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”

### A curious right triangle

The sides of a pentagon, hexagon, and decagon, inscribed in congruent circles, form a right triangle.

### Humor: Apple Pi

### The Arithmetic-Geometric Mean Inequality

A visual intuitive proof that **√ab** cannot be larger than **(a+b)/2**, where a, b ∈ R*+

### When a plane intersects a dodecahedron

A cross-section of the **dodecahedron** can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon.

### Target 10

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

### Pascal’s Theorem

### Math Humor

Mathematics is sometimes weird… Read more: The hole truth of topology.

### “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″