Math Is Fun Forum

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)

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

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

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...

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

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