Page 107 - TB_5B
P. 107
Math Story Leonhard Euler
The following is an equation that the eighteenth-century mathematician
Leonhard Euler invented using the number of vertices, edges, and faces.
Euler’s Theorem
When the number of vertices is v, the number of faces is f, and the number
of edges is e, the following equation is always true for every solid figure.
v fe2
4 vertices 2 5 vertices 2
4 faces 5 faces
6 edges 8 edges
446 558
6 vertices 2 8 vertices 2
5 faces 6 faces
9 edges 12 edges
659 8 6 12
96
The following is an equation that the eighteenth-century mathematician
Leonhard Euler invented using the number of vertices, edges, and faces.
Euler’s Theorem
When the number of vertices is v, the number of faces is f, and the number
of edges is e, the following equation is always true for every solid figure.
v fe2
4 vertices 2 5 vertices 2
4 faces 5 faces
6 edges 8 edges
446 558
6 vertices 2 8 vertices 2
5 faces 6 faces
9 edges 12 edges
659 8 6 12
96
