To Be Presented in the 11th Asian Technology Conference in Mathematics December 12-16, 2006, Hong Kong SAR, China |
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## A Problem of Wetzel's: Fitting Triangle in a RectangleLu Yangluyang@casit.ac.cnInst. of Educational Softwares Guangzhou University
## Abstract A solution to a problem from elementary geometry is
presented: a set of polynomial inequalities describing a necessary and
sufficient condition for a triangle to fit into a rectangle (given in
terms of side lengths). First the possible configurations of the largest
similar triangles are classified, then for each of the three classes necessary
conditions for the largest similar triangle to fit into the rectangle
are derived and shown to be sufficient and finally the obtained conditions
are combined. The initial inequalities contain a parameter and (in one
case) two additional variables which are eliminated to obtain the final
result. |
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