## The Puzzling Ramanujan’s Magic Square

As you maybe know, a magic square is a square divided into smaller squares each containing a number, such that the figures in each vertical, horizontal, and diagonal row add up to the same value.

In this particular magic square by Ramanujan, fields of the same color add up to 139. The first row – highlighted in the bottom-right magic square – shows his date of birth.

A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?

This puzzle is available as greeting cards from my online store.

## Ghost Colors

This is one of my earliest color optical illusions. There is no yellow or green in the diamond shapes, just vertical black lines! (If you don’t believe it, use a eyedropper tool to check it.)

## Amazing Roman Rock-crystal Icosahedron Die

Here is an intriguing Roman crystal 20-sided die (icosahedron), used in fortune-telling, ca. 1st century AD.

## IXOHOXI Magic Square

The neat magic square featured on this stamp was created by Brazilian mathematician Inder Taneja. This square, called IXOHOXI magic square, not only shows common properties like other magic squares, as well as being pandiagonal, but also include extra properties such as symmetries, rotations and reflections.

## Impossible Structure

Perpetual Escher’s waterfall

## Smallest Prime Number Magic Square

American mathematician Harry L. Nelson won the challenge to produce a 3 × 3 magic square containing the smallest consecutive primes:

## Circles and Golden Ratio

The last digit of the numbers in the Fibonacci Sequence are cyclic, they form a pattern that repeats after every 60th number: 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1.