Lesson Three — Deriving Euler’s Formula

From: www.PlatonicSolids.info

 

 

Prep

• Create a handout with a grid like the following:

 

Shape Name	Edges	Vertices	Faces
tetrahedron
octahedron
icosahedron
cube
dodecahedron

 

• Create a poster-sized version of the same grid.

 

Procedure

• Pass out the shapes the students created in the previous lesson.
• Have students work in small groups counting edges, vertices, and faces and filling out their grids.
• When the groups have finished counting, create a class consensus of the counts and fill out the poster-sized grid.
• Ask students to try to find a pattern that holds for all of the shapes.  You can model this by trying out a relationship such as Faces + Edges – Vertices.
• Hopefully they will discover some variation on Euler’s formula: V + F – E = 2.  If students come up with different variations, discuss whether they are equivalent.