Day 22: Heart of Mathematics

• Last time: The sexiest rectangle (or is it just cute?). Does the golden rectangle appear all over the place, or is it an illusion, like faces in carpets, or doggies in clouds?

• Today:
  • Hand back homework, sections 3.1 and 3.2

  • Collect homework, sections 3.3 and 3.4

  • Establish homework assignment from last time....

  • Regular polyhedra start with regular polygons -- so what are those?

  • Platonic Solids - time to get out those 3-D glasses!

  • Now let's make them in 3-d! We're going to be using our kits (or the geomags) today to construct a set of Platonic solids (Problem I.1), and use them to fill in the table on page 275:

    	# of Vertices	Edges	Faces	faces at each vertex	sides at each face
    Tetrahedron
    Cube
    Octahedron
    Dodecahedron
    Icosahedron

  • If there's time, we'll look at the other problems:
    • I.2
    • I.3
    • II.1
    • II.2

• Next time: 4.7: The Fourth Dimension (ChrisB, KellyG)

Links:

• Java applets allow one to play with Platonic Solids
• Or use virtual reality software to view them!