Consider the following simple progression of whole and fractional numbers (with odd denominators):

1 1/3, 2 2/5, 3 3/7, 4 4/9, 5 5/11, 6 6/13, 7 7/15, 8 8/17, 9 9/19, …

Any term of this progression can produce a Pythagorean triplet, for instance:

4 4/9 = 40/9; the numbers 40 and 9 are the sides of a right triangle, and the hypotenuse is one greater than the largest side (40 + 1 = 41).

## Golden Ratio (And Its Inverse) In Yin Yang

The philosophy of the Yin Yang is depicted by the The “taichi symbol” (*taijitu*). In fact, Yin Yang is a concept of dualism, describing how seemingly opposite or contrary forces may actually be complementary,

Curiously enough, in the taichi symbol are hidden the golden ratio and its reverse. As shown in the picture. Continue reading “Golden Ratio (And Its Inverse) In Yin Yang”

## Target 10

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

## “Stubborn” Number 33

It is conjectured that ** n** is a sum of 3 cubes if

**is a number that is not congruent to 4 or 5**

*n**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”

## 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”