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IntMath Newsletter - Trigonometry tips and a puzzle

By Murray Bourne, 01 Dec 2008

1 Dec 2008

In this Newsletter:

1. Earth Puzzle
2. Math tip - Trigonometry
3. From the math blog
4. Solution
5. Final thought - 3 kinds of people

1. Earth Puzzle

I walk 20 paces North then turn left and walk another 20 paces West. I turn left again and walk a further 20 paces South. I am amazed to find that I'm back in the same place that I started.

Where am I?

[Hint: This puzzle is related to Earth Geometry that we talked about in the last edition. Solution at the end of this Newsletter.]

2. Math tip - Trigonometry

Introduction to trigonometryA reader asks, "what is trigonometry all about?".

See my reply here: What is trigonometry all about?

3. From the math blog

1) Project Euler
Project Euler has some interesting math questions that require the use of computer algorithms to solve.

2) Unicode characters for Chinese and Japanese numbers
Unicode characters use hexadecimal numbers (base 16) to display characters from languages like Japanese, Chinese, and Greek.

3) Friday Math Movie - Math Rules!
This week's math movie was a finalist in the X-Box Competition at the 2007 New York Television Festival.

4. Solution

The answer to the puzzle above is that I started at the South Pole. I walked 20 paces North, then 20 paces West, then 20 paces South again, arriving back at the South Pole, where I started.

Earth geometry puzzle solution

In the picture, it looks like the second and third legs of the journey are not straight. This is one of the intriguing things about Earth Geometry — no lines are straight. (The first leg appears straight because North is straight up on the picture.)

4. Final thought - 3 Kinds of People

There are 3 kinds of people:

1. Not very clever people — the ones who never learn from their mistakes
2. Smart people who do learn from their mistakes
3. Successful people who learn from the mistakes of others

Which kind of person are you?

Until next time.

See the 18 Comments below.

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