Apollonius' Circle Construction Problems - Famous Math Problems

Explore the fascinating world of Apollonius' circle construction problems in this 44-minute video lecture. Delve into the history and solutions of these famous geometric challenges, dating back to 200 B.C. Learn about Euclid's approach to two of the problems and gain insights into relevant circle geometry concepts, including the Subtended spreads theorem, power of a point, pole-polar duality, and inversion. Discover the educational and theoretical importance of geometric constructions, and understand how modern mathematics can benefit from revisiting ancient Greek and 17th-18th century approaches to mathematical objects. Challenge yourself with this problem set, ranging in difficulty from 1 to 5, and enhance your understanding of geometry through this comprehensive exploration.