Math Interesting Geometry Problem

[fireballs619]

Just to tie up loose ends here, I have the generalization.

[math]\frac{b\sqrt{a^2+b^2}}{a}[/math]

This is only true where:

[math]a>b[/math]

I think that's about as much math that we can suck from that problem :lol:

 

[ex-orbinaut]

I'm afraid I don't follow. Where does this 3x5 triangle come from that you are referring to? Do you mean a triangle of side lengths 3 and 5, because I don't see how you could get that from folding the note card.

No, it was is the ratios of the triangle that interested me, not the actual dimensions. You said fold as in drawing 1 (see diagram). I say folding from corner to corner will inevitably create a triangle of the same ratio, ie, 3 x 5 (please note the blue line that makes your crease into a triangle).

Angle b in triangle 2 is going to be the same as angle a (from the blue line to the crease). That blue line happens to be the adjacent to the angle (31º) of your new triangle, and that base is 3 units long. It would be the same process if you did it for a sheet of A4 paper.

8.27 x 11.69

8.27 / Cos(Atan(8.27 / 11.69)) = 10.13

Never mind that the angle for a sheet of A4 is 35.277º, it still works. It was a very simple problem, really.

 

[C3PO]

I don't think we can get it any simpler now.:lol:

[math]Crease=\frac{3}{5}\sqrt{5^2+3^2}[/math]

"Are we there yet?"