Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Ishaan94
Group Title
Whom of you can explain it to me?
http://jeremykun.files.wordpress.com/2011/06/triangleproof.png
 2 years ago
 2 years ago
Ishaan94 Group Title
Whom of you can explain it to me? http://jeremykun.files.wordpress.com/2011/06/triangleproof.png
 2 years ago
 2 years ago

This Question is Closed

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

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

asnaseer Group TitleBest ResponseYou've already chosen the best response.3
BTW: Nice site.
 2 years ago

asnaseer Group TitleBest 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?
 2 years ago

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

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

hosiduy Group TitleBest ResponseYou've already chosen the best response.0
i 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
 2 years ago

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

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

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

asnaseer Group TitleBest ResponseYou've already chosen the best response.3
\[1^1+2^2+3^3+...\]
 2 years ago

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

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

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
oh I see it
 2 years ago

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

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

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

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

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

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

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

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

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

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
it is. and thanks a lot asnaseer. :)
 2 years ago

rational Group TitleBest ResponseYou've already chosen the best response.0
really beautiful xD
 3 months ago
See more questions >>>
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.