Fermat's Christmas Theorem - Visualising the Hidden Circle in Pi/4 = 1-1/3+1/5-1/7+...

Fermat's Christmas Theorem - Visualising the Hidden Circle in Pi/4 = 1-1/3+1/5-1/7+...

Explore the hidden geometry behind Leibniz's iconic pi formula pi/4 = 1-1/3+1/5-1/7+... in this 25-minute video. Discover how a surprising circular pattern emerges from this seemingly abstract series of fractions involving odd numbers. Delve into the mathematical concepts presented by Hilbert and Cohn-Vossen in their book "Geometry and the Imagination," and compare this approach with related visualizations by other mathematicians. Examine the connections between this formula and other mathematical problems, such as the Basel problem and its higher-dimensional counterparts. Gain insights into the elegant and unexpected ways that fundamental mathematical constants like pi can be represented and understood through geometric interpretations.