25
Nov
09

64 = 65 ?

while I was giving score for Final Project PTI  (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…

64 = 65 ?

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

 

Matematika merupakan hal yang sudah tidak aneh lagi di dunia ini. Bahkan anak kecil sekalipun sudah mengenal matematika, setidaknya dengan menghitung jumlah jari mereka sendiri, mereka menghitung berkali-kali yang jelas tujuan mereka bukan ingin mengetahui jumlah jari mereka. well, yang aku bahas di sini bukan soal matematika biasa, tapi menguak tentang soal sederhana yang di buat sulit: apakah 64=65?  terdengar konyol memang. tapi hal tersebut tergambar jelas di ilustrasi berikut:

64 = 65 ?

Nah, ilustrasi di atas seakan membuktikan bahwa 64=65. heum, it must be wrong. ada yang bisa memberi solusi?

kalo gambar diatas nggak jalan, coba: klik disini


4 Responses to “64 = 65 ?”


  1. January 12, 2009 at 10:17 pm

    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.😉

  2. 2 Lambertus Wahyu Hermawan
    January 16, 2009 at 9:33 am

    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.

  3. 3 hadi suyitno
    February 28, 2011 at 11:52 am

    zal, ndak sama itu hehehe. memang kelihatan gambare sama padahal tidak. kalau di hitung luas dari masing2 perpotongan bidang nya :

    Luas segitiga 1 : 1/2 * 8 * 3 = 12 satuan
    Luas segitiga 2 : 1/2 * 8 * 3 = 12 satuan
    Luas trapesium 1 : 20 satuan
    Luas trapesium 2 : 20 satuan

    Jadi total 64 satuan.
    Yang bikin animasinya hebat, bisa membuat bidang datar setelah dipotong dan digabung in lagi bentuknya bisa pas. padahal kalau kenyataan, pasti ada sedikit nggak pas nya. hehehe
    Menurut mu gmn ?^^


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struggling for whole happiness "Muhamad Rizal Avif Khan"
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