# Math Induction HW

• 10-05-2003
axon
Math Induction HW
hey all,

I'm on my last problem and I'm stuck. I think it is just too late, but i desperately want to finish this today. Anyhow here is what it reads:

In any group of k people, k>=1, each person is to shake hands with every other person. Find a formula for the number of handshakes, and prove the formula using induction.

Once i get the formula the proof is cake, but the formula is driving me crazy, and it is probably very simple.

so here is what I have
Code:

```1 person = 0 shakes 2 people = 1 shake 3 people = 3 shakes P(4) = 6 P(5) = 10 P(6) = 15 ...and so on```
can anyone put me on the right track?

thanks,

axon
• 10-05-2003
axon
I finally found the formula so please disregard this post!

for all interested here it is: k( k -1 ) / 2 for k >=1

so simple!!!:o :o and it took an hour of my life
• 10-05-2003
Iamien
Damn i was alogn those lines workign on it, ah well shoulda given me another 5 minutes
• 10-06-2003
axon
thanks anyways: if you want I have one for extra credit, here goes:

A simple closed polygon consists of n points in the plane joined in pairs by n line segments: each point is the endpoint of exactly two line segments. Use the first and second principal of induction to prove that the sum of the interior angles of an n-sided closed polygon is ( n - 2 ) 180degrees for all n >= 3.

I'll work on this one now, until I'm too sleepy to do anymore.
• 10-06-2003
axon
well, this one was fairly simple...the proof below is using the second principal of induction:

Code:

```when k = 3, we have a triangle. Sum of all angles = 180° so for each n > 3, if P(k) is true for all k with  3 <= k < n, then P(n) is true. 180°(k-2) + 180°[(n-k+2)-2] = 180°(k-2) +180°(n-k)                                               = 180°[(k-2) + (n-k)]                                               = 180°(n-2)  => DONE```
basically you can divide each k-sided polygan with k-3 lines to form
triangles. Multiply the number of triangles by 180°....simple