The key to the puzzle is the fact that neither of the 13×5 “triangles” is truly a triangle, because what would be the hypotenuse is bent. In other words, the hypotenuse does not maintain a consistent slope, even though it may appear that way to the human eye. A true 13 × 5 triangle cannot be created from the given component parts.

Missing square puzzle.svg

The four figures (the yellow, red, blue and green shapes) total 32 units of area, but the triangles are 13 wide and 5 tall, so it seems, that the area should be S=\frac{13\cdot5}{2}=32.5 units. But the blue triangle has a ratio of 5:2 (=2.5:1), while the red triangle has the ratio 8:3 (≈2.667:1), and these are not the same ratio. So the apparent combined hypotenuse in each figure is actually bent.

The amount of bending is around 1/28th of a unit (1.245364267°), which is difficult to see on the diagram of this puzzle. Note the grid point where the red and blue hypotenuses meet, and compare it to the same point on the other figure; the edge is slightly over or under the mark. Overlaying the hypotenuses from both figures results in a very thin parallelogram with the area of exactly one grid square, the same area “missing” from the second figure.

According to Martin Gardner,[1]the puzzle was invented by a New York City amateur magician Paul Curry in 1953. The principle of a dissection paradox has however been known since the 1860s.

The integer dimensions of the parts of the puzzle (2, 3, 5, 8, 13) are successive Fibonacci numbers. Many other geometric dissection puzzles are based on a few simple properties of the famous Fibonacci sequence


Welcome to my blog. My name is Nico. Admin of this blog. I am a student majoring in mathematics who dreams of becoming a professor of mathematics. I live in Kwadungan, Ngawi, East Java. Hopefully in all the posts I can make a good learning material to the intellectual life of the nation. After the read, leave a comment. I always accept criticism suggestion to build a better me again .. Thanks for visiting .. : mrgreen:

Posted on August 16, 2011, in ALAT PERAGA and tagged , , , , . Bookmark the permalink. 8 Comments.

  1. wah jadi inget jaman SMA nihblom pernah baca blog ttg math … salut saja, pasti yg punya blog ini pinter orgnya 🙂

  2. udah sering banget liat yang ini..
    tapi ga pernah sekalipun ketemu pemecahannya..

    • coba kamu hitung nilai gradien dari sisi miring segitiga warna merah dan biru. hasilnya tidak sama. karena tidak sama gradiennya, maka kedua sisi miring itu tidak segaris. jadi itu sebenarnya bukan segitiga. tetapi segiempat dengan satu titik sudut tumpul yang mendekati 180 derajat.

  3. masalah slope kayaknya ini, kemiringannya tidak sama..

  4. Missing impossible nih, pusiiiingg…

  1. Pingback: daftar isi « matematika blog for education


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