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The IntMath Newsletter - Dec 2007

By Murray Bourne, 15 Dec 2007

In this Newsletter

  1. Sine and Cosine Graphs - and why they matter
  2. Solution to last month's puzzle
  3. New in Interactive Mathematics - more interactives
  4. Poll Results - math software
  5. New Years' Math
  6. Latest from the math blog

1. Sine and Cosine Graphs

Some of the big issues facing mankind involve events that repeat on a regular basis:

  • Wave heights: There is a need to predict rises in sea level and corresponding wave heights associated with global warming.
  • Efficient and clean electricity production: The extraordinary increase in energy demand, especially in India and China, is leading to overwhelming pollution from coal-fired power plants.
  • Regular earth tremors: One way of predicting earthquakes, tsunamis and volcanoes is to look for regular tremors. Analysis of such tremors can help to predict when the big ones will hit.
  • Clean engines: Pollution from the internal combustion engine, used by most cars, trucks and buses, is a major concern.

Each of the above examples involves periodic functions in some way. A function is periodic when a pattern of values repeats after a certain time (eg the height of water waves, size of earth tremors, current in AC electricity, piston height in an engine).

Most of these events can be described using sine and cosine graphs. (Actually, a cosine graph has the same shape as a sine graph - it is simply shifted to the left on the x-y plane.) Scientists and mathematicians use sine and cosine graphs when analysing problems like those above.

Go to the chapter on Trigonometric Graphs where you can explore periodic graph concepts using Flash and java applets, and see more examples.

2. Solution for November's Puzzle

In last month's newsletter I posed the following question from Edward MacNeal's book, Mathsemantics:

On NBC News in 1987, the Secretary of Transport said, "Last year 415 million people were passengers on airlines in the US." This is a ridiculous statement. Can you figure out why?

The answer: In 1987, there were only 240 million people in the United States. Even allowing for a few million tourists, we can't get up to 415 million.

The statement should have been:

"Last year there were 415 million passenger journeys on airlines in the US."

This is quite a different statement. It counts the number of journeys made and is quite a reasonable number. It means some people had multiple plane journeys, some had one and some had none at all.

Why does it matter? Many people are very confused when it comes to mathematics and this makes it very easy for companies to manipulate people and extract money from them. For a recent example, have a look at the mess that many people find themselves in as a result of the sub-prime loans crisis.

Much of the math confusion arises because people (and companies) are not careful about how they express themselves mathematically. So banks, credit card issuers, insurance companies and many other businesses can fool people into signing for things that they will never be able to afford.

Math matters...

3. New in Interactive Mathematics - more interactives

There are some new interactives on the Interactive Mathematics site.

In the trigonometric graphs chapter, there are new Flash animations for sine and cosine curves, and also graphs of sec, cosec, tan and cot functions.

In the differentiation chapter, there is an interesting differentiation of polynomial functions applet. This one has several built-in examples for you to explore.

In the integration chapter, there is a nice demonstration of Riemann Sums using an applet. [A Riemann Sum allows us to approximate the area under a curve. This is an important concept in integration.]

4. Poll Results - Math Software

Last month's poll asked whether readers (and/or their teachers) use math software (like Matlab, Scientific Notebook, Maple, etc).

It was quite disappointing to me that more than 50% of readers do not use math software at all, and neither do their teachers. Only 29% of respondents indicated that both they and their teacher uses math software. Watch for more on this issue next month.

See the math software poll results.

Latest Poll: The latest poll asks about your feelings towards mathematics. You can answer on any page of Interactive Mathematics.

5. New Years' Math

Some dates for the upcoming festivals:

  • Western New Year: 1 January 2008 (adopted by Germany in 1700, England in 1752 and Japan in 1873)
  • Islamic New Year 10 January 2008 (which is year 1429 in the Islamic calendar)
  • Chinese New Year 7 February 2008 (which is year 4705 in the Chinese calendar)
  • Jewish New Year sunset 29 September 2008 (which is 5769 in the Jewish calendar)

My hope for 2008:Throughout history, man has used his intelligence and creativity to destroy or hurt others and to almost ruin our precious Earth.

My hope for 2008 is that the readers of the IntMath Newsletter will use their education in ways that will improve relationships between people and improve the sorry state of the world.

As the Japanese say on 1st January each year:

akemashite o-medetoo-gozaimasu which means "Happiness to you on the dawn of a New Year!"

6. Latest from the Math Blog

What do you think about this University of Washington professor who says the math skills of incoming students is 'abysmal'?

This week's Friday Math Movie is an explanation of differentials, a calculus topic.

Why are there so many under-performing Australians in the literacy, numeracy and problem solving domains?

A reader asked why we have to study math since it is so boring.

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