summer break

We are taking a break from our TV broadcasts for the summer, but we will be keeping up with this blog, so feel free to leave any comments or suggestions. We will be back with live broadcasts in the fall.

Each week on the TV program we highlight some mathematics as seen in the "real world," and if you have any ideas for these segments we would love to hear them. Perhaps you use math in your job or hobby, or know someone who does. We could even visit a workplace and talk with people about how mathematics is used, as we have in the past.

Music and Mathematics

There are many connections between mathematics and music, and it seems that many people who enjoy mathematics also play musical instruments. This week we looked at the tones we hear in almost all western music. Almost all western music uses 12 tones in a scale. Why 12, rather than some other number? The tones we hear are based on sine waves of different frequencies, and it turns out that the combinations of tones that sound most pleasing to us are based on ratios of small integers. Splitting one octave into 12 equal steps gives a very close approximation to these ratios. Still, there are many other tunings used in other countries around the world.

This week's links:

a short and sweet look at our 12 tone scale

Wikipedia entry for Music and Mathematics

Hear a tuning based on pure ratios ("Just Intonation")

The Normal Distribution

The normal distribution is a probability distribution shaped like the classic bell curve. You will see a curve like this if you make a chart of, for example, the heights of a large number of adult women, you will see this curve take shape. There are many other instances where this distribution shows up, such as birth weights, the price of gas today at all the gas stations in the county, the amount of liquid in all the soda cans at the store, etc. This distribution is also linked to binomial probabilities.

Related links:

Wikipedia entry for Normal Distribution (gets fairly technical but you can read some of the basic details there)

simulation of a Galton Board (marbles bouncing down pegs on a board that we showed on the program)