A Super Factorial, Double Factorial, Hyper Factorial?!

Happy New Year everyone! You probably know what a factorial is. $$n!=n \left(n-1\right)\left(n-2\right)\left(n-3\right)\times3\times2\times1$$ Or, if you like calculus: $$x!=\int_{0}^{\infty} t^x{e^{-t}} dt$$ Like, for example, 8! = 8\(\times\) 7\(\times\)6\(\times\)5\(\times\)4\(\times\)3\(\times\)2\(\times\)1 = 40,320. However, what if we put two exclamation marks? Or a dollar sign? Well today, I am going to show you. Double Factorial The name comes… Continue reading A Super Factorial, Double Factorial, Hyper Factorial?!

Recamán Sequence

The Recamán Sequence might look like a jumble of numbers at first glance. But then it becomes clear. THE BIG PICTURE The 0th term is 0. To find the \(n\)th term, you usually subtract, \(a(n)-n\), however if that results in a negative number or a number already used in the sequence, you add, \(a(n)+n\). So… Continue reading Recamán Sequence

Erwin Schrödinger and the Half-Alive Cat

Austrian physicist Erwin Schrödinger is one of the founders of quantum mechanics. In 1935, he posed this problem: imagine you take a cat and place it in a sealed box along with a radioactive device that had a 50% chance of killing the cat. In an hour, is the cat dead or alive? What do you think?

Srinivasa Ramanujan, taxicabs, and nested radicals

Srinivasa Ramanujan Aiyangar (22 December 1887 – 26 April 1920) is a 20th century mathematician who lived during the British Raj. Today, we are going to talk about 3 numbers related to Ramanujan: 1729, 3, and -1/12. Let us start the blog with 1729. Ramanujan’s professor Godfrey Harold Hardy came to visit him in hospital… Continue reading Srinivasa Ramanujan, taxicabs, and nested radicals

A Piece of Pi

Hello mathematicians! Today we are going to talk about \(\pi\) (aka Pi).

The discoverer of Pi is also the man who famously sat in a bathtub and discovered that the water level went up when he got in to the tub. Archimedes of Syracuse (287 BC – 212 BC) was an Italian-Greek mathematician, and he had come up with an approximation for Pi. We know that \(\pi = \dfrac{\text{Circumference}}{\text{Diameter}}\), but to get Pi, we need to measure a curved surface (the circumference). But Archimedes thought of it another way: a circle is actually a regular polygon, but it has an infinite number of sides and every side is infinitely small. Hence, the circle looks round.