The following is NOT HOMEWORK unless you miss part or all of the class. See the Main Class Calendar for ALL homework and due dates.

Plimpton Cuneiform 322 and interpreting data

Usury is Piracy Discuss 142 years compounding monthly versus annually. Each student comes up with their own formula. Lump sum philisophy. Real-life bank situation. Past student was told that her c.d. will be compounded monthly at 8% for 8 months, and is told that this 8% will apply each and every month. Let's say that she put in $1000. How much would her c.d. be worth at the end of 8 months?

(a) 1000(1+.08)

(b) 1000(1+.08/8)

(c) 1000(1+.08/12)

(d) 1000(1+.08/12)

(e) none of the above

What did the bank really mean? Discuss other possibilities for unknowns - the time length, the rate, or the number of times compounding per year.

Review themes from mathematicians:

Viewing objects that are impossible to see by managing small pieces at a time (Jeff Week's research).

Impossibility of checking all the cases, but finding a solution by shifting our viewpoint or finding a non-constructivist approach (Andrew Wiles' research). If time remains, then begin David Blackwell.

Highlight some books from my office that are useful for the project.

Sphere questions:

Experiencing Geometry by Henderson

Geometry Theorems and Constructions by Berele and Goldman

The Heart of Mathematics by Burger and Starbird

Symmetry, Shape and Space by Kinsey and Moore

Universe questions:

Beyond the Third Dimension by Banchoff

Exploring the Shape of Space by Weeks

Geometry, Relativity and the Fourth Dimension by Rucker

The Heart of Mathematics by Burger and Starbird

Hyperspace by Kaku

The Math Book by Pickover

Shape of Space by Weeks

Symmetry, Shape and Space by Kinsey and Moore

Escher's space and Poincare's disk model of hyperbolic geometry.

Escher drawing

Sphere with Angels and Devils, 1942. Sphere Surface with Fish. 1958

Discuss a computer model of Escher's space called hyperbolic geometry.

Hyperbolic worksheet.

In the weeks to come, we will see that there are many real-life applications of hyperbolic geometry, such as models of the internet that hope to reduce the load on routers, building crystal structures to store more hydrogen or absorb more toxic metals, mapping the brain, mapping the universe, and modeling Mercury's orbit.

Discuss physical models of small pieces of hyperbolic space. Crochet model of hyperbolic geometry Reef Crochet reef. If time remains, discuss homework for Thursday and project 1.

Butterfly

Globe wrong view

Globe correct view

Accident