Math 444, Monday, November 4

Class: Building and Analyzing Cubes

Part 1: Polydron cube

·        Make a cube with Polydrons.  Look at cutting by planes.

·        From an index card, cut out a rectangle that is approximately a diagonal cross-section of the cube.

·        Tell the (theoretical) dimensions of this rectangle if the cube has edge length s.

·        Then tell the radius of the insphere and circumsphere of the cube.

Part 2: Constructions

Handout: A net for a cube.  This is a figure made up of 6 squares that can be cut out, folded and taped to make a cube.

·        Construct with straightedge and compass the rectangle above.

·        Construct with straightedge and compass a net for a square-based pyramid with vertex in the center of the cube. 

·        What are the edge lengths of the pyramid?