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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: 86,666

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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: 86,666

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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: 15,523

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: 86,666

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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: 86,666

Hi GeniusIsBack;

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,666

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,666

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,666

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,666

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,666

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,666

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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