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IntMath Newsletter: MAM, modulus of complex number, Google Solve for x

By Murray Bourne, 03 Apr 2012

3 Apr 2012

In this Newsletter:

1. April is Math Awareness Month
2. Modulus or absolute value of a complex number?
3. Google's "Solve for <x>"
4. IntMath Privacy Statement
5. Math puzzle
6. Friday math movies
7. Final thought - Tenant farmers

1. April is Math Awareness Month

Math Awareness Month

The theme for this year's Math Awareness Month is Mathematics, Statistics, and the Data Deluge.

It's a great theme, since so many people are producing a mountain of new data every day. And there are some really good job opportunities for you in this - data analysis will be huge for the foreseeable future.

2. Modulus or absolute value of a complex number?

Modulus or absolute value of a complex number?

A reader challenges me to define modulus of a complex number more carefully.

Modulus or absolute value of a complex number?

3. Google's Solve for <x>

This is an interesting initiative from Google. It's an invitation to suggest "radical technological solutions for today's big problems".

You can hear some insights by people who've already suggested good ideas, in TED-style talks.

This is the kind of thing we should be doing in schools to make learning more meaningful and relevant! Is there space for it in your school?

The link: Solve for <x>

4. Updated IntMath Privacy statement

You probably hear endlessly about privacy updates from Facebook, Google and other sites.

Well, I keep certain information about you too, my faithful readers. The updated IntMath Privacy Statement indicates what that information is, and how it is used.

Brief summary: I never share your private information with anyone, ever.

5. Math Puzzle

There were many "correct" answers for last Newsletter's math puzzle about birds and beasts. Special mention goes to all those (too many to mention) who showed full working - that's a very good habit to get into!

But here's the thing. In the "real" world, nothing is ever as straightforward as it seems (especially when considering typical math text book questions).

Some of the respondents considered there may be more to the question. Take Guido's comment "Birds are animals, too", and gfrblxt who amusingly said "Assuming that the zoo had no push-me pull-yous ^_^ ".

Devin included an excellent feature in his answer - he stated the assumptions for his solution (always a good thing to do when solving problems):

"Assuming all animals have 1 head, each beast has 4 feet and birds have 2."

Ricky, Anthonette and Alex also stated their assumptions, making their answers much more "correct".

But Tomas thought about it some more and began with:

Assuming snakes, snails, fish, and all other footless beasts are excluded...

Now, the original question used both of the terms "beast" and "animal" and for most of us, that means "tiger", "elephant" and so on. But strictly, an animal is any living creature belonging to the kingdom "Animalia", which includes 6-legged insects, 8-legged spiders, many-legged millipedes, and even zero-legged fish and sponges.

While we wouldn't call most of those "beasts", they are certainly not plants!

How about chimpanzees and other apes? They use all four limbs for walking, but we generally don't say they have 4 feet. Kangaroos are another example of a 4-limbed "beast" with only 2 feet.

As for the number of feet birds have, we won't even consider here Leviticus 11:20, where a few translations have "All fowls that creep, going upon all four, shall be an abomination unto you."!

All this makes the question a bit more difficult to answer! Of course, the question writer had the simple case in mind so the answers given are fine.

The bottom line is, when answering any math question that involves the "real" world, it's a good idea to think about what else could be included and what should be excluded - and then state your assumptions.

For the teachers who have read this far, math questions should probably be either clearly "close-ended" (all assumptions are stated in the question, and students should aim for the one correct answer), or (better), more "open-ended", like "real" problems, where the process of thinking through the possibilities makes it more interesting, more motivating and more useful for developing future problem-solving skills.

New puzzle: (This puzzle is close-ended and has only one correct answer - promise!)

What is the coefficient of x99 in the expansion of

(x − 1)(x − 2)(x − 3) ... (x − 100)?

You can add your answer here.

6. Friday math movies

Real meaning of mph

(a) The real meaning of MPH

Here's an agonizing video demonstrating how we really should spend more time on fundamental concepts in math class.

Friday math movie: The real meaning of MPH


Calculus Rhapsody

(b) Calculus Rhapsody

This is clever - and funny: a calculus parody of the classic Queen song, Bohemian Rhapsody.

Friday math movie: Calculus Rhapsody


Escher animation

(c) Inspirations - animation of Escher art

Here's a celebration of Escher, and it includes many crucial math concepts.

Friday math movie: Inspirations - animation of Escher art

7. Final thought - Tenant farmers

Inventor and businessman Thomas Edison held over 1,000 patents for inventions ranging from the lightulb to the phonograph. He founded General Electric, an energy, technology and finance conglomerate.

His view on renewable resources is very interesting:

We are like tenant farmers chopping down the fence around our house for fuel when we should be using Nature's inexhaustible sources of energy - sun, wind and tide... I'd put my money on the sun and solar energy. What a source of power! I hope we don't have to wait until oil and coal run out before we tackle that. [Thomas Edison (1847-1931)]

Until next time, enjoy whatever you learn.

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