The bad haircut

The symmetrical figure bounded by 4 black semicircles is what Archimedes called the “salinon” or “salt cellar”. Show it has the same area as the green disc of the same height.

Scroll down for a solution to this problem.


Solution by Stéphane Bernard.


What has Archimède to do
With haircut ?
It’s the salt on the cake
The salinon in the salted cellar
Maybe salted and pepper
Or white hair
In youth
Tender innocence
In old age
A lot of tenderness
Before cut the hair in four
And solve the problem


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One reply on “The bad haircut”

This problem appears as Proposition 14 in what is known as “Archimedes’ Book of Lemmas”. Apparently, not all scholars agree on the authorship. T.L. Heath says “The probability is that they were propositions collected by some Greek writer of a later date for the purpose of elucidating some ancient work, though it is quite likely that some of the propositions were of Archimedean origin, e.g. those concerning geometrical figures called the shoemaker’s knife and the salinon (probably a “salt-cellar”),…”

Thus, in all probability, Archimedes is the true author of the “Bad Haircut” problem.

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