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).

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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:

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1. At what angle did I take this photo?

 

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

 

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3. How thick will the layer of caramel be?

 

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4. How many slices of banana will I need?

 

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

 

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

 

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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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