Wednesday, February 5, 2014
Discussed briefly two types of symmetry for assignment due next week:
- Reflection Symmetry across a vertical or horizontal line.
- Rotational symmetry by 180 degrees.
Miscellaneous: Some topics we will study (subject to time
for adequate discussions).
- The Sphere and the Torus. Surfaces
- Proof and Truth in Geometry and Arithmetic.
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.
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:
- Activity: Tile plane with playing cards.