Did you know?
In 1915, Danish psychologist Edgar Rubin wrote about a famous picture. You can see a white vase, or two dark faces looking at each other, but never both at the same moment! Your brain keeps switching.
The 'impossible triangle' looks like a solid 3D shape, but it could never be built. Swedish artist Oscar Reutersvärd first drew it in 1934. A sculpture in East Perth, Australia, looks just like it when seen from the right angle!
Only three regular shapes can cover a floor all by themselves, with no gaps or overlaps: equilateral triangles, squares and regular hexagons. Six triangles, four squares or three hexagons fit exactly around each corner point.
Try this: Hidden Squares Hunt
Draw a big square and divide it into a 3 × 3 grid of 9 small squares, like a noughts-and-crosses board with a border. How many squares can you find in it altogether? Don't forget squares made of 2 × 2 small squares, and the big square itself!
Show answer
14. There are 9 small squares, 4 medium squares and 1 big square.
Go further: Why Pentagons Don't Fit
Each corner of a square is 90 degrees. Four squares meet at a point: 4 × 90 = 360 degrees, a full turn, so they fit snugly. Each corner of a regular pentagon is 108 degrees. Three pentagons make 324 degrees, leaving a gap, while four make 432 degrees and overlap! The Dutch artist M. C. Escher loved tilings and turned them into interlocking birds, fish and reptiles. Try designing one of your own!