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IntMath Newsletter: Phi, music and maps

By Murray Bourne, 05 Sep 2013

5 Sep 2013

In this Newsletter:

1. Resource: Dr. Geo
2. Music and Phi
3. Maps that help you make sense of the world
4. IntMath Poll
5. Math puzzles
6. Friday math movies
7. Final thought: Clear vision

1. Resource: Dr. Geo

Dr Geo

Dr Geo is a free download that allows us to construct a wide variety of geometric objects.

Review: Dr. Geo

2. Music and Phi

Music and phi

Phi (Φ) is known as the "Golden Ratio" and has value 1.618 033 988... It is the positive solution to the equation Φ2 − Φ − 1 = 0 and has some quite remarkable properties.

Phi and its reciprocal, 1/Φ = 0.618 033 988... have been observed to occur in nature. The Φ ratio has a connection to the Fibonacci numbers (the ratio of successive Fibonacci numbers approach the value Φ.)

Many people believe that beauty is related to this Golden Ratio. If someone has body proportions (and facial proportions) which follow the Golden Ratio, we tend to find such people "attractive". (See Math of Beauty.)

I came across the following article recently, where it talks about how the Golden Ratio is used in computer game music, to make it more pleasing to the ear, and to provide contrast via climaxes:

Zelda Music of Golden Proportions

And here's a short music video based on Phi by Michael Blake:

What Phi (the golden ratio) sounds like.

3. Maps that help you make sense of the world

Here's a nice resource. I love maps and I love visual statistics, and this interesting collection has both.

In Maps that will help you make sense of the world, by "Twisted Sifter", we learn about global distribution of all sorts of things, including researchers, vegetation, McDonalds, alcohol consumption, writing types and many more.

Here's one of the maps, showing the distribution of people by latitude.

Maps that help you make sense of the world

This is how math relates to the real world - it helps us to describe the human condition.

4. IntMath Poll

The recent IntMath poll asked readers how they feel about summer holidays.

The most interesting thing about this result is the 17% who regard summer holidays as "too long".

I feel summer holidays are:

Not long enough: 63%

About the right length: 20%

Too long: 17%

Total votes: 1800

Current IntMath poll: Now that summer holidays are over for most of you, the latest poll asks how you feel about school. You can answer on any (inner) page of

5. Math puzzles

The puzzle in the last IntMath Newsletter asked about the distance travelled by a car in a fuel efficiency test.

Correct answers with explanation were given by Francis Kisner and Sai Krishna.

New math puzzle

Estimate the probability that a woman who has a positive mammogram actually has breast cancer, even though she's in a low-risk group: 40 to 50 years old, with no symptoms or family history of breast cancer. Assume the following statistics:

  • The probability that one of these women has breast
    cancer is 0.8 percent.
  • If a woman has breast cancer, the
    probability is 90 percent that she will have a positive
  • If a woman does not have breast cancer, the probability is 7 percent that she will still have
    a positive mammogram.

Please leave your responses here.

6. Friday math movies

These 2 math movies show how art and math can be intertwined.

The math of coral

(a) The beautiful math of coral (and crochet)

How do we get the message out about saving corals from destruction? Here's one way involving community crochet.

Friday math movie: The beautiful math of coral (and crochet)


African fractal designs

(b) Fractals and African designs

This is an interesting story about how Africans used fractal ideas for their designs.

Friday math movie: Fractals and African designs

7. Final thought: Clear vision

Richard Nelson Bolles was talking about job-seeking when he wrote in the book What Color is Your Parachute?:

The clearer your vision of what you seek, the closer you are to finding it. For what you are seeking is also seeking you.

I see it all the time when students have a clear vision about what they are doing and where they are going. Such students tend to be more successful in their studies.

Until next time, enjoy whatever you learn.

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