I need explanation (triangle)...

[moje_ime]

I am not quite good in mathematics, but it makes me confused.

How is that possible

w ww.twisty.com/misc/puzzles/triangle/bizarre.gif

[IDMclean]

It's pythagorean theorm. The thing is an optical illusion. the whole appears because it's not a true triangle.

[Jay-qu]

what do you mean its not a true triangle? It has three sides, a perimeter and an area, then with the same dimensions below the area has a hole in it..

[Tim_Lou]

i remember there was a similar post some long long time ago..

 

anyway, notice how the slope of the green and red triangles are NOT equal, they cannot possibly form a big triangle like that.

[Jay-qu]

right you are, the ratio of the lengths of the two triangle are: red - 3:8 blue - 2:5 ie they wont have the same sloping angle.

[CraigD]

what do you mean its not a true triangle? It has three sides, a perimeter and an area, then with the same dimensions below the area has a hole in it..

Try actually measuring the pieces as shown in the 2 drawings. You’ll discover that they’re not actually the same. They’re close enough to fool your eye, but if you were to print the page and cut out the pieces from one diagram, you wouldn’t be able to arrange them as shown in the other.

[Qfwfq]

It's a very old trick, the first time I saw it was in a Martin Gardiner book. It was around '83 I saw it and I imagine it had been published quite a time before then, in his Mathematical Games columns in Scientific American.

 

It just goes to show that you can't rely on appearance in an argument for geometry. Sheesh, Galileo made a delightful blunder in his dialogue, by considering a "manifest equality" between curved lines, he missed the idea of explaining the planetary orbits by the skin of his teeth!

:hihi: