Hobbies
The Fields Medal
“Rise above oneself and grasp the world” These are awarded every four years for advancement in the field of mathematics. There is an age limit of 40 on the recipients. It is a recognition [more…]
Mathematics
Hobbies
Euler’s Totient Function
Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all . These numbers are called the totatives of . [more…]
Hobbies
Triangular, Square and Pronic Numbers
The triangle numbers are equal to the sum of the natural numbers from to . The sequence begins : So the sum to the tenth natural number is : The square numbers are equal to [more…]
Hobbies
The Plastic Number
The golden ratio is well known and is associated with the Fibonacci sequence of numbers. is the positive root of the quadratic equation . The exact value is given by Its continued fraction [more…]
Hobbies
0.999 … = 1
It really does. Many people have a problem accepting this equality. The ellipsis denotes that the nines continue forever; there is no last nine. Jen the Blue brought this up one night recently. I didn’t [more…]
Mathematics
A Hamiltonian Path in the Natural Numbers – from 1 to 15
We wish to arrange the natural numbers such that adjacent pairs of numbers sum to a square number. Why can we find a Hamiltonian path for some numbers and not others? For a Hamiltonian path, [more…]
Mathematics
Are We living in a Simulated Universe?
Firstly to have any understanding of this theory, one must admit the possibility of our universe existing within a Multiverse. “A multiverse (or meta-universe) is the hypothetical set of multiple possible universes (including our universe) [more…]
Hobbies
A Hamiltonian Path in the Natural Numbers
In graph theory, a graph is a mathematical structure. It has vertices and edges and we are interested in pairwise relationships. A Hamiltonian path is a walk that visits each vertex exactly once, as opposed [more…]
Mathematics
The Barnsley Fern
Michael Barnsley is an English mathematician born in 1946. The code developed by Barnsley is an example of an iterated function system. The code is composed of four affine transformations. of the code is the [more…]