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**circlemaker****Member**- Registered: 2011-04-03
- Posts: 20

r (radius) = any number

y (cosine) = any number between 0 and radius

tangent = √((r/y)²-1) or Math.sqrt(Math.pow(1/cos,2)-1) - I prefer computer speak

x (sine) = tangent x cosine

Say you want to make a circle with a radius of 100 on a computer. What you'd do is get every pixel on the y axis and find it's x value using the aforementioned algorithm, then draw a line to each point.

I made a function for html5 canvas that does this in quarter circles. It's optimized to not draw outside the screen boundary, though despite my efforts the built-in arc function is still more efficient. I suspect it takes some kind of shortcuts, though my method is certainly 'cleaner' as you can see with this comparison: http://www.perspectiveinfinity.com/images/arc-circle_root-circle_comparison.jpg

If your still interested here's the link where I talk about it in more detail: http://www.perspectiveinfinity.com/root_circle.html

And here's the actual function in case you wanted to use or analyze it: http://www.perspectiveinfinity.com/Scripts/rcf.js

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

Hi circlemaker;

Awesome! Thank you so much for doing this work and sharing it.

My Gallery of Math Art: benice equation

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

Now Try to Calculate a Sphere inside another Sphere!?

And Show the Image with the Outside Sphere Transparent So that it's Possible to See the Inner Sphere!?

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Hi GiB;

The software he is using may not do 3D yet.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

Who Said anything about 3D ?

You can Post an Image...That Looks like 3D But is in fact a Flat 2D Image!

ARBGenius.

*Last edited by ARBGenius (2012-02-07 03:28:59)*

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Hi GiB;

I think you did, when you said sphere. Take Geogebra for instance, just works in 2 dimensions.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

You can Post a Sphere Image...That Looks like 3D But is in fact a Flat 2D Image!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

then that's not a sphere,but it's orthogonal projection on a 2D plane

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

And the Image Looks like a Sphere!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Not unless you have software that can work with x,y,z coordinates.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

Stuff the Software!...Use the Tools & Methods you have a Hand!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Hi GeniusIsBack;

Okay, why don't you do it by hand and then post it.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

I Gave the Challenge! Any Takers!?...

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Yes you! Only you would have the courage and the genius for such a task.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

Thank you! Time Teaches... The Stubbornest!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

Respect Takes Time! The Sheep Find Their Way!...

ARBGenius.

*Last edited by ARBGenius (2012-02-07 23:32:15)*

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Hmmmm? So we are all sheep to the mighty GeniusIs Back?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

For You to Join the Other Sheep takes Extra Time!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

No, I was thinking about that picture you posted, you know the filthy one after you lost that argument about Houdini...

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

Never Ever! Lost an Argument to You!!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Then why did you post that picture and run away? It was just getting good...

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**ARBGenius****Banned**- Registered: 2012-02-06
- Posts: 22

You Remember Unimportant Things! SAD!!

ARBGenius.

Infinity...Is Between The Start!... & ... The End!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

I remember that you have been barred at least13 times under different names and for posting a lewd picture at me. For anti semitic and gay comments. For rudeness to many members. For calling people idiots and bad language. For defacing the forum. For picking offensive usernames.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**circlemaker****Member**- Registered: 2011-04-03
- Posts: 20

Aww too bad the thread went off-topic. Anyway I just stopped by to add that while people intuitively go from a circle to a sphere when thinking of 2D to 3D projections, this geometry is easier to project as a helix when going from 2D to 3D.

A sphere is a surface while a helix is still just a curve, so all that's required is to add a dimension and stretch the circle in the direction of the new dimension (in this case, z). This geometry matches that of a sine wave when viewed from a certain perspective: http://www.perspectiveinfinity.com/sinewave3d.html

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,723

Hi circlemaker;

My apology for what transpired in your thread. Normally I would clean it up but it had to be left for further review.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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