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Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
A Mathematician's Apology, London, Cambridge University Press, 1941.
Loci: Convergence
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An Investigation of Historical Geometric Constructions
Conclusion and References
Although the three famous geometric construction problems are closely linked, we choose to deeply examine the trisection of an angle and the quadrature of the square with the use of dynamic geometry software. The dynamic capabilities of Sketchpad allow a user to analyze endless representations of trisecting an angle and calculating the area of a lune. Having opportunities to dynamically investigate these constructions may be extremely beneficial for students to visualize the construction beyond one static example to multiple dynamic examples.
References
Burton, D.A. (2003). The history of mathematics: An introduction (5th ed.). New York: McGraw-Hill.
Cajori, F. (1924). A history of elementary mathematics with hints on methods of teaching. Rev. and enl. Ed. New York: MacMillan.
Heath, T.L. (1921). A History of Greek Mathematics (vol. 1). New York: Oxford University Press.
Heath, T.L. (1963). Greek mathematics. New York: Dover.