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IntMath Newsletter: Reuleaux triangles, hour of code

By Murray Bourne, 14 Dec 2015

14 Dec 2015

In this Newsletter:

1. Reuleaux triangles
2. Butterfly map of the world
3. Resource: Hour of code
4. Most popular stories in 2015
5. Math puzzles
6. Math movie: Rubik's cube and pianos
7. Final thought: head knowledge or skills?

1. Reuleaux triangles

Reuleaux triangles

Reuleaux triangles have a property similar to circles - they have constant diameter when rotated.

Reuleaux triangles

2. Butterfly map of the world

This article follows on from the one above. These maps are quite neat!

Butterfly map of the world

The butterfly map of the world is based on Reuleaux triangles. This article explores some of the story behind this interesting map.

Butterfly map of the world

3. Hour of code

I'm a bit late for this, but no matter — it's available anytime.

Last week was "Hour of Code", one of the main events of Computer Science Education Week. The idea is to get students interested in programming by offering bite-sized tutorials in coding concepts, javascript and visual coding.

A lot of it appears to be aimed at younger kids, but there's lessons by Khan Academy, Codecademy and Google that could prove useful for older learners.

Should everyone learn code?

I attended a talk recently by a young professional programmer whose main point was that maybe not everyone needs to learn to code. There are many tools (like drag and drop types, and outsourcing) available to get things done without having to spend time actually coding.

This struck a chord with me because it's been my argument about (some parts of) mathematics for a long time now. That is, why do we make students spend hours solving equations, drawing graphs, finding derivatives and integrals, when most of it can be done using a computer algebra system more accurately, and in seconds?

Of course, "black box" solvers are dangerous if we don't know what we're doing (garbage in, garbage out, and if we don't understand what the computer gives us for an answer, then it's all quite useless).

Also, somebody needs to learn all the mathematics, otherwise who will create the useful tools in the future?

Similarly for computer programming. If everyone just uses tools without knowing what the tool is doing for them, then the overall skill level drops and eventually, no progress would be made.

For both fields, there should be a certain "cut off" point, where students know enough, and can be able to do enoough on paper, to appreciate what the machine can do for them, and what the machine's answer means. For example, in mathematics, it's silly getting students to solve 3x3 systems of equations on paper. If they can do 2x2 systems successfully, and can explain what to do with the answer, then good enough - let the computer do anything bigger.

An example from computing science is that anyone can build a Website now without any coding knowledge (see e.g. Google Sites, which promises "single click page creation" and "no HTML involved"). However, such tools always have limitations and it's always good to know how to tweak the code to get what you really want.

So what do you think - should all school students learn to code?

Coding credit?

On a related note, this news item has some interesting comments about the relative value of coding skills and mathematics:

University of California pressured to count computer science toward high school math requirement

Some students expect to get science credit for computer science qualifications. I agree with UC that it shouldn't happen, but it raises several issues about what skills students should really be gaining in school - especially schools in Silicon Valley.

4. Most popular stories in 2015

In case you missed any of them, here are the most popular IntMath Newsletter stories during the year, arranged by popularity (based on traffic).

Fundamental Theorem of Calculus applet

Is cube root the same as raising to power 1/3?

How to find the length of a spherical spiral

Pedigree collapse

Polar to Rectangular Online Calculator

Newton's Method Interactive Graph

Sampling to create mathematical function graphs

Work by a Variable Force using Integration


Is a 1x1 matrix a scalar?

Always popular this time of year:

The Twelve Days of Christmas - How Many Presents?

4. Math puzzles

The puzzle in the last IntMath Newsletter asked about the distance an ant walks on a coordinate plane.

Correct answers with explanation were given by: Rika (who nicely used the math input facility), Tomas, Nour (who correctly allowed for both arcs of the circle), Thomas, Saikrishna, and Darrell (who gave an exact answer).

As is often the case, the approaches used were quite varied.

New math puzzle

What is the ratio of the areas of the original equilateral triangle PQR (step 1) to the final Reuleaux triangle (step 3) in the Reuleaux triangle article, given that the segment through PQ in step 3 is 1.4 times the length of PQ?

You can leave your responses here.

5. Math movie: How to play a Rubik's Cube like a piano - Michael Staff

How to play a Rubik's Cube like a piano - Michael Staff

This movie explores the connections between Rubik's cube and the group theory concepts behind music.

Math movie: How to play a Rubik's Cube like a piano

6. Final thought: head knowledge or skills?

While conducting training for university teachers recently, I asked them to consider the following:

Employers don't care that much about what new graduates know. They care more about what employees can do with what they know, and their attitude towards doing it.

My point was it doesn't make sense to emphasize head knowledge (which we all forget as soon as we walk out of the examination), rather we should spend more time on developing skills and attitudes (which stay with us for much longer, and become more critical to our success in the future).

Do you agree with me?

I'd like to take this opportunity to wish everyone a Happy New Year, and a peaceful, happy and successful 2016.

The IntMath Newsletter will be back in mid-January.

Until next time, enjoy whatever you learn.

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