Famous Modern Math Problems: Squaring a Circle
The quest to solve an ancient problem in mathematics.
It’s been a few weeks since I have been able to continue my series of articles about famous mathematical problems. For today’s discussion, I didn’t exactly pick a modern problem but rather a modernized version of one of the more ancient problems in mathematics. Around 450 BC, Greek mathematician, Anaxagoras of Clazomenae posted a puzzling question about geometry: Using a compass and a straightedge, can you produce a square of equal area to a given circle? That simple problem has sparked variations that have puzzled the mathematicians for centuries.
Anaxagoras’ original problem was solved in 1882 by German mathematician Ferdinand von Lindemann. In an interesting approach, von Lindemann showed that the number pi is what is known as transcendental which is a category that describe non algebraic numbers. Given that constructing a square with a compass and a straightedge is fundamentally an algebraic operation, von Lindemann discovery determines that Anaxagoras problem was impossible to solve using classical tools. However, that was not the end of the story.
