This Week's Number: 7

We were talking in class about probability. Here is a podcast on the number 7. What does this number have to do with probability? Well is a central number to the study of riffle shuffling. Listen to BBC radio’s series on numbers. The episode is titled "The Number Seven". It is a radio series hosted by Simon Singh.

The Normal Distribuiton

Here are two applets that I created to help you visualize the normal distribution. The first applet shows how the graph changes given a different mean and/or standard deviation. The shape is of course always a 'bell curve'. The second applet is better suited if you want to look at probabilities with data that is normally distributed. Notice how the function that generates this curve contains both pi as well as the natural base, e. The importance of these numbers cannot be underestimated.

Cellphone Tower Problem

What cellphone towers are responsible for a given area in a city? This is the problem was given in class along with the rubric and the Geogebra solution.

Voronoi Diagrams

To review some basics in Algebra in SL Math, we played with Voronoi Diagrams. Here is the problem that was asked and the solution using Geogebra. There are many fascinating sites about these diagrams. Explore these sites: Voronoi Game 1, Voronoi Game 2 (and an introduction to the idea behind the game), A paper on Ornamental Design using these diagrams with a web gallery, a very brief explanation on how to generate fractals using these diagrams, an art installation that I would love to build about the idea of personal space, another fractal site, finally some images and explanations (also on wikipedia). I apparently went a little crazy looking up some of these things.

Three Planes Question

Here is a little question about the intersection of three planes. There is also a movie to help you visualize. The planes move through the values of k through 0 to -5. (That should give you a rough idea of the possible range for the answer)

Gödel’s Incompleteness Theorems

There should be more place for the philosophy and history of mathematics presented to students. There are some decent resources on the web and there has been more research done on the history of mathematics recently. There are many misconceptions in mathematics and its foundations. Here is a BBC radio program about the foundations of mathematics. You may be surprised by what is discussed. The program is called "GÖDEL'S INCOMPLETENESS THEOREMS" and subtitled "The Dirty Secrets of Maths". If people only knew...