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Convergence articles

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Given the frustum of a circular cone with height h.
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
Illustration of a counting board in Strasbourg
Download the three winning essays to learn about Kepler's mathematical astronomy, the roots of modern algebra, and the Quadrivium of Isidore of Seville.
I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.
The first page of Pathway to Knowledge by Robert Recorde (1510-1558). A version of Euclid's Elements, with commentary by Recorde to make it easier to understand. This page includes Euclid's first three postulates.
A biography stressing Agnesi's deep commitment to help those in need.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
There is a mound of earth in the shape of a frustum of a cone.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.