Banoffee pie: mathematical musings

This evening I made a banoffee pie, and at every stage I wondered about the mathematical questions I could be asking about the process…

Background: One of my Sixth Form classes has a rota declaring whose turn it is to bring in cake each week. A few weeks back, I made a banoffee pie that was decorated with a mathematical chocolate chip pattern (specifically, a dissection of the circle into congruent pieces that do not all meet at the centre).


Since then, the mathematical theme has escalated. Pupils have brought in, amongst other things, a Rubix cube, a Penrose tiling and a cakeulator:

Now it’s my turn again, and I spent a while trying to find some new ideas (the empty cake was high on my list of possibilities, having seen it as an entry in a MathsJam baking competition). Eventually I settled on making almost exactly the same thing as before, but with added mathematical questioning:


1. At what angle did I take this photo?



2. Use this image to find an approximation for the value of pi.



3. How thick will the layer of caramel be?



4. How many slices of banana will I need?



5. Why is there this curve of light in my cream?



6. What is the scale of this photo? Give the approximate area in terms of banana slices.



7. If I were to keep making stars inside stars in this way, what would be the total length of the edges? (unit: chocolate chip widths)



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