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Geogebra to Cake in Five Steps

Flower design using Reflect Object in Circle tool in Geogebra
Tessellated squares design using Reflect Object in Circle tool in Geogebra

In the Aperiodical’s Big Internet Math-Off 2019, Becky Warren posted an entry about Geogebra’s ‘reflect object in circle’ tool (it’s the second article in the post). I enjoyed playing with the tool and, after making a few colourful designs, it occurred to me that one of them would make a great cake for the MathsJam bake-off. It would only work if the curves were accurate; sadly this would be beyond my drawing abilities, and definitely beyond my piping abilities. But with some help from 3D printing I thought I might be able to manage it.

Here are the steps I used to transfer the design to a cake.

That which we call an identity

I’m grateful to Jemma Sherwood and Rob Low for reading an early draft of this and for their comments thereon. All opinions are, of course, my own.

This post is inspired by something that I see crop up now and again in discussions with other Maths teachers. It usually manifests itself as a rallying cry to use ≡ in place of = in identities and reserve = for equations. My standard response is to mutter something about identities being equations and leave it at that. But in the latest round, Jemma Sherwood challenged me, in the nicest possible way, to explain a bit further. This is that explanation.

Although I’m going to state my case here, I’m well aware that there are different opinions. In matters of opinion, such as this, agreement and disagreement is less important than that all sides think. So if what I write seems to you wrong, that’s fine so long as it makes you think about why you think that it is wrong.

Small Sets of Arc-Sided Tiles

Tim has previously written guest posts here about tiling by tricurves, and is now looking at ways of tiling with other shapes.

In an earlier post elsewhere I covered some basic arc-sided shapes that tile by themselves. Lately I’ve been playing with groups of curved tiling shapes, asking a question common for me: how to get the most play value as an open-ended puzzle? This means getting the most interesting possibilities from the simplest set. “Interesting” includes variety, complexity, challenge and aesthetic appeal. “Simplest” covers not only size of set and the shapes, but also the least total information needed to describe or construct the shapes.

The Maths of Life and Death – The God Equation

Aperiodicolleague Kit Yates has recently had a new book out: The Maths of Life and Death. He’s kindly agreed to share a sample chapter with us, explaining the God Equation: it’s used by NICE to decide whether to fund new drugs.

In my new book, The Maths of Life and Death, I explore the true stories of life-changing events in which the application (or misapplication) of mathematics has played a critical role: patients crippled by faulty genes and entrepreneurs bankrupt by faulty algorithms; innocent victims of miscarriages of justice and the unwitting victims of software glitches. I follow stories of investors who have lost fortunes and parents who have lost children, all because of mathematical misunderstanding. I wrestle with ethical dilemmas from screening to statistical subterfuge and examine pertinent societal issues such as political referenda, disease prevention, criminal justice and artificial intelligence. I aim to demonstrate that mathematics has something profound or significant to say on all of these subjects, and more.

High definition

We asked #bigmathoff competitor Lucy Rycroft-Smith to tell us a little about her latest project – CM Define It, an app aiming to collect and define mathematical vocabulary, which launches today.

When you teach mathematical vocabulary, how do you define its meaning?

Are you exact, choosing your words specifically?  Do you give a written definition?  Do you give multiple explanations?  Do you use diagrams?  Metaphors? Connect to previous vocabulary?

As part of our work at Cambridge, creating a Framework for mathematics learning, we are creating a network of semantic links across nodes in our mathematical layer – and we initially thought we could just import a mathematical glossary from somewhere else to populate this.  But we found so many inconsistencies, technical errors, and definition loops in many existing glossaries that we decided to make an app to ask the mathematical community what they thought, with the aim of developing a crowdsourced, multi-layered collage which takes into account different layers of mathematical experience.

MathsJam’s “Back of an Envelope” Fermi Challenge

Aperiodipal and MathsJam regular Rob Eastaway organised an inter-MathsJam competition for last month’s events, challenging Jams to make Fermi estimates on the back of an envelope. The prize was a copy of his new book, Maths on the Back of an Envelope. Here Rob gives a summary of the entries he received, and shares his favourites.

Regular attendees of MathsJam will know that in September, Katie Steckles kindly allowed me to hijack the evening (in the nicest possible sense) by posing some envelope-related challenges, in celebration of the publication of my new book Maths On The Back Of An Envelope. In addition to some envelope-related puzzles, there was also an open challenge to Maths Jam groups to come up with their own back-of-an-envelope problems, with the chance to win the book as a prize.

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