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IntMath Newsletter: Quadratrix, resources, news

By Murray Bourne, 15 Jan 2020

15 Jan 2020

In this Newsletter:

1. New on IntMath: Quadratrix, quadratic
2. Resources: Desmos, e-book
3. Math in the news: Review and teaspoon
4. Math movies: Coin, key
5. Math puzzle: Race
6. Final thought: Real cost

1. New on IntMath

(a) Quadratrix of Dinostratus

Challenge: Using only a straight edge and compasses,

  • Trisect an angle (divide it evenly into 3)
  • Square a circle (construct a square with the same area as a given circle)

Don't work too hard on it, since neither is possible. The ancient Greek mathematicians put quite a bit of effort into solving these two problems.

Quadratrix of Dinostratus

One of the approaches Hippias and Dinostratus used was to construct a quadratrix curve.

See: Quadratrix of Dinostratus and Tschirnhaus

The page has animations of how the curve is constructed, and some background.

(b) Solving quadratic equations - Po-shen Loh's method

I noticed a lot of my students would rather use the Quadratic Formula rather than solving a quadratic by factoring. One big reason for this is factoring can involve an amount of guesswork (finding 2 numbers that add to a certain number, and whose product is another number).

Mathematician Po-shen Loh recently outlined a method (not entirely original, and somewhat similar to completing the square method) which does away with the guesswork.

Solve quadratic equations Po-shen Loh method

I added his method as alternative solutions in IntMath.

See: Solutions for Examples 4 and 5, and Exercise 2 on the page:

Solving Quadratic Equations by Factoring

Po-Shen Loh is associate professor of mathematics at Carnegie Mellon University.

2. Resources

(a) Desmos Webinars

Desmos, the excellent free online graphing site, is offering some free Webinars over the next few weeks.

Desmos Webinars

These ones are mostly for teachers who want to create activities on Desmos.

You can see details here: Desmos Webinars

There are sessions on 14 Jan, 21 Jan and 28 Jan. Don't miss the links to recordings of previous seminars on the same page.

(b) e-book: A Programmer's Introduction to Mathematics

This is an interesting book, targeted at programmers, which aims to "show how to engage with mathematics".


The book is by Jeremy Kun, engineer at Google.

See: Pimbook

You'll find:

  • A (free) preview of the book
  • A "pay what you want" PDF version of the whole book
  • Demos of the concepts in the book

3. Math in the News

(a) The Year in Math and Computer Science

Mathematics is not a static thing. New discoveries and ways of thinking about old problems occur all the time.

The year in mathematics and computer science

Here's a review by Quantamagazine of the main developments during 2019.

See: The Year in Math and Computer Science

The discussion about replacing "equality" with "equivalence" is interesting, and reminded me of my rant in The equal sign - more trouble than it’s worth?

(b) Storing YouTube in a teaspoon of DNA

We're heading for a "storage crisis". The amount of data generated each year (around 400 zettabytes by one estimate) will mean we won't have enough raw materials to manufacture all the optical and magnetic storage devices needed by the end of the century. We need to find other ways to store data.

One possible solution is to follow nature, and store the massive amounts of data in synthetic DNA. Scientists in Singapore are working on how to reduce the massive costs in such an approach.

data stored in DNA

See: All of YouTube's data stored in a teaspoon of DNA

4. Math Movies

(a) The coin flip conundrum

Proability has a knack for throwing up counterintutitive situations.

Coin flip conundrum

This TED-Ed video is an exploration of extensions to the simple coin flip.

See: The coin flip conundrum

(This video is by Poh-shen Loh whose quadratic equation approach I mentioned above.)

(b) In the Key of Genius

I've been fascinated with savantism for a long time. Savants demonstrate extraordinary mathematical, artistic or musical abilities.

In the Key of Genius: Derek Paravicini

Derek was born prematurely and is blind, had learning difficulties, autism but also amazing musical abilities, including perfect pitch and improvisation skills.

See: In the Key of Genius: Derek Paravicini

So it begs the question - are we all born with such abillities and it just happens that some of us get to express them, while most of us don't?

5. Math puzzles

The puzzle in the last IntMath Newsletter involved a substitution cipher. No-one actually had a go at it (I know there are a lot of distractions in December...) so I'll leave it there and give you another chance to solve it.

New math puzzle: A race

math puzzle race

Alana, Bob and Chaitali are running against each other in pairs over a 2 km distance. If Alana can beat Bob by 100 m, and Bob can beat Chaitali by 200 m, by what distance could Alana beat Chaitali (assuming their speeds are constant)?

You can leave your responses here.

6. Final thought - Paying the real cost

subsidise fossil fuels

The "real" cost of any commodity should include the negative impacts the extraction and processing of that commodity have on all of us - the environment, our health, our future.

The IMF estimated that, in 2017, global fossil fuel subsidies grew to $5.2 trillion, or 6.5% of global GDP. [Source]

Why are we subsidising fossil fuel companies at all?

There are so many better things governments could be doing with our tax money...

Until next time, enjoy whatever you learn.

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