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June 13th, 2018, 03:42 AM  #1 
Newbie Joined: Jun 2018 From: Groningen Posts: 3 Thanks: 0  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 
June 14th, 2018, 02:13 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,056 Thanks: 1618 
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.

June 14th, 2018, 12:49 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,526 Thanks: 588 
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?

June 14th, 2018, 03:41 PM  #4  
Senior Member Joined: Aug 2012 Posts: 1,919 Thanks: 533  Quote:  
June 14th, 2018, 06:25 PM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,038 Thanks: 423  Quote:
In two dimensions, using a reference angle $\theta$ relative to the xaxis 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 coordinates of the end points of lines drawn from the origin with length a at various angles to the xaxis. 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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