# Sam Hartburn

sam@samhartburn.co.uk

# Hyperbolic Paraboloid in Matchmakers

For this year’s MathsJam Bakeoff I made a hyperbolic paraboloid out of matchmakers. For anybody who doesn’t know, matchmakers are thin chocolate sticks with crunchy bits, traditionally mint but now available in orange, salted caramel and possibly other flavours. They are delicious even when they are not being used for maths.

Matchmakers are not strong. They snap easily. They are not ideal for building with. It took some experimentation to get it to work, so here are some tips for anybody who is interested in matchmaker construction.

## Structure

The key to getting the whole thing to stand was a strong base structure. I pushed the uprights as far into the cake as possible to keep them vertical. The diagonal supports are also pushed slightly into the cake. Most importantly, they are all held in place with blobs of fondant icing. It looks ugly (and I wish I had coloured it brown to match the chocolate) but this was the only thing I found that stopped the base collapsing as soon as I put any weight on it.

## Glue

To stick the cross pieces in place I tried:

• glacé icing
• melted Curly Wurly
• chocolate ganache
• edible glue

Glacé icing was by far the most successful, but it needed to be very thick. Add as little water as possible. The wetter it is, the more likely the matchmakers are to slide down to cake level.

## Construction

The steps I used for construction are as follows.

1. Push the vertical supports into the cake, one matchmaker-length apart.
2. Add the diagonal supports. The points where these touch the cake should also be one matchmaker-length apart.
3. Secure all the supports with fondant icing.
4. Use glacé icing to glue a matchmaker to two opposite diagonal supports, going from the top of one to the bottom of the other. Continue to glue matchmakers across these supports, placing them equal distances apart, until you reach the other end.
5. Repeat the process for the other pair of diagonal supports. Your glacé icing blobs for these supports will need to be thicker to make up for the fact that matchmakers have a particular property that mathematical lines do not – thickness.
6. Enjoy your hyperbolic paraboloid in all its glory!

## Alternatively…

If you prefer not to use matchmakers, you could always construct your cake in Geogebra. Download the applet

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## Comments

### One response to “Hyperbolic Paraboloid in Matchmakers”

1. Jody Walker

I’d like to make a curve of pursuit (square – 4 vertices) using only a single piece of paper. I’m planning to glue thin strips (probably about a 8mm wide) end to end to create a single long strip of multiple colours. I think that will look so pretty! I’ve found a ton of resources that are helpful for drawing, but none that helped me figure out exactly how long I will need to make my strip and how far apart I would need to make each of my individual folds. This is probably because although I want it to take the form of a curve of pursuit, it won’t actually be one! The one I’d like to make first is very small – around 40mm x 40mm square with just a few mm of spacing between each square as they wind towards the centre. I can draw this and take the measurements, but I’d like to have a way of finding the precise measurements for squares of different sizes without having to draw and measure each one first. Do you have any ideas? I did not take trigonometry in school and I’ve actually just now come to regret it! LOL I sadly don’t even know which buttons to push on the calculator to try out any formulas that I’ve seen! I would be grateful for any advice!

Hello! I’m Sam Hartburn, a freelance maths author, editor and animator. I also dabble in music and write mathematical songs. Get in touch by emailing sam@samhartburn.co.uk or using any of the social media buttons above.