A community for students.
Here's the question you clicked on:
 0 viewing
Ishaan94
 2 years ago
Whom of you can explain it to me?
http://jeremykun.files.wordpress.com/2011/06/triangleproof.png
Ishaan94
 2 years ago
Whom of you can explain it to me? http://jeremykun.files.wordpress.com/2011/06/triangleproof.png

This Question is Closed

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0http://mathoverflow.net/questions/8846/proofswithoutwords/69756#69756

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0If it's fairly easy and you think I am not pushing myself please do tell me, instead of giving out the answer.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3@Ishaan94  do you know how to get the sum of all the components in the last triangle?

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0Is it like this? (2n+1)+2(2n+1)+3(2n+1)+...+n(2n+1)

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3exactly  now factor out the (2n+1)

hosiduy
 2 years ago
Best ResponseYou've already chosen the best response.0i think like this way: i will assume that this is true until line n+1 (go downward from first line), i have: first line is true, 1+n+n = 2n + 1. so with line: n+1 we have: (n+1) + ... (n+1) at first triangle, at second triangle, we have: 1+ 2 + ... + n+ n+1, and at third: n+1 + n + ... + 1, sum last line, we still get: 2(n+1) + 1 + .... 2(n+1) + 1

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{n\left(n+1\right) \left(2n+1\right)}2\]What about the six?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3that is correct  now you have to subtract the sum of the previous 2 triangles from this

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3what you are trying to find is the sum of the numbers in the 1st triangle

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3that should have started with \(1^2\)

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3it is a visual proof of this sum

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3It's an interesting proof  I suggest you try and do it yourself  you'll have greater pleasure from that :)

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0thanks, i will try my best.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3let me know if you require a clue.

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3when you do "see" how to do it  it is quite remarkable!

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3@Ishaan94  try turning your head as you view the triangles on the left...

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3this really is a "visual" solution  so don't think about any complex math here

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0OMG this is the best proof I have seen in my life so far

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3:) glad you "saw" it at last!

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.3it is a very pleasing proof

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.0it is. and thanks a lot asnaseer. :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.