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IntMath Newsletter: Solid of revolution, resources, news

By Murray Bourne, 10 Oct 2018

10 Oct 2018

In this Newsletter:

1. New on IntMath: Solid of Revolution maker
2. Resources: Grasshopper, Sketchup
3. Math in the news: Light beam
4. Math movies: Ballet, Mars
5. Math puzzle: Tokens
6. Final thought: Jack Ma

0. Happy Metric Day!

Today is 10/10 and this week is designated National Metric Week. Of course, this is probably only relevant in the USA only, as every other country in the world officially uses metric units (except Myanmar). The US Metric Association advocates completion of the ongoing US conversion to the metric system.

1. New on IntMath

Math Art in Code: Solid of Revolution maker

Solid of Revolution maker

Create your own solid of revolution using this interactive 3-D graph. Drag across the canvas and the shape automatically appears.

Solid of Revolution maker

2. Resources

(a) Grasshopper

Grasshopper: Learn javascript while playing

Learn to code using the Grasshopper game for Android and iOS devices. It's by Google, and it teaches you javascript basics in a fun and painless way.

Go to: Grasshopper codes

(b) Sketchup Viewer is now free

Sketchup model

Sketchup is a 3-D modeliing software for desktops. The "core" version comes at zero cost, with education and Pro versions also available.

They recently provided Sketchup Viewer for iOS and Android devices, so you can view the thousands of models made using Sketchup for $0.

(c) Gun violence data visualizations

On average in the USA there are around 10 teenagers killed by guns each day. I've lived my whole life in countries where guns are illegal, and I'm yet to understand how any country can allow such violence to continue.

Teens killed or injured - gun violence

For a sobering set of visual statistics, see the Gun Violence Archive.

3. Math in the news

(a) Needle pulse light beam

Obtaining precise images is extremely important in many fields of science, engineering and medicine. Ultrasound, radar and precise metal etching are notable applications.

Needle pulse light beam

Researchers at University of Rochester used a mathematical approach to cause a light or sound wave to collapse inward, forming a short duration, incredibly thin intense beam, which they call a "needle pulse" beam.

Here's an overview: New 'needle pulse' beam pattern packs a punch

Here's the original paper, containing all the juicy mathematics involved:

Longitudinal iso-phase condition and needle pulses (link no longer exists)

(b) Teaching for understanding?

Sadly, far too many students think of mathematics as a series of formulas that just require subsituting a number or two, getting it right (hopefully), and moving on to the next one.

Teaching for understanding

But what is mathematics really about and how should it really be taught?


Challenging the status quo in mathematics: Teaching for understanding

4. Math Movies

(a) The physics of the "hardest move" in ballet

In the third act of "Swan Lake", the Black Swan spins around and around ... thirty-two times.

The physics of the hardest move in ballet

How is this move — which is called a fouetté — even possible? Arleen Sugano unravels the physics of this famous ballet move.

See: The physics of the "hardest move" in ballet

(b) What time is it on Mars?

We often feel everyone else has the same experience of time as we do. But what if you were on Mars? Or at least, your job required you to study Mars? This video does a good job of challenging our perspective.

What time is it on Mars?

As a spacecraft engineer at NASA's Jet Propulsion Laboratory, Nagin Cox works on the team that manages the United States' rovers on Mars, whose day is 40 minutes longer than Earth's.

See: What time is it on Mars?

5. Math puzzles

The puzzle in the last IntMath Newsletter asked about dividing factorial numbers. Correct answers were submitted by Gerard, Francis, Aaron, and Rajat.

New math puzzle: Tokens

I have tokens labelled 1, 2, 3, ... and ten boxes labelled 1 to 10. In the first box I place the first token, in the second box the next two tokens, in the third box, the next three tokens, and so on. What is the sum of the numbers on the tokens I place in the tenth box?

You can leave your response here.

6. Final thought - Jack Ma and teaching

Chinese billionaire Jack Ma is stepping down from Alibaba to pursue philanthropy in education. He will follow in Bill Gates' footsteps, putting his fortune to good use. Here are two recent quotes which I found interesting, especially as teaching is not always given the respect it deserves.

"I also want to return to education, which excites me with so much blessing because this is what I love to do." [Source]

Here's an indication of how he intends to approach education given his experiences. It will be interesting to see what innovative things he does.

"I'm not going to teach you math. I'm not going to teach you English. I'm not going to teach business in the schools. I'm going to teach young people how to face challenges." [Source]

Until next time, enjoy whatever you learn.

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  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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