The Magic and Mystery of Pi - Real Numbers and Limits

Explore the fascinating world of pi in this 42-minute lecture from the MathFoundations series. Delve into the historical significance and mathematical complexity of this enigmatic number, tracing its evolution from ancient times to modern computations. Examine various formulas for calculating pi, including those developed by mathematical luminaries like Archimedes, Newton, and Ramanujan. Consider the logical challenges in rigorously defining pi and its relationship to real numbers and geometry. Reflect on the speaker's perspective regarding pi's nature as a "meta number" rather than a real number, and contemplate its future role in understanding the mathematical continuum.

Intro to the magic of "pi"
"Pi" is usually defined by area or circumference
Logical difficulty
Brief history of "pi"
The first formulas of "pi"
Formulas for "pi" discovered by Newton
"Pi" formula by S. Ramanujan 1914
Page 269 of 'Divine Proportions'
Irrational real numbers
My attitude to "pi"
"Pi" is not a real number, it's a meta number