What do they all have in common?

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Presentation transcript:

What do they all have in common? Pyramids What do they all have in common?

Pyramids Definition A solid object where: • The base is a polygon (a straight-sided flat shape) • The sides are triangles which meet at the top (the apex).

What do they all have in common? Prisms What do they all have in common?

Prisms Definition A solid object with two identical ends and flat sides: • The sides are rectangles (or parallelograms) • The cross section is the same all along its length The shape of the ends give the prism a name, such as "triangular prism"

face

edge

vertex (plural vertices)

Fill in the table for each of the pyramids Solid Number of Faces Number of Edges Number of Vertices Can you find a predict the results for a heptagonal or octagonal based pyramid? What about an n-agonal based pyramid?

Pyramids Fill in the table for each of the pyramids Solid Number of Faces Number of Edges Number of Vertices Can you find a connection between the Faces, Edges and Vertices?

V + F - E = 2. Euler’s Formula for Polyhedra The formula was discovered by and bears the name of the famous Swiss mathematician Leonhard Euler (1707 - 1783) It is true for all polyhedra. (singular – polyhedron)

Fill in the table for each of the prisms Solid Number of Faces Number of Edges Number of Vertices Can you find a predict the results for a heptagonal or octagonal prism? What about an n-agonal prism?

Prisms Fill in the table for each of the prisms Solid Number of Faces Number of Edges Number of Vertices Verify that Euler’s formula also works for the prisms in this table

Other Polyhedra Fill in the table for each of these platonic solids Number of Faces Number of Edges Number of Vertices Octahedron Dodecahedron Icosahedron How can you use Euler’s formula to fill in this table?

Why are there only 5 platonic solids?