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A wonderful coincidence or an expected connection: why π² ≈ g


Let’s take a brief trip back to our school years and recall some lessons in mathematics and physics. Do you remember what the number π equals? And what is π squared? That’s a strange question too. Of course, it’s 9.87. And do you remember the value of the acceleration due to gravity, g? Of course, that number was drilled into our memory so thoroughly that it’s impossible to forget: 9.81 m/s². Naturally, it can vary, but for solving basic school problems, we typically used this value.

Serious people decided that such chaos was hindering serious business, so they set a goal: to come up with a definition of a unit of length that wouldn't depend on any arbitrary standards. The Dutch mechanic, physicist, mathematician, astronomer, and inventor Christiaan Huygens suggested using a simple pendulum for this purpose. Intelligent people suggested maintaining the definition of the meter through the pendulum, but with the clarification that it should specifically be a French pendulum—at the latitude of 45° N (approximately between Bordeaux and Grenoble).

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