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”

### 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?

### Intriguing Geometric Dissections

Any two polygons with equal area can be dissected into a finite number of pieces to form each other. One of the most interesting dissection or geometric *equidecomposition* puzzles is that discovered by Harry Lindgren in 1951 (see Fig. 2 further below). As you know, in this kind of puzzles, the *geometric invariant* is the area, since when a polygon is cut and its pieces are distributed differently, the overall area doesn’t change.

Lindgren was the first to discover how to cut a dodecagon into a minimal number of pieces that could pave a square, when rearranged differently. His solution is very elegant, he first built a regular Euclidean pavement by cutting a dodecagon as shown in fig. 1.a, then arranging the four pieces symmetrically on the plane (fig 1.b). The tessellation achieved with these pieces corresponds, by superposition, to a regular paving of squares. The example in fig. 2 shows how the puzzle appears once finished.

### 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

### Rolling Polygons

Imagine the wheels of your bike are polygons. Then, to ride smoothly the road should be made of ‘catenaries‘ (yes, those bumpy things).

It is the math professor Stan Wagon who first demonstrated this concept with a real square-wheel bike at Macalester College in St. Paul, Minnesota. Continue reading “Rolling Polygons”

### Linear to rotational motion

Intriguing linear motion perceived as circular motion! Watch as the black balls rotate in a circle, then focus on one ball at a time and you will notice that it follows a straight line. Also, watch at the moment when there are only four balls moving, it forms a rotating square between the four balls. This is just neat example of looking deeper into something so simple and discovering a hidden pattern.

**More**

Pattern with Arabesque paths moving in a linear fashion induces rotational motion to a hexagonal device.

### “Magic” Factorials

There are many fun facts regarding the factorials. For instance:

- 0! = 1 by convention. As weird as it may sound, this is a fact that we must remember.

- The number of zeroes at the end of
*n*! is roughly*n*/4. - 70! is the smallest factorial larger than a
.*googol* - The sum of the reciprocals of all factorials is
.*e* - Factorials can be extended to fractions, negative numbers and complex numbers by the
.*Gamma function*

It is possible to “peel” each layer off of a factorial and create a different factorial, as shown in the neat number pattern below. A prime pattern can be found when adding and subtracting factorials. Alternating adding and subtracting factorials, as shown in the picture, yields primes numbers until you get to 9! Continue reading ““Magic” Factorials”

### Haruki’s Theorem

Given 3 circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy: ace/bdf = 1