Wednesday, February 5, 2014
Class #5

Discussed briefly two types of symmetry for assignment due next week:

Miscellaneous: Some topics we will study (subject to time for adequate discussions).

Should we believe these dissection proofs? Closing discussion?

Discussion: The angles of the triangles in the figure are not complementary.
The triangles are not similar: the green/purple triangles have sides  3 by 8 while the triangle in the quadrilaterals have sides 2 by 5. Therefore they do not combine to have a right angle in the corners of the 5 by 13 figure.

Curry's Paradox: How Is It Possible?

Other visual tricks ... 

so why should we believe Pythagoras? Because we demonstrated that in the argument for the activity we did, the angles did form a right angle because the triangles were all congruent.

Theme Question: Who first showed the earth was a sphere or shaped like a sphere?

Dissection of the plane--- Tilings of the plane: