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*+
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 n is a number that is not congruent to 4 or 5 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
A clever visualization of a Cauchy Product.
Each black square has value 1, each red square has value -1.
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.
Math Ambigram
(by Peter Rowlett)
Solve this equation for x. Then rotate 180° and solve for x again.
The equation works either ways as 𝑥, 1, 8 and the unusual 5 have rotational symmetry. The same is true of +, =, and the horizontal line in a fraction.
“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”