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#1 2008-04-29 06:19:54

Dragonshade
Member
Registered: 2008-01-16
Posts: 147

Folding book

I was bored and started folding my book idly

then I started to think what's the sum of the triagles if I fold it like this

Then I started to find the sum


How do I finish it
The sum should be covergent

Last edited by Dragonshade (2008-04-29 06:26:32)

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#2 2008-04-29 07:13:16

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Folding book

I don't get everything you wrote, but I noticed that the 1st
fold is based off of 2 opposite corners, but the folds after
that probably are cutting the remaining angles in half.
So when I folded it, A1 folded 1st, then A3, then the A2.
Sort of like on a ruler, 1/2's the quarters, the eighths,
the sixteens, etc...


igloo myrtilles fourmis

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#3 2008-04-29 08:07:31

Dragonshade
Member
Registered: 2008-01-16
Posts: 147

Re: Folding book

John E. Franklin wrote:

I don't get everything you wrote, but I noticed that the 1st
fold is based off of 2 opposite corners, but the folds after
that probably are cutting the remaining angles in half.
So when I folded it, A1 folded 1st, then A3, then the A2.
Sort of like on a ruler, 1/2's the quarters, the eighths,
the sixteens, etc...

for example, The right triangle C_1 A_2 B is what I got when I folded the second page, making the DB of the second page lie on the A_1B,     then I continue to fold the third page,  I will get another right triangle C_2 A_3 B,  the DB of the third page lies on A_2B..... I could fold infite right triangle in this way, I want to get the sum of these triangles

my apology if I am not clear enough

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#4 2008-04-29 08:20:37

Dragonshade
Member
Registered: 2008-01-16
Posts: 147

Re: Folding book

Oh, I overlooked something, I could find a formula for  sequence z_i , ok, problem solved, tons of calculation indeed

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