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WikiProject Mathematics (Rated Start-class, Mid-importance)
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 Field: Geometry

area property -- why multiply out?[edit]

The proof given seems overly complicated.

The area of the circle of diameter h is pi h^2 / 4.

The area of the arbelos is pi/8 - pi r^2/8 - pi (1-r)^2/8

The pythagorean theorem on BHC implies that x^2 + y^2 = 1. But x^2 = r^2 + h^2, and y^2 = h^2 + (1-r)^2.

Thus r^2 + 2h^2 + (1-r)^2 = 1, which implies that h^2 = 1/2 (1 - r^2 - (1-r)^2), and thus pi h^2/4 = pi/8(1 - r^2 - (1-r)^2). QED.

(I'd be tempted to replace "r" and "1-r" with "a" and "b"; r isn't a radius, and the fact that the diameter of the second circle is related to r is only needed in setting up the triangle BHC.) —Preceding unsigned comment added by (talk) 17:10, 8 February 2011 (UTC)

Cannot find alleged Greek misspelling[edit]

The previous version of the article had the word "arbelos" in Archimedes' blockquote spelled in Greek letters "αρβελοσ":

[ ... ] the three semicircles is [what Archimedes called "αρβελοσ"{{sic}}]

with the following invisible comment appended to it:

αρβελοσ instead of ἄρβηλος/ἄρβυλος — a typo in the article; see MOS:QUOTE

The reference given for the blockquote is an archive copy of a Cut-the-Knot article on the arbelos, but I cannot find the alleged misspelling there: the name is in Roman letters, "arbelos". Is "αρβελοσ" a misspelling in the original translation by T. L. Heath, The Works of Archimedes? I do not have access to it unfortunately. I am leaving the Roman version and deleting the comment until the issue is clarified. --Jorge Stolfi (talk) 21:18, 8 October 2014 (UTC)

For whatever it's worth, the only αρβ-word in Liddell & Scott's dictionary is αρβύλη or αρβυλί(δ)ς, "a strong shoe or half-boot, used by country-people, hunters, travellers". —Tamfang (talk) 21:51, 8 October 2014 (UTC)