Estimation of π via experiment

Keiko I. Nagao, Yuga Sakano, Takashi Shinohara, Yuji Matsuda and Hisashi Takami

In this study, we conducted an experiment to estimate π using body-to-body and body-to-wall collisions. By geometrically analyzing the system’s motion, we first review how the collision count corresponds to the digits of π. This method utilizes the property that the number of collisions corresponds to π to the nth decimal place by setting the mass ratio of bodies to 1:100n under ideal conditions. In particular, when the mass ratio is 1:100—which is the case we tested experimentally—the number of collisions is 31, and π to the tenths decimal place (3.1) can be derived. In the experiments, a suspended apparatus was developed to minimize energy losses such as friction and air resistance. We also devised the shape and material of the colliding bodies’ surface and the characteristics of the suspension string, aiming for measurements under stable conditions. Based on the experimental results, we reproduced the number of collisions consistent with the theoretical values and confirmed that estimating π to the tenths decimal place is possible under realistic conditions.

European Journal of Physics

IOP Publishing

46

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