With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner (1961, p. 34), Stewart (1987, p. 169), and Wells (1991, pp. 61-62). The solution can be hinged so that the four pieces collapse into either the triangle or the square. Two of the hinges bisect sides of the triangle, while the third hinge and the corner of the large piece on the base cut the base in the approximate ratio 0.982:2:1.018.
Explore with Wolfram|Alpha
ReferencesChuan, J. C. "Geometric Construction." http://www.math.ntnu.edu.tw/gc/chuan/gc.htmlDudeney, H. E. Amusements in Mathematics. New York: Dover, p. 27, 1958.Frederickson, G. N. Hinged Dissections: Swinging and Twisting. Cambridge, England: Cambridge University Press, 2002.Gardner, M. "Mathematical Games: About Henry Ernest Dudeney, A Brilliant Creator of Puzzles." Sci. Amer. 198, 108-112, Jun. 1958.Gardner, M. The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York: Simon and Schuster, 1961.Stewart, I. The Problems of Mathematics, 2nd ed. Oxford, England: Oxford University Press, 1987.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 61-62, 1991.
Referenced on Wolfram|AlphaHaberdasher's Problem
Cite this as:
Weisstein, Eric W. "Haberdasher's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HaberdashersProblem.html