IntMath Newsletter: Model, animations, software

By Murray Bourne, 29 Aug 2018

29 Aug 2018

1. New on IntMath

(a) EFFEKT bridge model

Spiral around a hyperboloid - the Effekt bridge

In the last Newsletter, the puzzle was to model the EFFEKT bridge, a spiral in the shape of a hyperboloid. Here's my solution:

Spiral around a hyperboloid - the Effekt bridge

(b) Math Art in Code: Animated Lissajous figures

Animated Lissajous figures

We can get interesting and beautiful curves when combining two signals. See:

Animated Lissajous figures

2. Resources

(a) oPhysics interactive simulations

oPhysics: Interactive Physics Simulations

Here's over 100 physics simulations including kinematics, forces, waves, fluids. There's even circuit drawing tools.

Go to: oPhysics: Interactive Physics Simulations

(b) Topology and Geometry Software

In the article, With new technology, mathematicians turn numbers into art, we read how various mathematicians are pushing the envelope when it comes to exploring mathematical concepts within the real and virtual realms.

Mathematical visualization
[Image source: Frank Farris, CC BY]

One of the resources mentioned in that article is the following, developed by Jeff Weeks, one of the "rock stars" of the mathematical world.

Topology and Geometry Software

In these games with a mathematical underpinning, you can explore polyhedra (tetrahedrons, icosidodecahedrons, etc) and 4-D mazes. You can even play pool on a hyperbolic surface. Some are for mobile devices, others for desktop.

Go to:

Topology and Geometry Software

The development of these games was supported by the (US) National Science Foundation.

3. Math in the news

What is the smallest number of colors that you'd need to color any graph consisting of points connected by segments of the same length?

This puzzle has fascinated mathematicians since the 1950s when it was first posed. It was long held that 4 colors should do the job.

4 color problem

However, earlier this year, amateur mathematician Aubrey de Grey proposed the first unit-distance graph that requires at least five colors.

Here's the article: Decades-Old Graph Problem Yields to Amateur Mathematician

4. Math Movies

(a) 3 Ways to spot a bad statistic

3 Ways to spot a bad statistic

We're living in a world of "alternative facts", but this is a dangerous situation. It's crucial we understand how statistics are collected, funded, interpreted and used.

See: 3 Ways to spot a bad statistic

(b) How does your body know what time it is?

How does your body know what time it is?

The story of Michel Siffre is a fascinating one. He went into a cave for months to see the effect on his perception of time.

See: How does your body know what time it is?

5. Math puzzles

The puzzle in the last IntMath Newsletter was about the EFFEKT bridge, which I addressed earlier in this Newsletter.

New math puzzle: Factorial

What's the maximum number of times 2 can divide exactly into factorial 50 (written 50!)?

You can leave your response here.

6. Final thought

"Learning is not compulsory - neither is survival."
[W. Edwards Derning]

Until next time, enjoy whatever you learn.

See the 3 Comments below.

3 Comments on “IntMath Newsletter: Model, animations, software”

  1. Siggy says:

    I am interested in determining the velocity of Time; i.e., At what speed does time elapse between second 1 and second 2.

    At the moment I am stuck with the proposition that times moves at the rate of 15 degrees per hour.

    Can you point in the right direction?


  2. Murray says:

    @Siggy: Well, I'm not sure that you can find the velocity of time, or whether that quantity actually has any meaning.

    However, you could find the angular velocity of an analogue clock's hand as it rotates. So for the hour hand, the rotation in one second would be:

    15° / 3600 = 0.00416666°

    So the (angular) velocity of the hour hand is 0.00416666° / sec.

  3. Joaquin Orias says:

    I Have learned a lot, computer software is amazing.

    ThankX for teaching all that stuff

Leave a comment

Comment Preview

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't mix both types of math entry in your comment.