Philippine E-Journals

The Use of Platonic Solids in Probability Concepts

Renan P. Limjuco

Discipline: Mathematics

 

Abstract:

The author discusses the geometries of Platonic solids and their relevance to some probabilistic situations. Platonic solids such as tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, are all solids each of them bounded by a definite number of congruent faces. Just like what is usually done in hexahedron, each of the solid’s faces will be numbered and the probability of getting a specific number for a certain activity is determined. Ordinarily, two cubes are used in measuring the probability of getting a certain sum if they are rolled in a game of chance. As an extended treatment, one may use two tetrahedrons, or two octahedrons, to come up with 4 x 4 – matrix or 8 x 8 – matrix tables respectively, to enumerate all the possible elements of the sample space for the situation. This is not difficult to imagine if one is familiar with the 6 x 6 table formed to list all the possibilities of numbers showing up if a pair of dice is thrown. The odd pairing of a hexahedron and a tetrahedron can also be explored. To top it all, any pair-combination of these Platonic solids can without a doubt deepen and enhance the concepts of probability.