the center of gravity of polygonal regions and conic sections ( hal 84-93 )
Tilak de alwis;
8th asian technology conference 2003 in mathematics tecnology connecting mathematics desember 15-19,2003 chung hua university,hsinchu taiwan,r.o.c.
Lokasi : Perpustakaan Fakultas Ilmu Komputer
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in this paper, we will consider the center of gravity, or the center of mass, of several types of polygonal regions in the XY-plance. in order to calculate the center of grafity of such regions, instead of techniques from calculus, one can conveniently use geometric ideas. our regions are of grafity of a certain region that we will consider turns out to be a hyperbola with axes parallel to the coordinate axes. this observation can be reversed to come up with a new definition for a hyperbola, without involving eccentricity. we will use this new definition along with the dynamic geometry softwar geometer's sketchpad to present a novel construction of a hyperbola. the locus of the center of grafity of some other polygonal regions yield other types of interesting curves as will. in addition to geometer's sketchpad, we have also used the computer algebra system mathematica to facilitate the center of gravity calculations. the paper also shows the importance of using different types of software hand-in-hand to experiment with mathematical problems.