## Magic Inscribed Lotus

Indian mathematician Nārāyaṇa (1356) is the originator of the “Inscribed Lotus” (Padma Vrtta, a magic diagram constructed with the numbers of the 12×4 magic rectangle), in which every group of 12 numbers has the same sum 294. Continue reading “Magic Inscribed Lotus”

A strange right-triangle involving the unit imaginary number i ## Four Constants in Four 4’s

The infamous problem of representing numbers with four 4’s appeared for the first time in 1881 in a London science journal. In 2001, a team of mathematicians from Harvey Mudd College found that we can even get four 4’s to approximate four notable constants: the number e, π, acceleration of gravity, and Avogadro’s number. ## Math Hack of the Day: 66 + 99 = ?

Maths à la De Funès… ## Life, the Universe, and Maths

For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1 to 100. This theory is true in all cases except for an unproven exception: 42.

By 2016 and over a million hours of computation later, researchers of the UK’s Advanced Computing Research Center had its solution for 42. More intriguing number facts here.

## Prime Square

3,139,971,973,786,634,711,391,448,651,577,269,485,891,759,419,122,938,744,591,877,656,925,789,747,974,914,319,422,889,611,373,939,731 produces reversible primes in each row, column and diagonal when distributed in a 10×10 square.
Diagram by HT Jens Kruse Andersen. ## Mirror Squares

10² = 100 <-> 001 = 01²
11²  = 121  <->  121 = 11²
12² = 144 <-> 441 = 21²
13² = 169 <-> 961 = 31²

## Inverse Powers of Phi

Summation of Alternating Inverse Powers of Phi… ## The Kepler Triangle, Phi and Pi

A “Kepler triangle” is a right triangle having edge lengths in a geometric progression, in which the common ratio is √ϕ, where ϕ represents the golden ratio.
Well, let’s construct a square with side length √ϕ that inscribes a Kepler triangle, that is, a right triangle with edges 1 : √ϕ : ϕ (or approximately 1 : 1.272 : 1.618), as shown in the picture. Draw then the circumcircle of the Kepler triangle (highlighted in orange in the picture) whose diameter is the hypotenuse of the triangle.
Then, the perimeters of the square (4√ϕ≈5.0884) and the circle (πϕ≈5.083) coincide up to an error less than 0.1%. From this, we can get the approximation coincidence π≈4/√ϕ ## Fibonacci Right Triangle

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. 