Mathematics

Exponential Growth

Linear vs. exponential

The term “exponential growth” strongly implies quick growth. However, something that grows exponentially will seem to grow quite slowly at first. In practice, there is a good chance that you won’t notice it at all until it suddenly “pops into view”. Take the adoption of…

Submitted on 26 May 2013

7 Cool Reference Sites on Mathematics

We all have to look things up once in a while, and I can tell you right now that Wikipedia is the best source for practical information on mathematics. But, there are some others out there that are also worth knowing. Most of these sites are encyclopedic, and not meant for browsing top down, so I’ve used the entry for eigenvector as an example for…

Submitted on 9 January 2013

Fractal Dimension

The concept of a fractal dimension is based on the idea of measuring things with differently sized rulers, as already mentioned in the article on the Mandelbrot Mandelbrot set. Mathematically (but very loosely), the fractal dimension is defined as: if I cover an object with…

Submitted on 17 June 2012

Infinity and Beyond

If you think about a set with an infinite number of elements, you might conclude that there is not much to say about the number of elements anymore. Infinite is infinite, right? Well, it turns out that not every infinity has the same “value”, and that there’s actually quite a lot to say about it. Take the natural numbers…

Submitted on 26 March 2012

What's in a Distance

The distance between two points is a concept that is, in every day use, clear and unambiguous. Mathematically, the normal (every day) distance between two points is called the Euclidean distance, but mathematicians generalize this definition. I show how, and I try to make you think by showing how circles look using some of these alternative definitions…

Submitted on 6 July 2011