re: The Squarcle

Hi bobbym,

Thanks for posting a link.

The squarcle is just a fun name for it. It's a sine wave projected into 3 dimensions.  As it rotates it looks like a circle from one perspective and a square from another.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Squarcle

Hi;

Your prime hexagon. Back in the old days we used that fact to generate primes quicker. We would use numbers of the form 6n + 1 and 6n - 1 for n =1,2,3,4... This was faster than trying every odd number.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

circlemaker

Member

Registered: 2011-04-03

Posts: 20

Re: The Squarcle

Hi;

Your prime hexagon. Back in the old days we used that fact to generate primes quicker. We would use numbers of the form 6n + 1 and 6n - 1 for n =1,2,3,4... This was faster than trying every odd number.

That's cool.  So the idea has been around for a while then?  I can't say I'm surprised given the simplicity of it.

My isolation from academia means I tend to rediscover stuff.  It's fun and frustrating at the same time.  There is something to be said for reinventing the wheel though.  Sometimes possibilities are missed the first time.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Squarcle

My isolation from academia means I tend to rediscover stuff.  It's fun and frustrating at the same time.  There is something to be said for reinventing the wheel though.

Nothing wrong with rediscovering things. Your way actually makes the idea clear. I only knew it as a fact, I did not know why.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

circlemaker

Member

Registered: 2011-04-03

Posts: 20

Re: The Squarcle

I made another, simpler version of the squarcle that perhaps lends better to it's name:
perspectiveinfinity.com/squarcle2.html

Note that when sine and cosine are matched (1/2sqrt) and tangent is 1, the guide vectors form a tetrahedron.  Cool stuff.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Squarcle

Hi circlemaker;

I edited your post to turn that into a link.

Yes, that is nice!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: The Squarcle

Cool, thanks circlemaker!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman