## Wednesday, January 31, 2007

### LCM question using Astronomy

Who says teaching Arithmetic is boring? Perhaps having a context will help students get more interested in finding the lowest common multiple (LCM) of numbers and highest common factor of numbers (HCF), and perhaps understand the importance of these 2 concepts. One area of science where LCM can be applied is astronomy as illustrated by the following:

Suppose Jupiter takes 12 years to make on revolution around the sun, and Saturn takes 30 years. If these 2 planets were to line up in the Earth sky, how long would it take for them to line up in the Earth sky again?

Adapted from Teaching Secondary Mathematics through Applications (2nd Ed.), Herbert Fremont. A highly recommended read for any one who would like to find interesting applications of high school mathematics.

## Tuesday, January 30, 2007

### Flatland the movie

In 1884, Edwin Abbott wrote the novel Flatland depicting the adventures of a square in a two-dimensional world. It is an extremely useful novel to teach geometry. Topics that can be taught include polygons, circles, plane geometry and triangles.

You'll be interested to know that Flat Land the Movie is coming out this year. Check out its trailers at www.flatlandthemovie.com

## Wednesday, January 10, 2007

Algebraic manipulation can lead to certain fallacies can give raise to surpising results. Here is a sample of 2 of them taken from the book "one equals zero" by Nitsa Movshovitz-Hadar and John Webb (1998). These paradoxes can be used in class for students to think about.

1) suppose we have the equation x-x^2=1.

Since 0 is not a root of this equation, we can divide both sides by x:

x+1/x=1

So

x-x^2=x+1/x

subtracting both sides by x,

-x^2=1/x

which gives

x=-1

But -1 isn't the answer. What went wrong?

2) Given the equation

log(x-1)^2=2 log 3
2log(x-1)=2log 3
log(x-1)=log 3
x-1=3

so x=4

Is this the only solution? If not? What went wrong in the working above?

Overall, the book proved very interesting for me. There is a variety of paradoxes ranging from algebra to statistics. It also includes calculus and geometry.