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”

“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

Morley’s Trisector Theorem

In any triangle, the 3 points of intersection of the adjacent angle trisectors ALWAYS form an equilateral triangle (in blue), called the Morley triangle.

Prime Fractions

Did you know? You can write the number 1 as a sum of 48 different fractions, where every numerator is 1 and every denominator is a product of exactly two primes.

This problem is related to the Egyptian fractions.

Math-Magic Vanishing Space

Inspired from the astrological tables, here is a new puzzle of my creation designed according to the ‘Golden Number Rules’, which is reflected in the proportion of each single piece of the game. Thanks to the balanced dimensions of its pieces, this puzzle acquires some intriguing magical properties!

This “math-magical” puzzle is composed of a tray in which the pieces are assembled.

Sum of Infinite Power Series

Have a look at the two distinct sums of series of powers below.

Same procedure, different result accuracy levels… Can you guess what went wrong in the operation of fig. 2?