Cube slices and geometric probability

• Main Authors: Ifurung, Carlo B., Miranda, Enrique P.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Cube; Geometry, Solid; Geometric probabilities
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16169
• Institution: De La Salle University

This thesis shows how slicing a cube perpendicular to the main diagonal produces the row entries of Pascal's triangle. It also shows how the result obtained from this can be used to solve for the area of the cross sections. The area will then be used to get the volume of slabs. All these will make solving problems on geometric probability much easier.When a cube is sliced, the number of lattice points which is contained in each cross section, is equivalent to that of an entry in the coefficients of Pascal's triangle. The area of a slice is obtained by multiplying the number of lattice points on a slice with the area of a parallelepiped.The volume on the other hand is just an integral of the area of the slice over a certain number of values. The result of this is then used to obtain a formula for the volume of a region of specified width.Some geometric probability problems are then solved using the formula which was also used above.