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June 13th, 2018, 03:42 AM   #1
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How can I make lines of equal lengths to all directions from a central point?

I made a problem in my mind that I can't seem to solve. I need an answer because it is quite fundamental to me, because it is about the expansion of things like the universe. This is the problem; I can't understand how to make lines of equal lengths to all directions from a central point. I wrote a blogpost on my website to explain the thoughts and methods I have tried. Could someone please help me?

How can I make lines of equal lengths to all directions from a central point? JUSTIN TIMMER
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June 14th, 2018, 02:13 AM   #2
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Start my making one line of the required length, then fix one end of it and allow the other end to move freely while the (moving) line is kept straight.
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June 14th, 2018, 12:49 PM   #3
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In two dimensions draw a circle and three dimensions a sphere, centered at the point in question. In both cases radii are the lines you want. This sounds too simple, so what am I missing?
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June 14th, 2018, 03:41 PM   #4
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Oh I see. You want to study computer graphics. How you make smooth-looking circles, how you determine if a point is inside or outside of a region, etc. You're looking for an algorithm for drawing a circle or a sphere. Computer graphics has solved all these problems.
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June 14th, 2018, 06:25 PM   #5
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Quote:
Originally Posted by justintimmer View Post
I made a problem in my mind that I can't seem to solve. I need an answer because it is quite fundamental to me, because it is about the expansion of things like the universe. This is the problem; I can't understand how to make lines of equal lengths to all directions from a central point. I wrote a blogpost on my website to explain the thoughts and methods I have tried. Could someone please help me?

How can I make lines of equal lengths to all directions from a central point? � JUSTIN TIMMER
I have no idea what that linked site is supposed to mean. But you seem to be asking a question in basic trigonometry.

In two dimensions, using a reference angle $\theta$ relative to the x-axis in degrees and a length a from the origin when $\theta = 0$:

$\sin( \theta ) = \dfrac{y}{a} \implies y = a * \sin ( \theta ); \text { and}$

$\cos ( \theta ) = \dfrac{x}{a} \implies x = a * \cos ( \theta ).$

That gives you the x and y co-ordinates of the end points of lines drawn from the origin with length a at various angles to the x-axis. Be sure to use sine and cosine functions in degrees. I do not want to explain radians.

Last edited by skipjack; June 15th, 2018 at 06:10 AM.
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