| Popis: |
The problem of creating a three-sided dice with the probability of it landing on each of its sides being equal to 1/3 has been around for many years. Various approaches have been attempted, but as different authors achieved at different results, no uniform answer has been found. In this paper, the probability of a cylinder-shaped coin landing on its side is investigated, aiming to predict the final position of the coin, based on the starting physical and geometrical parameters of the coin. Pure physical methods and computer modeling have been used to find the parameters of a "fair" coin and to determine which parameters of the system affect the probability of the coin landing on an edge, and in what way. Statistical analysis of the situation has been made, to ensure that the probabilities we are trying to find, correspond to the appropriate physical events. Overall, two main possibilities for modeling the situation are considered: single-axis rotation (flat rotation) and the superposition of rotation against multiple axes (volumetric rotation). For each, a model was built and it was compared with computer modeling and real-life experiments. Dynamical and energetic approaches have been considered, and a model of the coin during its impact with the ground has been created. A robot that is capable of launching cylindrical coins, picking them up, and recording the result of the experiment, controlling starting parameters precisely, and distributing them to our needs, and automatically record the results of the experiment, was created. In conclusion, the parameters of a "fair" coin are provided, which have even probabilities landing on all its sides, as well as the dependencies of the probability of a coin landing on its edge, on different parameters. |
