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IntMath Newsletter: Computational essays, random numbers

By Murray Bourne, 24 Apr 2018

24 Apr 2018

In this Newsletter:

1. New on IntMath
2. Resources: Computational essays
3. Math in the news: Random numbers
4. Math movies
5. Math puzzle: Parking
6. Final thought: Eating plastic

1. New on IntMath

(a) Updated CO2 graphs

As an example of composite trigonometric graphs, I model the weekly CO2 concentration data as observed in Mauna Loa, Hawaii. I used to create a static graph from time to time, but it was tedious and since the NOAA data is updated regularly, it would become quickly out of date.

CO2 concentration - composite trigonometric graph

So now it makes use of an SVG (scalar vector graphics) image, using the latest data obtained from the NOAA site.

See: Composite Trigonometric Graphs

You may also find the interactive spring activity on that page interesting.

(b) Math Art in Code: Moiré effect

The Moiré pattern is the shimmering effect we see when a repeated pattern (like stripes on a shirt) interact with other similar patterns that are slightly out of phase.

Moire pattern

This animation illustrates Moiré effect. It involves quite simple CSS, and no javascript.

See: Moiré Effect animation

2. Resources

(a) Computational essays

Stephen Wolfram, of Mathematica and Wolfram|Alpha fame, has proposed the idea of a computational essay. Such an essay is interactive, and has great potential for expressing mathematical and scientific concepts more clearly. It has become easier recently to develop such essays.

computational essay example

A computational essay not only contains text and fixed images, but it can contain interactive content that can calculate math expressions, or import and manipulate data.

See: What is a computational essay?

You can author a notebook in the native Wolfram Desktop application (Mac, Windows, Linux)—or on the web through any web browser, or on mobile through the Wolfram Cloud app. Then you can share or publish it through the Wolfram Cloud, and get access to it on the web or on mobile, or download it to desktop or, now, iOS devices.

(b) 10 Award-Winning Optical Illusions and Brain Puzzles

One of the first things you learn in psychology is that your perception of the world is not (necessarily) the same as mine. We all construct a "best guess" at the meaning of what we are looking at, and illusionists make the most of this to trick us.

10 Award-Winning Optical Illusions and Brain Puzzles

These optical illusions come from Champions of Illusion: The Science Behind Mind-Boggling Images and Mystifying Brain Puzzles. Go to:

10 Award-Winning Optical Illusions and Brain Puzzles

3. Math in the news

a. Truly random numbers?

We rely on random numbers a lot, especially for good security on our digital communications. But computers are not very good at producing truly random numbers, it seems.

Any gambling system to be fair needs to be random, but this table for Drawn number frequency for the Singapore Toto shows big discrepancies in frequencies (almost twice the frequency for ball number 46 as for ball 45!).

Up to now, most random number generators are either software- or hardware-based. Neither has produced "truly" random numbers.

random numbers

Quantum methods: What if we use some "spooky action at a distance" (as Einstein called it)?

See: New quantum method generates really random numbers

According to the article, using quantumn approaches provides a superior source of randomness...

... because measurements of some quantum particles (those in a "superposition" of both 0 and 1 at the same time) have fundamentally unpredictable results.

I came across this masters thesis which looked at how good the random number generation process is in Android phones: Analysis of Android Random Number Generator (PDF, 84 pages).

b. IBM research projects: 5 in 5

Here are "5 innovations that will change our lives in the next 5 years", according to IBM researchers.

5 in 5 innovations

The stories include the use of 3D microscopes to clean the oceans, articifial intelligence and quantum computing.

See: Five innovations that will help change our lives within five years

4. Math Movies

(a) OK Go Sandbox - One Moment of Math

OK Go is probably best known for their brilliant one-take music videos, involving extraordinary coordination..

OK Go - One Moment of Math

In "One Moment of Math", we get some insights into the math behind how they designed and implemented the video for The One Moment, released in 2014.

See: OK Go Sandbox - One Moment of Math

Here's the original music clip: OK Go - The One Moment

(b) How many ways are there to prove the Pythagorean theorem? (TED-Ed)

Proofs for the Pythagoras Theorem

There are several ways ti prove Pythagoras' famous result regarding right angled-triangles. This may give you some new insights.

See: How many ways are there to prove the Pythagorean theorem?

I liked the quote at the beginning of this video:

"Reason is immortal, all else is mortal." [Pythagoras]

5. Math puzzles

The puzzle in the last IntMath Newsletter asked about a lost book mark.

There was one correct answer with explanation, given by StevieX.

New math puzzle: Parking

A city block has 12 parking meters in a row. Eight of the parking spaces are occupied by cars. A bus requiring 4 parking spaces is trying to park. Assuming the car drivers chose their spots at random, what is the probality the bus will be able to find a suitable space?

You can leave your responses here.

6. Final thought: Eating plastic

Plastic waste in river
Plastic waste. [Image source]

Most of us have some seafood in our diets. With an estimated 275 tonnes of plastic waste generated worldwide and 10 million tonnes of that washing offshore per year [source], it's likely that we're eating some of it every time we eat seafood.

Litterati is an organisation whose mission is to tackle the problem of litter "one piece at a time". They provide an app that you can use to photograph and tag litter in your own environment. This is a useful piece of data collection and can be a good class project. As Litterati says:

Geotags provide insight into problem areas, while keywords identify the most commonly found brands and products. This data will be used to work with companies and organizations to find more sustainable solutions.

Earth Day was this week. Let's not wait for politicians to do something meaningful about the world's serious environomental problems - let's start doing it ourselves.

[Hat-tip to PiPo for alerting me to some of the items in this Newsletter.]

Until next time, enjoy whatever you learn.

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