Maximum intersections of Lines

M

mackdaddy

Junior Member
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Mar 6, 2013
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The other day, my math teacher was recapping on maximum intersection made by "n" lines. He reminded us that the formula for finding the maximum intersections is

n(n-1)/2.

In another thread I posted I talked with a member about the sum of all whole numbers from A to B. He showed a formula that gives you the sum of all whole numbers from 1 through n, like this

n(n+1)/2

I realized then that If you wanted to find the sum of all numbers from 1 to n-1 the formula was the exact same as the maximum intersections formula

n(n-1)/2

This means that given "n" lines the most intersections possible is n(n-1)/2 OR n-1 + n-2 + n-3...+1

I thought this was very interesting!
 
mackdaddy said:
The other day, my math teacher was recapping on maximum intersection made by "n" lines. He reminded us that the formula for finding the maximum intersections is

n(n-1)/2.

In another thread I posted I talked with a member about the sum of all whole numbers from A to B. He showed a formula that gives you the sum of all whole numbers from 1 through n, like this

n(n+1)/2

I realized then that If you wanted to find the sum of all numbers from 1 to n-1 the formula was the exact same as the maximum intersections formula

n(n-1)/2

This means that given "n" lines the most intersections possible is n(n-1)/2 OR n-1 + n-2 + n-3...+1

I thought this was very interesting!
Click to expand...
You have just learned that much of math is a series of interconnecting relationships: the same things keep coming up again and again. It is more than interesting: sometimes it is almost uncanny. Geometry and numbers are closely related.

Keep having fun with math.
 
Subhotosh Khan said:
However, remember slight difference between those two expressions:

Sum of first n natural numbers = n * (n+1)/2

Maximum number of intersections with n st. lines = n * (n-1)/2


If you get a chance, read the following book:

Mathematics: A Human Endeavor - Harold R. Jacobs
Click to expand...

yes but if you don't include "n" in the sum then the equation would be n(n-1)/2, and I'll try to read that book some time! thanks!
 
JeffM said:
You have just learned that much of math is a series of interconnecting relationships: the same things keep coming up again and again. It is more than interesting: sometimes it is almost uncanny. Geometry and numbers are closely related.

Keep having fun with math.
Click to expand...

Thanks and I will!
 
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