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The IntMath Newsletter - Nov 2007

By Murray Bourne, 16 Nov 2007

In this Newsletter:

  1. Your updated IntMath information
  2. Thanks for your positive comments
  3. What's New in Interactive Mathematics
  4. Answer to the Apples and Oranges Puzzle
  5. Asymptotes
  6. Latest from the Math Blog
  7. Final thoughts - your future

1. Thanks for Updating your IntMath Information

I sent a request a few weeks ago for everyone to update their information. Thank you to all of those who did so and for giving me your Newsletter suggestions. I replied to as many of your suggestions and comments as I could.

Some of the great topic suggestions for the Newsletter included:

  • Algebra
  • Asymptote stuff
  • Biological math
  • Calculus applications
  • Cauchy Sequence
  • Circle theorems
  • Cryptography
  • Differential equations
  • Entrance and aptitude test problems
  • Exact Equations
  • Formulas for temperatures
  • Fractal geometry
  • Fractions
  • Geometry
  • Group theory
  • Integration
  • Logarithms
  • Math programming and available software
  • Numerical methods
  • Operation of radicals
  • Pre-algebra
  • Probability and statistics
  • Quadratic polynomials
  • Real analysis
  • Relationship of math and fine art
  • Straight lines - slope-intercept form
  • Trigonometry applications
  • Sine and cos graphing
  • Vectors

I will address these over the next few months (or longer!).

Beyond the scope of the Newsletter: Some of the requested topics are probably not what most readers of this Newsletter are doing right now (like Laplace), but I'll see what I can do.

Award for most suggestions: One guy requested 51 high-end math topics. I love his enthusiasm!

Most unusual request: "I am here to learn english with with you. Can i married with somebody?!!!!!!!!!"

50+ Countries: The subscribers to this Newsletter come from over 50 countries.

Cost for this Newsletter? One reader asked if there are any costs accompanying the news letter. The answer is no. Both Interactive Mathematics and the IntMath Newsletter are free.

Instructors: One teacher asked for engaging math instruction ideas for 6th graders, which he called a 'tough audience'.

2. Thanks for the Positive Comments

There was a lot of really positive feedback from many of you when you updated your details. I really appreciate your kind comments and I am glad that you find Interactive Mathematics and the IntMath Newsletter useful.

Some of the comments included:

  • I think it's so helpful not only me but also everyone who is interested in math. Because all the instruction in topics of this website provides us with a reliable foundation.
  • The IntMath Newsletter is really excellent.
  • The newsletter is superb
  • The interactive mathematics has helped me a lot i am grateful to you entirely
  • Precise & educative
  • Very useful.
  • I am enjoying the Newsletter very much. Thank you for putting it together.
  • It helps me a lot not only in class but also in solving problems
  • Congratulations and lots of thanks for this wonderful Math site! Well done! Keep up the good work!

One of my favorites: This response was a pleasant surprise:

I come from the Netherlands. Age 83. I enjoy your newsletter very much.

You are never too old to learn mathematics!

3. What's New in Interactive Mathematics

Four new things this month:

  1. Music While You Math: On every page of Interactive Mathematics, you can listen to a range of music from classical, through pop, rock and ambient. You'll see it on the right margin under the navigation links. [If you are into music, you might like to check out What are the Frequencies of Music Notes?]
  2. Matrix Operations Flash interactive: The old interactive had a problem so I rewrote the whole thing recently. Check out in Multiplication of Matrices.
  3. The latest poll asks if you, or your teacher, uses math software. Please vote on any page of Interactive Mathematics.
  4. This is now an HTML newsletter. Let me know if you have trouble reading any of it.

4. Answer to the Apples and Oranges Puzzle

In the 'mini-mail' a few weeks back I asked this question:

What is the answer to "2 apples plus 5 oranges"?

The question comes from the excellent book by Edward MacNeal called Mathsemantics - Making Numbers Talk Sense. MacNeal is an aviation consultant who needs to defend his company in court cases involving the airline industry. For him, the way that most people talk about mathematics concepts is very sloppy.

When hiring new people for his company, MacNeal includes a requirement that the applicants should be 'good at numbers'. He gives them a test to see if they really are 'good at numbers'. Fully 1/3 of the applicants could not answer the fruit addition question in a way that would be acceptable in court.

The correct answer is "7 pieces of fruit" (or "7 fruits" or perhaps "7 fruit"). You see, this is not an algebra problem at all - it is a problem about the language of math. It turns out that lots of people (even those who think they are 'good at numbers') have trouble with such things.

Still not sure about the answer? Think about this... If I show you a red pen and a black pen and ask you to count the objects, the answer is pretty easy, right? (I hope you are thinking "2 pens"). The fruit problem is similar.

Ready for another puzzle?

Being an aviation specialist, MacNeal includes this story in his book. On NBC News in1987, 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?

5. Asymptotes

One of your topic requests was asymptotes. Let's keep it simple.

Say you are facing a wall which is 10 m from you. You walk half way to the wall (5 m) and stop. Then you do the same thing - walk half the remaining distance to the wall. Now you have a quarter of the distance left (2.5 m). You do the same again and you have 1/8 of the original distance to travel. Again leaves 1/16th left, again gives 1/32nd, and so on.

Now you are getting pretty close to the wall, but you haven't reached it yet. We keep going. 1/64th, 1/128th, 1/256th, etc. We can keep doing this for a long time and we will never reach the wall. Our distance is never zero meters.

Asymptotes are just like this. On a graph, when a curve gets closer and closer to a line but doesn't actually touch that line, we say the line is an asymptote to the curve.

In our wall example, it is like the curve y = 1/x. As x gets bigger and bigger, the value of 1/x gets smaller and smaller, but never actually reaches zero. In this case, the x-axis is an asymptote to the curve.

Check out the graph of y = 1/x. It is Example 4 on the page The Hyperbola.

Asymptotes are an important concept in mathematics. This idea of 'closer and closer but not actually getting there' is used a lot in calculus.

[The wall example is based on Zeno's Dichotomy Paradox.]

6. Latest from the Math Blog

Algebrator is an interesting product - but I'm not sure that I can recommend it.

Carnival of Mathematics #20 has an interesting array of topics from 14 contributors, covering math education, number theory, computing, Internet and videos. Enjoy.

CrazyEgg gives us a wealth of information about visitors to a Website - where they came from, how long they stay and where they go next.

7. Final Thoughts - Your Future

Robert Kiyosaki, who wrote the book Rich Man, Poor Man, said:

Your future is created by what you do today, not tomorrow.

Enjoy reading.

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HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


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