# The Fourth Dimension -- The Mathematics of Angels, Aliens, and Miracles

The Fourth Dimension (page numbers, etc. reference sections of the Heart of Mathematics):

• What thoughts and questions do you have about the fourth dimension? What is the "fourth dimension"? Where have you already encountered the fourth dimension?

• Sweeping out additional dimensions ("inked points")
• point (imprisoned!)
• point -> line (imprisoned by two points, each on one side)
• line -> plane (imprisoned by a circle)
• plane -> three-space (imprisoned by a sphere)
• three-space -> the fourth dimension!

• Slicing and dicing: Problems II.6, II.7 (parts -- these are for your homework, afterall!;)

• What if there were creatures confined to two dimensions? How would we mess with their heads?

http://www.cwru.edu/artsci/engl/VSALM/mod/ricca/resources/COVER.JPG

• Safes aren't safe (p. 312)
• 3-D surgery (p. 311)
• 3-D rope tricks (p. 313)
• How might a cube dipped into two-space appear to creatures stuck in two-space?

• Now: what if there are four dimensional creatures living with us? How might they mess with our heads?