My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 13th, 2018, 03:42 AM   #1
Newbie
 
Joined: Jun 2018
From: Groningen

Posts: 12
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
justintimmer is offline  
 
June 14th, 2018, 02:13 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,712
Thanks: 1806

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.
skipjack is online now  
June 14th, 2018, 12:49 PM   #3
Global Moderator
 
Joined: May 2007

Posts: 6,610
Thanks: 616

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?
mathman is offline  
June 14th, 2018, 03:41 PM   #4
Senior Member
 
Joined: Aug 2012

Posts: 2,044
Thanks: 584

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.
Maschke is online now  
June 14th, 2018, 06:25 PM   #5
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,148
Thanks: 479

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.
JeffM1 is offline  
June 21st, 2018, 08:04 AM   #6
Newbie
 
Joined: Jun 2018
From: Groningen

Posts: 12
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?
justintimmer is offline  
June 21st, 2018, 08:57 AM   #7
Senior Member
 
Joined: Aug 2012

Posts: 2,044
Thanks: 584

Quote:
Originally Posted by justintimmer View Post
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.
This is an interesting question. Perhaps some kind of space-filling curve applied to a circle. It seems reasonable that there's a sphere-filling curve.
Maschke is online now  
August 9th, 2018, 12:35 AM   #8
Newbie
 
Joined: Jun 2018
From: Groningen

Posts: 12
Thanks: 0

Thanks for appreciating the question. With a space-filling curve, would you mean a fractal like curve?
justintimmer is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
central, directions, equal, lengths, lines, make, point



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Ratio of two central angle to the arc lengths of sides cmdahal Algebra 5 December 31st, 2012 09:19 AM
Help :: To find the central point hgphtgi Calculus 7 September 4th, 2012 09:24 AM
Find the point of intersection of the following lines: mathsm111 Algebra 3 July 3rd, 2011 10:40 AM
One point infinite amounts of lines g_litched Algebra 0 March 23rd, 2010 01:16 PM
Help :: To find the central point hgphtgi Linear Algebra 2 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.