Euclid’s Mathematics of polyhedron

Hello learners,

Hope you’re doing well.

In this tutorial I’m​ going to share and explain some of the illustrated topics which had given a boost to various fields of MATHEMATICS and being explained and derived by a great Mathematician named

EUCLID: Polyhedron

sir Euclid was a great mathematician and physicist and had a great impact over other mathematicians​ of the same time, because of his sense of understanding the topic and providing Solutions of hard known problems

  • He is also considered as Father of Geometry.

I’ve picked this mathematician to elaborate some of the explanation given by him, so let’s start,

  • Euclid’s law for Polyhedrons-

      Euclid has given a concept for Polyhedrons that ” there is some relation between vertices, edges and faces of any polygon and this relationship stands true for each Polyhedron” and this relationship can be 

  • V + F = E + 2

cuboid

  • For any cube

Cube

 there is    V (vertices) = 8
                F ( faces )    = 6
                E ( edges)    = 12
then
 8 + 6 = 12 + 2
14      = 14
this relationship stands constant for any of the polyhedron
likewise 

  • For triangular pyramid

there is V (vertices) = 4
                F ( faces )    = 4
                E ( edges)    = 6
then 4 + 4= 6 +2
            8    = 8

  • for Square Pyramid / Rectangular Pyramid

square pyramid/ rectangular pyramid
there is V (vertices) = 5
                F ( faces )    = 5
                E ( edges)    = 8

then 5 + 5 = 8 + 2
             10  = 10

  • Square/ Rectangular Prism

Prism
there is V (vertices) = 6
                F ( faces )    = 5
                E ( edges)    = 9
hence   6 + 5 = 9 + 2
                 11  = 11
so we’ve seen Sr Euclid has given a very useful concept for various 3D shapes/ polyhedrons
Hope you have found this post valuable.
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