The New Turkish Currency

In 2009, the New Turlish Lira (YTL) will be renamed simply the Turkish Lira (TL). What does this have to do with math. Well... to my great surprise, they have a mathematician on the 10TL note. Here is the information from the Turkish Mint: "The back of the note features a portrait of Ord. Prof. Dr. Cahit Arf (1910 – 1997). Cahit Arf was one of the most significant mathematicians of Turkey and is renowned internationally for many theorems in his name. Other elements on the back of the banknote are mathematical motifs consisting of a section of Cahit Arf’s “Arf Invariant” as well as “arithmetical progressions, an abacus, numbers and figures that represent the binary system, which is the basis of computer technology. "

Continuous Probability Function

Here is an example of a CDF problem. Try to solve it manually and check your answer using the CDF Geogebra applet. Email me if you want to change the function. I will send you the .ggb file that you can alter and play with.

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)