Any two polygons with equal area can be dissected into a finite number of pieces to form each other. Below are two neat minimal dissections of a dodecagon into a square.

## The Infinite Chocolate Bar

Although the principle of these kinds of “vanish puzzles” is really quite simple, they still confound countless numbers of puzzle enthusiasts!

**Related puzzles**

· The Area Paradox

· Math-Magic Vanishing Space

## Rolling Polygons

Imagine the wheels of your bike are polygons. Then, to ride smoothly the road should be made of ‘catenaries‘ (yes, those bumpy things).

It is the math professor Stan Wagon who first demonstrated this concept with a real square-wheel bike at Macalester College in St. Paul, Minnesota. Continue reading “Rolling Polygons”

## “Magic” Factorials

There are many fun facts regarding the factorials. For instance:

- 0! = 1 by convention. As weird as it may sound, this is a fact that we must remember.

- The number of zeroes at the end of
*n*! is roughly*n*/4. - 70! is the smallest factorial larger than a
.*googol* - The sum of the reciprocals of all factorials is
.*e* - Factorials can be extended to fractions, negative numbers and complex numbers by the
.*Gamma function*

It is possible to “peel” each layer off of a factorial and create a different factorial, as shown in the neat number pattern below. A prime pattern can be found when adding and subtracting factorials. Alternating adding and subtracting factorials, as shown in the picture, yields primes numbers until you get to 9! Continue reading ““Magic” Factorials”

## Haruki’s Theorem

Given 3 circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy: ace/bdf = 1

## Morley’s Trisector Theorem

In any triangle, the 3 points of intersection of the adjacent angle trisectors ALWAYS form an equilateral triangle (in blue), called the **Morley triangle**.

## Surprising Limit

Amazingly, this sequence of fractions converges to 0.70710678118…, or to be precise, to √2/2. The sequence is related to the Prouhet-Thue-Morse sequence.

## Prime Fractions

Did you know? You can write the number 1 as a sum of 48 different fractions, where every numerator is 1 and every denominator is a product of exactly two primes.

This problem is related to the Egyptian fractions.

## Mug to Doughnut

Showing why a doughnut and a mug are topologically equivalent…

## Very Large Numbers In Real Life

Most people know about Zimbabwe’s trillion dollar bill notes or have heard stories about Germans using worthless Marks during the Weimar Republic for wallpaper, but what few realize is that Hungary broke all the records. Just after the WWII, between 1945 and 1946, Hungary was in a state of hyperinflation, with inflation rates reaching **41.9 quintillion percent** (that is 41,900,000,000,000,000,000%). Continue reading “Very Large Numbers In Real Life”