Saturday, April 02, 2011

Puzzling Week Returns: Coxeter's Pippin

Apples (1 of 4).jpg
Peeled & equatorially cut apples ready to be cored for making apple slab.
January 24, 2011

John and I peel dozens of apples for pie, sauce, and slab. Depending on the size and quality of the apples, we will either peel and core by hand (with or without a corer) or by crank. John recently taught me that cutting apples equatorially and then coring them takes less time then the traditional cutting and coring. I have often wondered if there was an even easier or better way than all of the methods we have tried. I found a way tonight! But this is a puzzle. Your clue is the photo I took (above) of equatorially cut apples from January when I made two huge slabs for the weekend. By the way, I no longer use the King Arthur slab recipe. I double a pie crust recipe for a double 9” pie, use a 13x9 Pyrex pan, and just make an apple pie (butter, flour, brown sugar, cinnamon, nutmeg, ginger, cloves are all measured by feel and sight) in the rectangular Pyrex.

New Scientist Magazine December 21, 1961

There are many ways of eating an apple. At one extreme is the child who met the request, "Can I have the core of your apple?" with a flat, "There ain't going to be no core!". Various procedures with various implements are designed to remove the core, but probably not one apple in a million is cored in the most efficient fashion possible. How in fact should an apple be cored, to remove all the core with the least possible waste?

Spoiler Alert! The answer is the first comment to this post.

_/\_/\_

1 comment:

  1. The solution to Coxeter's Pippin:
    New Scientist, December 21, 1961:

    Internally, an apple retains the pentagonal symmetry of the apple blossom, and to a first approximation this core is a void in the shape of a doubly tapering cylinder with a pentagram section; this is surrounded by a hard internal skin, and it contains the pips. Cut the apple equatorially first: this exposes the orientation of the pentagram. Make five radial cuts on each piece, through the points of the pentagram; pips will fall out, and the internal skin can be removed with as little waste as with the outer skin. (With acknowledgments to Professor H. S. M. Coxeter, and his Introduction to Geometry — a book to be recommended!).

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