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The ‘hitchhiker triangle’ and the problem of perimeter = area. (English) Zbl 1384.51006

From the text: The triangle with sides \(a=7\), \(b=15\), \(c=20\) is a curious one. It has both perimeter and area equal to 42. In his Hitchhiker’s guide to the galaxy Douglas Adams thought ‘42’ the ‘answer to the ultimate question of life, the universe, and everything’ and it has achieved cult status. For this reason, we may term this particular triangle the ‘hitchhiker triangle’.{ } The investigation of integer-sided triangles with perimeter = area originated in the nineteenth century with mentions in the Lady’s diary (1828) and the Lady’s and gentleman’s diary (1865). In 1904 William Allen Whitworth (1840–1905) and Daniel Biddle (1840–1924) added to triangle lore by proving the startling result that there are exactly five such triangles with this property, one of which is the hitchhiker triangle.

MSC:

51M04 Elementary problems in Euclidean geometries

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References:

[1] 1.Problem 2012.5Math. Gaz.97 (March 2013) p. 185.
[2] 2.DicksonL. E., History of the theory of numbers, vol. 2Carnegie Institute of Washington (1919) pp. 180, 195, 199.
[3] 3.WhitworthW. A., Mathematical questions from the Educational Times, vol. 5, pp. 62-63 (1904).
[4] 4.BiddleD., Mathematical Questions from the Educational Times, vol. 5, pp. 54-56 (1904).
[5] 5.SloaneN. J. A., The on-line encyclopedia of integer sequences, accessed June 2015 at: http://oeis.org/A057721 · Zbl 1044.11108
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[7] 7.SloaneN. J. A., The on-line encyclopedia of integer sequences, accessed June 2015 at: http://oeis.org/A120062 · Zbl 1044.11108
[8] 8.ReadEmrys, On integer triangles, Math. Gaz. 98 (March 2014) pp. 107-112.
[9] 9.MarkovL., Heronian triangles whose areas are integer multiples of their perimeters, Forum Geometricorum, 7 (2007) pp. 129-135. · Zbl 1162.51007
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