## 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…

Color is a straightforward way to make those boring QR codes special. This seems to have caught on with quite a few people, as a quick Google image search reveals. But, there’s a problem. Deviating from the ideal black-and-white makes the QR code more difficult to scan. In this article, I show a way to…

The Mars Science Laboratory (MSL) is one of the most spectacular planetary missions ever. The MSL homepage gives lots of details, and includes a countdown clock to the landing in…

After the fun with the “doctored” photo from a previous article, I thought it would be nice to show another example of a photo that “fades to gray” if you’re not careful. This time the image disappears if it is converted to grayscale in the wrong way. This is…

You have probably already encountered a few *QR codes*. These codes are becoming more and more common, and can be found on business cards, ads, historical buildings, T-shirts, etc. You're meant to scan them using your smartphone. They can contain all sorts of information, the most common being plain text, URLs, and contact information. The information is… *[This article contains a demo in which you can create your own QR codes!]*

This article points out the danger of assuming that astronomical images are encoded using linear intensity. It is meant for the many people that are performing astronomical observations using regular cameras. Not because there’s something wrong with that, but because those cameras are optimized for “normal” photography and video, not for numerical calculations on their images. The illustration below…

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…

The Large Hadron Collider (LHC) must surely be the greatest physics experiment ever. Remarkably, you can follow the day-to-day operations of this experiment on the web, through the online dashboard. Have a look! The fascinating thing is that such a large machine is needed to study the smallest of things, elementary particles. The LHC is a particle collider that…

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…