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June 13th, 2018, 03:42 AM  #1 
Newbie Joined: Jun 2018 From: Groningen Posts: 14 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: 20,746 Thanks: 2133 
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: 6,763 Thanks: 697 
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: 2,321 Thanks: 714  Quote:  
June 14th, 2018, 06:25 PM  #5  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  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.  
June 21st, 2018, 08:04 AM  #6 
Newbie Joined: Jun 2018 From: Groningen Posts: 14 Thanks: 0  Further explanation of my problem
Hi, sorry for not being clear in the blogpost/introduction of the thread. But very much thanks for your responses either way! I hope I can make it a little more clear this way: Basically, I want to find out how you make a structure that expands evenly to all directions (like with the big bang). How did the universe expand from one point to a "spherical" filled structure? Example, suppose you stand at the origin of the axes (x,y,z) with a hosepipe turned on. How do you fill the area around you to the shape of a sphere? Fixing one end and move the other end wouldn't be allowed because that is only expansion towards one side. Drawing a circle and finding the center is also not allowed because, then you don't start at the center. But how do you do that? 
June 21st, 2018, 08:57 AM  #7 
Senior Member Joined: Aug 2012 Posts: 2,321 Thanks: 714  This is an interesting question. Perhaps some kind of spacefilling curve applied to a circle. It seems reasonable that there's a spherefilling curve.

August 9th, 2018, 12:35 AM  #8 
Newbie Joined: Jun 2018 From: Groningen Posts: 14 Thanks: 0 
Thanks for appreciating the question. With a spacefilling curve, would you mean a fractal like curve?


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