Tuesday, January 31

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

• Discussion (brief) on the The Sphere  and the Torus.
• Coop work- 3-4 partners- record responses of group. 5 minutes, followed by discussion.

Question 1. How can one distinguish the sphere from a plane (Flatland) based solely on experiences on the surface?

Question 2. How can one distinguish the sphere from a torus based solely on experiences on the surface?

• Measurement and the Pythagorean Theorem (PT)

• a2 + b2 = c2

Show video on PT. Starting with "pythagoras"
Outline:
Area of triangles = 1/2 bh
Area of parallelogram= bh
Scaling: a linear scale change of r gives area change of factor r2.
3 questions: running, moat, wind power...
Proof of the PT: Similar right triangles: c= a2 /c + b2 /c .
applications and other proofs.
Prop. 47 of Euclid.
Dissection Proof.
Prop 31 Book  VI  Similar shapes.
Simple proof of PT using similar triangles of the triangle.
Use in 3 dimensional space.

Puzzles and Polygons
• Tangrams. More
• Tangrams – Use all seven Chinese puzzle pieces to make shapes and solve problems.
• Tangram Activity

Use templates to cut out pieces from larger (blue) sheets. [#Partners=3.]

• Cutting and reassembling polygons. More next class. :)