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.

If you count the number of faces ($F$), edges ($E$), and corners ($V$), they follow the following mathematical relation:

$$V-E+F = 2$$

Intent: Find the number of faces in a polyhedron when given the number of its edges and corners.

• Find F (the number of faces) by using V and E. You need to rearrange the equation above a little and then update the value of the F

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