flynn017

I thought I would wrote a small article on some numbers which I find interesting, I may expand upon this topic in the future, but for this article I'm going to restrict myself to three forms of number: Kaprekar's Constant, Polygonal Numbers and Highly Composite Numbers. Kaprekar's Constant:  Kaprekar's Constant is a special constant discovered by the Indian Mathematician called D.R.Kaprekar. The constant has the value of 6174. The constant comes from a simple algorithm known as Kaprekar's Routine. The constant can be produced from at most 7 iterations. Kaprekar's Constant will always be produced after iterating through Kaprekar's Routine, when given an arbitrary 4 digit integer, providing that at least two of the digits are different otherwise the constant will not be produced. For example, using 3524 from Wikipedia (since the number of steps is knowingly small), arrange the number in descending order and then ascending order. Subtract these two numbers, and...

As with Bull Graphs, House Graphs are simple graphs (not the Graph Theoretic definition) which have been neglected. They may not be interesting or yield any important findings to professional research mathematicians, but I haven't been able to find a paper or website which lists or shows any of the House Graphs properly at all. My intention is simply to state and prove of these properties. Please note I'm not a professional mathematician and I'm not even studying for a Mathematics degree (Computer Science), and therefore may make mistakes or misunderstandings. There are two main variants of House Graphs, and in this article I will listing the Vertex Colouring and Edge Colouring properties of such graphs. The two graphs are the House Graph and the House-X Graph. House Graph House-X Graph Both of the graphs are simple graphs, and the same number of vertices. In terms of the structure of the graph, the only difference between the graphs are the number of edges. The number edge...