## “Stubborn” Number 33

It is conjectured that n is a sum of 3 cubes if n is a number that is not congruent to 4 or 5 mod 9. The number 33 enters this category, but for 64 years no solutions emerged — that is, whether the equation 33 = x³ + y³ + z³ has an integer solution. Continue reading ““Stubborn” Number 33″

## Sangaku: Semicircle inscribed in a right triangle

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

show solution

## 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.

## 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.

## 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”

## Limited Signed Edition (less than 100 samples) 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”

## 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.

## 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?