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MEASUREMENT
Lesson 3 - Page 3

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Red area is a "face".  there are 12 faces showing. "a" is a vertex with 3 edges

A polyhedron is a set of 4 or more polygons that enclose a three dimensional structure or solid.  Each flat plane is called a face and has a common segment called an edge and form a dihedral angle.  The angle is measured in the plane perpendicular to the edge.  Three or more edges form a vertex.

Leonhard Euler, a Swiss mathematician (1707-1783),  wrote 866 mathematical papers and books covering subjects from number theory, geometry, trigonometry, and calculus.  The last two decades of his life he was blind.  He discovered many theorems.  A theorem is developed by mathematicians to prove a formula is always true.  Proofs are associated with theorems that can be repeated. Euler discovered many theorems.  He discovered a relationship between the number of faces, vertex points, and edges in all polyhedrons, no matter how irregular its shape.  Euler could compute the sum of all of the face angles in any polyhedron without knowing any of their measures. The relationship is called Euler’s formula for polygons.  The following activity will have you construct several polygons and then you will collect data to see if you can develop a formula.