PHYSICAL SCIENCES Ė MEASUREMENT
LESSON 3. Eulerís Formula for Polygons (Lab)
Objective: Students collect data and determine a relationship of different polygons.
Early mathematicians or philosophers would try and develop relationships by closely observing shapes. Leonhard Euler, a Swiss mathematician, was a sharp observer of solids.
As you try and figure out the relationship it is importance that the angles on each face of the polyhedron are what is important, not the angles between the faces.
Recreating the data and plotting the information and then graphing the data will help us determine how Euler came up with his formula. Use F = faces; V = vertex. Eulerís equation for determining the total measure of all the face angles is m=360(V-2) where m represents the total measure of all the face angles and V represents the number of vertex points. As you should have determined adding a vertex point in a polyhedron increases the total angle measure by 360 degrees. This is Eulerís equation.
The only restrictions on the figures were that there were no holes in them, that every face of a polyhedron had to be a polygon, and that all the faces were flat and edges straight.
Vertices + Total Measure of Face Angles / 360 +2
It does not work. These shapes have circular faces which do not have vertices