The animation demonstrates the looming effect that you get when something (a motorbike in this case) approaches you at a constant speed. At first nothing seems to happen, but then the bike suddenly jumps into view. A general explanation of this dangerous effect that often causes motorbikes to be missed by other drivers is…

Happy Valentine’s Day! I might not be very romantic, but I had to do something with it. Imaging the heart is an important application of tomography and other techniques in medical imaging. Since hearts are everywhere on Valentine’s Day, let’s scan one. This article builds on…

This colorful bubble chart is a simple way of freshening up your CV by adding the time dimension to your skill list. A simple list has relatively little value, since it doesn’t indicate the importance of each skill. This can be improved by including an estimate of its strength. To do this, you could simply add the number of years of experience, but I propose to go a bit further…

All the standard caching options of my Drupal 7 site are enabled. I expected those mechanisms to ensure that the access to a cached page would always be quick, both for human visitors and for web spiders like Googlebot. However, for a small site, this is not so. The Drupal caching mechanism does not work as you might expect. For me, there is a clear difference between…

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…

I was going to call this article War on Spam. But, given how well my experiments went, I had to retitle it Skirmish with Spam. Lately, the number of spam attempts has risen so much that even Mollom lets through enough spam to get me a bit miffed. So, I decided to go “old school”… I was going to add math problems of increasing difficulty until…

The first three articles on tomography focused on analytic techniques, in which the reconstruction problem is attacked using mathematical analysis. When the step to real world scanners is made, the problem is discretized. Both the projections and the reconstruction area are divided into pixels, and a numerical approximation of the true mathematical technique is introduced. The algebraic techniques assume…

At the end of the second article on tomography, I left you with a very blurry reconstruction of the scanned object. Indeed, naive backprojection is not sufficient to create high-quality reconstructions. Why is that so? Intuitively, a simple backprojection cannot be expected to create a perfect reconstruction, since the contribution of…

This article shows that it is possible to reconstruct the inside of a person or object from (lots of) projections of that person or object. Mathematically, tomography is based on the fact that the function values of a two-dimension functional \(f(x,y)\) can be calculated from projections of that function. This basic fact was discovered…

Have you ever wondered how a CT (or CAT) scanner creates an image of the inside of a person? The answer is computing. CT and CAT are short for computed (axial) tomography. Computing is the secret sauce that is poured over the hundreds or thousands of X-ray photos that make up a CT scan, to merge them into a single image. This first article on tomography explains projections, the essential input data for tomography…