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″

### Sangaku: Semicircle inscribed in a right triangle

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

show solution

### 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:

### 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.