## Euler’s Identity

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…

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…

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…

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…