Euler_s Formula for 3D solids, Relation Between F, V & E

Euilers' Formula for solids, 3D Solids

1. EULER'S FORMULA

2. Euler Formula Examples OUTLINE

3. Leonard Euler, a great Mathematician, at a very young age discovered an i nteresting formula regarding the faces, vertices and edges of solid figures. The Euler Formula is given by, F + V = E + 2 Where F is faces, V is vertices, E is edges of solid figures. Lets see some examples to verify the above relation Euler Formula

4. Faces = 6 Edges = 12 Vertices = 8 L.H.S = F + V = 6 + 8 = 14 R .H.S = E + 2 = 12 + 2 = 14 Thus, the Euler Formula F + V = E + 2 is verified for cube. Cube : Similarly, the Euler Formula F + V = E + 2 can be verified for cuboid. Examples

5. Faces = 5 Edges = 9 Vertices = 6 L.H.S = F + V = 5 + 6 = 11 R .H.S = E + 2 = 9 + 2 = 11 Thus, the Euler Formula F + V = E + 2 is verified for Triangular Prism. Triangular Prism : Examples

6. Faces = 4 Edges = 6 Vertices = 4 L.H.S = F + V = 4 + 4 = 8 R .H.S = E + 2 = 6 + 2 = 8 Thus, the Euler Formula F + V = E + 2 is verified for Triangular Pyramid. Triangular Pyramid : Examples

7. Today we learnt about : Euler Formula RECAP