If you're reading this and don't have any idea what the title means, look back on our page and give it a try!

At first glance, it seems like maths has broken. The two big triangles have the same dimensions - 13 wide and 5 tall - and every other shape hasn't changed shape. If you draw it on your own piece of paper, everything looks the same! So what's wrong?

The problem was the assumption in our second sentence. The two triangles aren't triangles. Look very, very, very carefully. The longest, diagonal sides aren't straight lines; the red and blue triangles should have the same slope for the long diagonal side to be a straight line, but they don't - the red one has a slope of 2/5 = 0.4, while the blue one has a slope of 3/8 = 0.375.

What does this have to do with the missing square? Look really carefully at the longest sides. In the top "triangle", the slopes get steeper, so the total area is slightly less than the area of the triangle (5 by 13) that you expected. Don't believe me? Here's an accurate diagram:

The pink line at the top is the diagonal side that you would expect for a real 5 by 13 right angled triangle

Finally, in the second triangle, the diagonal side bulges slightly, so the area of the triangle is slightly greater than the triangle you expected. So where did the missing square go? It went into that tiny extra bulge on the diagonal side of the triangle. If you don't believe me, do the calculations!

BC