Here is a little puzzle of our creation you can make with your kids or in class…

## Pascal’s Theorem

## Sangaku: Semicircle inscribed in a right triangle

Find the radius* r* of the semicircle inscribed in the right triangle below:

show solution

## Cauchy Product

## 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.

## Math Ambigram

(by Peter Rowlett)

Solve this equation for x. Then rotate 180° and solve for x again.

The equation works either ways as 𝑥, 1, 8 and the unusual 5 have rotational symmetry. The same is true of +, =, and the horizontal line in a fraction.

## Transform a Ball with 2 Holes into a CD

Topology is a fascinating branch of mathematics that describes the properties of an object that remain unchanged under “smooth” deformations. If we imagine objects to be made of clay, a smooth deformation is any deformation that does not require the discontinuous action of a tear or the punching of a hole, such as bending, squeezing and shaping. These deformations are called “continuous deformations“. Continue reading “Transform a Ball with 2 Holes into a CD”

## Is seeing believing? This book will prove the contrary

##### We really enjoy communicate the mysteries behind the science of perception in a simple and clear manner with the use of instructive images.

We live in a “*reallusive*” world… Illusions are not totally unreal, because we feel them as they were real. Reality is also a kind of ‘illusion’. The outside world is mediated through our sense organs: vision, hearing, taste, touch and smell. All what we perceive and feel are just REPRESENTATIONS of reality, not the reality itself.

Children have a different way of looking at the world. So, writing and illustrating optical illusion books for kids is not an easy task, because they are less fooled by visual illusions than adults. This is due to the fact that brain’s capacity to consider the CONTEXT of visual scenes, and not just focus on SINGLE PARTS of scenes, develops very slowly.

“**Optical Illusions**” will make you question: “is seeing believing?”… The brain is an amazing thing, but it doesn’t always get things right when it comes to sight. My book is here to explain why, with astounding images, baffling puzzles, and simple reveals. Continue reading “Is seeing believing? This book will prove the contrary”

## Möbius Curiosities

An intriguing Möbius maze created by Dave Phillips. Did you notice that the arrows, which should indicate the direction to follow, are wrongly placed?

## The Infinite Chocolate Bar

Although the principle of these kinds of “vanish puzzles” is really quite simple, they still confound countless numbers of puzzle enthusiasts!

**Related puzzles**

· The Area Paradox

· Math-Magic Vanishing Space