A Singularity: Finite Function, Infinite Derivatives

AI Thread Summary
The discussion centers on identifying a specific type of singularity where a function remains finite while exhibiting infinite left and right derivatives. Participants confirm that this singularity is known as a "cusp." A link to a Wikipedia page on cusps is provided for further reference. The conversation emphasizes the mathematical properties of this singularity type. Understanding cusps is essential in the study of calculus and singularities.
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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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