The Lost Daughters of Gergonne
نویسندگان
چکیده
Given a triangle center we can draw line segments from each vertex through the triangle center to the opposite side, this splits the triangle into six smaller triangles called daughters. Consider the following problem: Given a triangle S and a rule for finding a center find a triangle T , if possible, so that one of the daughters of T , when using the rule is S. We look at this problem for the incenter, median and Gergonne point.
منابع مشابه
Iterated triangle partitions
For a given triangle there are many points associated with the triangle that lie in its interior; examples include the incenter (which can be found by the intersection of the angle bisectors) and the centroid (which can be found by the intersection of the medians). Using this point one can naturally subdivide the triangle into either three or six “daughter” triangles. We can then repeat the sam...
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