Free Response Question 1: Equation Construction

Background

You may have come across various online calculators that solve famous equations within a couple of seconds. After entering the respective values, a calculator gives the answer accordingly. In this exercise, let’s turn some famous mathematical equations and applications into Java programs.

Problem statement 1

Euler’s formula for the number of faces of polyhedra

Euler is famous for a number of his equations, including the legendary Euler’s identity. However, here, we will focus on his brilliant equation that sums up the geometry of all polyhedra.

A polyhedron is a $3$-dimensional shape consisting of flat faces, straight edges, and sharp corners. For example, a cube and a tetrahedron are examples of polyhedra.