Pondering pi in the pendulum's presence

Some days ago, you may recall, Weather Eye focused on Foucault's Pendulum. But that narrative was based on hearsay

Some days ago, you may recall, Weather Eye focused on Foucault's Pendulum. But that narrative was based on hearsay. On Sunday last, however, I visited the Pantheon in Paris and there, in sublime and stately splendour, le pendule de Foucault swung slowly to and fro.

And now I know where Umberto Eco found his postmodern, breathless inspiration:

"The sphere hanging from a long wire set into the ceiling swayed back and forth with isochronal majesty. I knew that the period was governed by the square root of the length of the wire and by pi, that number which, however irrational to sublunar minds, through a higher rationality binds the circumference and diameter of all possible circles.

"The time it took the sphere to swing from end to end was determined by a chance conspiracy between the most timeless of all measures: the singularity of the point of suspension, the duality of the plane's dimensions, the triadic beginnings of pi, the secret quadratic nature of the root, and the unnumbered perfection of the circle."

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The Pantheon itself is an awe-inspiring building. Architecturally in the classical tradition, it was once a church, and was transformed during the Revolution into a collective tomb for distinguished or heroic French. Mirabeau was the first to be buried in the crypt, followed by the ashes of Voltaire and Rousseau, and more recently by Victor Hugo, the Curies and the Resistance leader Jean Moulin.

But the nave belongs to Foucault's pendulum. As back and forth it swings, suspended from "the eye of God" in the centre of the painted dome, the Earth rotates beneath.

The bob is a golden sphere hanging by a wire that is 67 metres long; on the floor, a large white ring surrounds the zone of oscillation, and is marked with a series of numerals with which to gauge the slow precession of the pendulum. As time passes, the plane of oscillation appears to shift progressively around this circle, and at the latitude of Paris the plane of Foucault's pendulum describes 272 degrees in every 24-hour period.

I timed its motion, and found that it took eight seconds to move from side to side. And then I did the calculations, based on the stated length of the suspending wire, and found that the period, the time to go to and fro and to again, should be 16.47 seconds, and thereby found myself doubly reassured both that the Earth goes around, and that the Law of the Simple Pendulum appears to be correct.

And I have gone upon my way, strangely in awe of this great world we live in.