Wednesday 18 June 2014

The Maths of cutting cakes


Known on YouTube as Numberphile, Bellos first explained the problems with modern methods of cutting cakes.
Namely, he said that if a wedge is taken out of a cake but the rest of the food is then stored in the fridge, the edges of the cake open to the air will be ‘dry and horrible’, Bellos says.
‘You’re not maximising the amount of gastronomic pleasure that you can make from this cake.’
 
    There is instead, he explained, a better way of cutting cakes that dates back more than a century. 
    The method was first published in Nature on 20 December 1906 in the letters to the editor section by English mathematical scientist Francis Galton.
    Titled ‘Cutting a round cake on scientific principles’, Galton’s letter explained how the ‘ordinary method of cutting out a wedge is very faulty’.
    He went on to state the cake should be cut in parallel lines, starting in the centre, with the rectangular segments of the cake then taken out and eaten.
    This would allow the cake to then be closed, provided it is one with icing, keep the sponge inside sealed and retaining its freshness.

    HOW TO CUT A CAKE: FRANCIS GALTON'S METHOD PUBLISHED IN 1906

    Galton's original method redrawn
    'Christmas suggests cakes, and the wish on my part [is] to describe a method of cutting them that I have recently devised to my own amusement and satisfaction.
    'The problem to be solved was, "given a round tea-cake of some 5 inches across, and two persons of moderate appetite to eat it, in what way should it be cut so as to leave a minimum of exposed surface to become dry?"
    'The ordinary method of cutting out a wedge is very faulty in thi s respect. The results to be aimed at are so to cut the cake that the remaining portions shall fit together.

    'Consequently the chords (or the arcs) of the circumferences of these portions must be equal.
    'The direction of the first two vertical planes of section is unimportant; they may be parallel, as in the first figure, or they may enclose a wedge. 
    'The cuts shown on the figures represent those made with the intention of letting the cake last for three days, each successive operation having removed about one-thi rd of the area of the original disc. 
    'A common india-rubber band embraces the whole and keeps its segments together.'
    Stop, you're doing it all wrong! The 'new' method of cutting cakes was actually first described in a letter to the journal Nature on 20 December 1906. The modern method of cutting cakes into wedges has not seemingly been under much scrutiny, but perhaps this new technique will provide a useful alternative
    Stop, you're doing it all wrong! The 'new' method of cutting cakes was actually first described in a letter to the journal Nature on 20 December 1906. The modern method of cutting cakes into wedges has not seemingly been under much scrutiny, but perhaps this new technique will provide a useful alternative
    It is also recommended an elastic band is used to hold the cake together and keep it sealed.
    ‘I don’t know if you’ve thought about it before but these triangular slices are really annoying anyway because it’s not very satisfying,’ Bellos added.
    In reference to the new method he said having ‘a nice uniform slice like that is a lot better.’
    But, he concluded, most people choose to share their cakes rather than eating it themselves, meaning not much or any of it is often stored.
    ‘I think for the mathematical loners who don’t want to share their cakes it could be useful,’ he joked.


    Read more: http://www.dailymail.co.uk/sciencetech/article-2661278/Think-know-cut-cake-Think-Scientist-reveals-100-year-old-trick-involving-parallel-lines-rubber-bands.html#ixzz3509or8Fb
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