Studying Synthetic Geometry with Technology
Jen-chung Chuan
Department of Mathematics
National Tsing Hua University
Hsinchu, Taiwan 300
jcchuan@math.nthu.edu.tw
Abstract
Synthetic geometry is a branch of geometry that relies on the visual observation of figures and can be developed independently of number concepts and of algebraic notions. In the late nineteenth century synthetic geometry was developed to full perfection. During the twentieth century, however, the analytic aspect of geometry became the mainstream while the synthetic method fell into oblivion. Now a new kind of software, collectively referred to as dynamic geometry, is again arousing people's interest towards synthetic geometry.
In what follows we shall show how synthetic geometry can be investigated profitably under the environment of one dynamic geometry software, the Geometer's Sketchpad. Three examples, one from the area of elementary mathematics, one from the area of advanced mathematics, and one from the area of the linkage design, are given.
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