Talk:Apothem
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[edit] Contradiction
- "Regular polygons are the only polygons that have apothems. Because of this, all the apothems in a polygon will be congruent and have the same length."
- "A triangle has four centers, circumcenter, incenter, centroid, and orthocenter. The center that is used to find the apothem is the incenter."
1 renders 2 a null statement, since for an equilateral triangle all centres coincide. I can therefore make out only that either:
- whoever wrote 1 was considering a triangle not to count as a polygon, which contradicts the view taken at Polygon, and that the definition of apothem treats triangles specially
- somebody just didn't know what he/she was talking about
What is correct? ISTM the real definition of apothem should be a generalisation of both statements: for any polygon that has an inscribed circle (to which every side is a tangent), a radius of this circle that meets a side of the polygon (and is therefore perpendicular to it). But can anybody find a good source on the term? (MathWorld contradicts itself too - it defines the apothem of a general regular polygon as the same as the inradius, which it defines only for general triangles and polyhedra.)
On the basis of this definition, all apothems of a given polygon are the same length not for the reason given in 1, but because they are radii of the circle. What was the writer of 1 (mis)using congruent to mean, anyway? -- Smjg (talk) 11:46, 12 February 2009 (UTC)
