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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

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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
 4 months ago
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