Paul Yiu, Elegant Geometric Constructions,
Forum Geometricorum, 5 (2005) 75--96.
Abstract: With the availability of computer software on dynamic
geometry, beautiful and accurate geometric diagrams can be drawn,
edited, and organized efficiently on computer screens. This new technological
capability stimulates the desire to strive for elegance in actual geometric
constructions. The present paper advocates a closer examination of the
geometric meaning of the algebraic expressions in the analysis of a
construction problem to actually effect a construction as elegantly and
efficiently as possible on the computer screen. We present a fantasia of euclidean
constructions the analysis of which make use of elementary algebra and
very basic knowledge of euclidean geometry, and focus on incorporating simple
algebraic expressions into actual constructions using the Geometer's Sketchpad.
[ps file][pdf file] [Geometer's
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