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

show solution

### Cauchy Product

### 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:

### Fibonacci Spiral Jigsaw Puzzle

Each piece of this puzzle is similar (the same shape at a different size). The placement of the pieces is based on the golden angle (≈137.5º), and results in a pattern frequently found in nature (phyllotaxis), for instance on sunflowers. The puzzle features 8 spirals in one direction, and 13 in the other. You can build your own Fibonacci spiral puzzle by following John Edmark’s tutorial.

### 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.

### Illusive Number

If you can see the 8 in the middle of the 8 of diamonds you are a visual thinker rather than a verbal thinker.

### 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”

### NEW! “Illusion d’Optique” Magic Playing Cards

**Limited Signed Edition (less than 100 samples)**

For Art, Math and Magic Lovers!

For Art, Math and Magic Lovers!

Order now your exclusive “Illusion d’Optique” playing card deck designed by puzzle master Gianni A. Sarcone!

Packaging printed with optical ink and placed in a protective transparent plastic case.

Inside, you’ll find **54 eye-popping original optical illusions**. Watch closely as colors change, shapes transform and static, printed ink seems to come alive. Sarcone has included updated versions of classic illusions, plus innovative new concepts he developed after years of study. “Illusion d’Optique” is not only a beautiful deck, but it also serves as fascinating proof that seeing is not necessarily believing. Continue reading “NEW! “Illusion d’Optique” Magic Playing Cards”