while I was giving score for Final Project PTI 2008 (making website), I saw something interesting in Diar’s project (5208100060). something that make me keep thinking of it… it is an animation that simulate a strange theorem, 64 = 65.. check this out…
i almost think it is valid theorem, but i see something strange at lines of the final small squares. it seems that the lines is not exactly connected. but, i am sure there is a reason that explain it clearly.. Can you help me to explain about this phenomena? leave your comment please…
if the picture freeze and you can’t see the animation, click here…
You know that the area is 64 and that the sides of the other rectangle is 5 and 13 with 5*13 = 65. So there has to be a hole somewhere. This hole is probably hard to notice. Can you spot it?
Stop reading here if you find it on your own.
Check the green and blue part. They seem to be touching along the diagonal edge. But they actually touch only in the lower left corner. The diagonal edges have different gradients. One is 2/5 and the other one is 3/8. So, the hole is between the lower left corner and the upper right corner. The two triangles actually don’t touch at all. It just looks that way becase all the edges are thickly drawn.
You asked for it.
nah lo, aku sih setuju ae sama jawabane PIZER di atas. Tapi aku ga lihat sampe ke gradien-gradiennya.
Penjelasan pake bahasa sederhana:
Model pemotongan pada bidang tersebut berbeda. Aku lihat perbandingan di kedua gambar. Suatu kotak ketika dipotong dan dipasangkan lagi, aslinya pasangannya itu ga cocok. Jadi ada beberapa bagian yang dicuri kemudian dirangkaikan lagi secara diam-diam menjadi satu buah bidang yang luasnya sama seperti satu kotak.
Halah… Rizal bisa aja nemunya.