Mathematics

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… read more

Submitted on 26 March 2012

Euler’s Identity

Euler’s identity using Hama beads

Euler’s identity, \(e^{i\pi}+1=0\), must be the most beautiful formula in the whole of mathematics. The expression establishes an amazing relation between five important numbers… read more

Submitted on 11 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… read more

Submitted on 6 July 2011

The Harmonic Series

If you would have to guess the value of the infinite sum 1 + 1/2 + 1/3 + 1/4 + 1/5 + …, what would you do? The value of the individual terms clearly goes to zero. But does that mean that the total sum will be finite? Well, it doesn’t. This was already proven by Nicole Oresme in about 1350. The proof is actually… read more

Submitted on 24 May 2011

Formulas Ahead!

Showing mathematical formulas on the web is not straightforward, as HTML (Hypertext Markup Language) does not contain built-in commands to typeset mathematics. Although MathML (Mathematical Markup Language) was designed to be an extension of the standard markup language for mathematics, it is not yet supported by all browsers, so it’s not quite ready for prime time! So we are stuck with… read more

Submitted on 6 April 2011

Pages