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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.

@standupmaths’ petition has had a response from the government

Ewood Park football ground sign

Friend of the site Matt Parker recently made headlines because of his UK Government Petition to correct the heinous geometrical oddity that is the UK Tourist sign for a football ground. In the standard sign, somehow a sheet of tessellating hexagons is depicted as wrapping around a sphere in a highly improbable (and provably impossible) way.

The petition has achieved a modicum of success, in that it’s passed the 10,000 signatures required to elicit a response from the government. Sadly, the response isn’t quite what you’d like to hear.

Petition to update UK traffic signs to use a geometrically plausible football

Terrible signage (photo: The Independent)

Aperiodipal and number ninja, Stand-up Mathematician Matt Parker, has set up a petition on the UK parliament petitions website to change the awful, awful tourist board official symbol for a football ground (US readers: imagine I’m saying ‘soccer stadium’). In Matt’s words:

The football shown on UK street signs (for football grounds) is made entirely of hexagons. But it is mathematically impossible to construct a ball using only hexagons. Changing this to the correct pattern of hexagons and pentagons would help raise public awareness and appreciation of geometry.

Matt holding a football and pointing at the offending signTo end this madness, Matt needs 10,000 signatures for the petition to be responded to by the government (and 100,000 for it to considered for debate in parliament). It’s currently around the 3,000 mark – so it’s plausible that he might do it. It’s also had coverage in The Independent already, and Matt’s YouTube video on the campaign already has over 100,000 views.

To sign, you simply need to be a British citizen or UK resident, and fill in your details on the site (you’ll need a valid postcode). Ban this hexagonal filth!

Update the UK Traffic Signs Regulations to a geometrically correct football, on UK Parliament Petitions

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