Fractals are a new 21st century mathematics. They are patterns that repeat themselves at various scales. This one is based on the odd numbers in Pascal’s triangle. We learn to create it easily by using Conditional Formatting which enables us to color cells or text based on a quantitative relationship. To turn Pascal’s triangle into a Sierpinski fractal all we have to do is color cells that are odd numbers. Here again is an amazing pattern involving odds and evens. There are a wide number of other Sierpinski fractal patterns.
Tag: Pascal’s triangle
Normal Distribution
Most museums with math exhibits have a Pascal’s triangle made up of pegs with balls falling down between them and bouncing off of them. One of the things they want to show is probability and the Normal or Bell curve produced by these balls as they fall down most of us are familiar with. This is the curve produced if we flip a honest coin a large number of times and ask what are the chances of getting all heads, of all heads but one and one tail, of getting all but 2 heads etc. We ask what does a Normal distribution look like and why does this extremely simple pattern produce it?
Pascal’s Triangle
Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that adds the two cells in a row (horizontal) above it. This pattern is like Fibonacci’s in that both are the addition of two cells, but Pascal’s is spatially different and produces extraordinary results. Pascal’’ triangle is related to an amazing variety of mathematics, things like Fibonacci’s sequences, the triangular numbers, the powers of 2, the binomial theorem, the Bell curve, and more, so much more. We invite you to explore!