Using
only a stopwatch and a sneaker, find an approximate value for sqrt{2}.
Source: M.Levi’s "Why Cats Land on Their Feet" (2012).
Sure, there are more ways, just as there are many ways to measure the height of a building with a barometer (a story worth googling).
The period T of a pendulum goes as the square root of its length L, independently of the amplitude for modest excursions. So, swing the shoe from one and then two lengths of lace to give timed periods:
t1 = 2 pi sqrt(L/g)
t2 = 2 pi sqrt(2L/g)
ratioed, once again, gives:
sqrt(2)=t2/t1
Edited on March 25, 2021, 6:32 am
Swinging way
