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Mathematical Objects: Arbelos with Catriona Agg

Mathematical Objects

A conversation about mathematics inspired by an arbelos. Presented by Katie Steckles and Peter Rowlett, with special guest Catriona Agg.

Catriona mentions this proof without words, which is taken from Proof Without Words: The Area of an Arbelos by Roger B. Nelsen in Mathematics Magazine.

arbelos
Arbelos by Catriona Agg

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Mathematical Objects: Solids of constant width

Mathematical Objects

A conversation about mathematics inspired by some solids of constant width. Presented by Katie Steckles and Peter Rowlett.

Solids of constant width
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Mathematical Objects: Twenty Pence coin

Mathematical Objects

A conversation about mathematics inspired by a Twenty Pence coin. Presented by Katie Steckles and Peter Rowlett.

twenty pence coin
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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.

Curvahedra Geometry

Longtime friend of the Aperiodical, artist, mathematician and #BigMathOff semifinalist Edmund Harriss has come up with a new puzzle/toy/exploration set, developing his Curvahedra system. We asked him to explain the maths behind it in this guest post.

Curvahedra is a flexible system of connectors that can make all sorts of different things, combining puzzles (and self-created puzzles) with art. You can get your own to play with, explore, prepare for Christmas (they make great decorations, wreaths and presents) at our online store, and get 15% off with the discount code APERIODICAL.

As this is the Aperiodical, you might be most interested in how it can be used to explore mathematics. In the big math off I talked about the basic ideas behind the system, Gauss’ famous Theorema Egregium and Gauss-Bonnet theorems. A really simple version of this comes from just considering triangles, that can be built up to make this:

 

Review: Geometry Snacks, by Ed Southall and Vincent Pantaloni

Geometry Snacks cover

Exams have a nasty habit of sucking the joy out of a subject. My interest in proper literature was dulled by A-Level English, and I celebrated my way out of several GCSE papers – in subjects I’d picked because I enjoyed them – saying “I’ll never have to do that again.”

Geometry is a topic that generally suffers badly from this – but fortunately, Ed Southall and Vincent Pantaloni’s Geometry Snacks is here to set that right.

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