Hi,

For the Basel problem:

where the sum of 1/n^2 = Pi^2/6, for n=1 to n=infinity, there doesn't seem like there would be a relationship between Pi and 1/n^2, I checked on this page for the Basel problem:

from the page: " Sum_{m = 1..inf } 1/m^2.

"In 1736 he [Leonard Euler, 1707-1783] discovered the limit to the infinite series, Sum 1/n^2. He did it by doing some rather ingenious mathematics using trigonometric functions that proved the series summed to exactly Pi^2/6. How can this be? ... This demonstrates one of the most startling characteristics of mathematics - the interconnectedness of, seemingly, unrelated ideas." - Clawson

Pi^2/6 is also the length of the circumference of a circle whose diameter equals the ratio of volume of an ellipsoid to the circumscribed cuboid. Pi^2/6 is also the length of the circumference of a circle whose diameter equals the ratio of surface area of a sphere to the circumscribed cube. - Omar E. Pol, Oct 07 2011 "

Does that make sense as a intuitively as a geometric "proof" to relate these two things:

- length of the circumference of a circle whose diameter equals the ratio of volume of an ellipsoid to the circumscribed cuboid

- length of the circumference of a circle whose diameter equals the ratio of surface area of a sphere to the circumscribed cube

to both Pi^2/6 and to sum of 1/n^2, for n=1 to n=infinity?

Can things like the Basel problem have equivalent geometric proofs to the standard mathematical proofs?

cheers, Jamie