Pi appears in non-circular formulas mainly because of hidden rotational symmetry and because oscillations are mathematically tied to circular motion. Some appearances come from how constants are defined.
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Imaginary numbers solve equations that real numbers cannot and simplify calculations involving waves, so they are central to electrical engineering, signal processing, radar and physics.
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Not in everyday sinks, tubs or toilets. The Coriolis effect is real, but it is far too weak to set the swirl at that scale. Only carefully controlled experiments show it.
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No. Air resistance caps a falling penny at roughly 25 mph, so it would sting but not kill. The myth ignores drag, which keeps the coin from reaching lethal speed.
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We feel changes in motion, not steady motion. Earth's spin is smooth, we and the air move with it, and gravity far outweighs the tiny outward effect of rotation.
Starter thread · AI-reviewed against its sources
