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 September 6th, 2017, 10:13 AM #1 Newbie   Joined: Sep 2017 From: Usa Posts: 4 Thanks: 0 (People and Relationships) Can You Find The Equation? I discovered something cool about points and lines, wondering anyone else knew about this. I call it people and relationships, point=people and line=relationship There is 1 relationship between every 2 people. Here is the table: # people - # relationship 0-0 1-0 2-1 3-3 4-6 5-10 Take a look at this picture (Click) There is an obvious pattern in the table. See if you spot it. And see if you can find out the whole equation.
 September 6th, 2017, 10:48 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 The sum of the numbers in each row is the second number in the next row. Is that what you mean? The "whole equation" for what in terms of what?
September 6th, 2017, 11:50 AM   #3
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Quote:
 Originally Posted by skipjack The sum of the numbers in each row is the second number in the next row. Is that what you mean? The "whole equation" for what in terms of what?
Yeah you spotted the pattern. But can you make up an equation for this pattern?

# people = x
# relationship = y

Example equation
y=4(x)²+5

Last edited by Logix; September 6th, 2017 at 12:22 PM.

 September 6th, 2017, 01:44 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 $\displaystyle y = \binom{x}{2}$
 September 6th, 2017, 02:02 PM #5 Newbie   Joined: Sep 2017 From: Usa Posts: 4 Thanks: 0 Check your equations by substituting the numbers on my table into your equation. Hint: if you graph the table, it would look like a quadratic equation. Last edited by Logix; September 6th, 2017 at 02:04 PM.
 September 6th, 2017, 02:57 PM #6 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 For example, $\displaystyle \binom52 = 5(4)/2 = 10$.
September 6th, 2017, 03:23 PM   #7
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Quote:
 Originally Posted by skipjack For example, $\displaystyle \binom52 = 5(4)/2 = 10$.
5 on top of 2, I have no idea about that. But well, you found the equation.

September 6th, 2017, 04:32 PM   #8
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Quote:
 Originally Posted by Logix 5 on top of 2, I have no idea about that. But well, you found the equation.
That is combination of 2 people out of 5 people i.e. number of ways 2 people can be combined when we have 5 people to choose from.

$\displaystyle \binom {n}{x} = \frac {n!}{(n-x)!x!}$

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