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.

## Pascal’s Theorem

## “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″

## Cauchy Product

## 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:

## Circles and Golden Ratio

The last digit of the numbers in the Fibonacci Sequence are cyclic, they form a pattern that repeats after every 60th number: 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1.

## 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.