# You're reading: Posts Tagged: Geometry

### Geogebra to Cake in Five Steps

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.

## Step 1 (Geogebra) – Save as an image

I started by simplifying the design. Squares are straightforward, so I only needed the part within the centre circle. I hid all the squares and removed all the colours, then thickened the lines to make them easier to see. Finally, I took a screenshot and saved it as a bitmap image.

## Step 2 (Inkscape) – Convert image to path and generate scad

The next step was to use Inkscape to convert the image into an OpenSCAD file that can be used for 3D printing. If you google ‘Inkscape OpenSCAD’ you’ll find several extensions that will do this; I used Paths2OpenSCAD.

To generate the scad, start by importing the image into Inkscape. Then, with the image selected, go to Path > Trace Bitmap. This opens up a window with lots of options; accept the default and click OK, then close the window. Inkscape has now converted the image into a vector path; this means that it has coordinates for each point on the path.

Now go to Extensions > Generate from Path > Paths to OpenSCAD. This opens up another window. In the output file box, enter the location to save the scad file, then click OK. Now you can open the file in OpenSCAD.

## Step 3 (OpenSCAD) – Scale design

The generated OpenSCAD file starts like this.

It has a method called ‘poly_path854’ (a new number is generated for each file). This method uses the coordinates of the points on the path from Inkscape to make a polygon in OpenSCAD.

Pressing F5 to preview shows a replica of the image, rendered as a 3D model.

At the very end of the file is a line that calls the ‘poly_path854’ method, passing in a number. The number is the height of the object when printed – you can change this to suit your needs.

The part that I found difficult was to work out the size the model would be when it was printed. The axes on the OpenSCAD preview window give some indication, but it’s not possible to read accurate values from it. I wanted my model sized appropriately to match a square cutter that I already owned. In the end, I printed out a 1 mm high model so that I could measure the original size without wasting too much plastic, then I scaled the entire model to match the square cutter. The final line of the file became

scale([6/(4.2*sqrt(2)),6/(4.2*sqrt(2)),1]){
poly_path854(5);
}

## Step 4 – Print

I sent the model to the printer, and a few hours later I had my cutter!

## Step 5 – Imprint on cake

Once I had baked the cake and covered it in fondant, I used the cutter to make an imprint of the design on the icing.

Now it only remained to cut the squares around the edges and give it some colour. I used a small amount of vodka to thin out paste food colouring so that I could paint on the fondant icing. (Honestly, it was a tiny amount of vodka – less than 5 ml over the entire cake.)

That’s it! Geogebra to cake in five steps. Here’s the finished cake, alongside the original design in Geogebra.

### 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

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

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

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.

To 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

### Curvahedra is a construction system for arty mathsy structures

Edmund Harriss is a very good friend of the Aperiodical, and a mathematical artist of quite some renown. His latest project is CURVAHEDRA, a system of bendable boomerang-like pieces which join together to make all sorts of geometrical structures.

### Ohioans measure a really big π

Ohio State University mathematician Niles Johnson got in touch on Friday to tell us that our π Approximation Challenge last year had inspired him to hatch an audacious plan to measure a really big π.

The word ‘geometry’ is derived from the Greek for ‘measurement of land’, and Dr. Johnson took that quite literally: he wanted to measure the Great Circle Earthworks in Heath, Ohio; a part of the Newark Earthworks (not their original name) built over 2,000 years ago.