Tag Archives: angles

“Parabolas of Apollonius?” Spoiler

Posted on July 10, 2012 by

This is an answer to the question posed in Parabolas of Apollonius? which was inspired by Maria Monk’s blogpost on the Circles of Apollonius.

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Parabolas of Apollonius?

Posted on July 3, 2012 by

This question is inspired by Maria Monks’ blog post on the Circles of Apollonius. Pictured above are some parabolas from two families of parabolas. The Blue Family is given by the parabolas , for . The Red Family is given … Continue reading →

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Back to Basics: Arctangent

Posted on February 3, 2012 by

Recently, a student asked me about problem #8 on the 2008 AIME 1 competition, which is reproduced here for your convenience: Find the positive integer such that . She was able to solve this using the sum of arctangents identity … Continue reading →

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Stereographic Projection is Conformal

Posted on October 11, 2011 by

In Hana Kitasei and Tim Reckart’s animated video, Summer Vacation, Angela says that stereographic projection preserves angles. Here’s a proof.

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