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

Amy: http://www.oswego.org/ocsd-web/games/bananahunt/bhunt.html

Douglas: http://www.shodor.org/interactivate/activities/Angles/?version=1.5.0_13&browser=Mozilla&vendor=Apple_Inc.

Jessica: http://www.frontiernet.net/~imaging/pythagorean.html

Karen: http:nlvm.usu.edu/en/nav/vlibrary.html,

http://www.sw-georgia.resa.k12.ga.us/Math%20Aerobics/Math%20Aerobics.htm,

http://www.mathplayground.com/logicgames.html,

http://www.eduplace.com/math/brain/index.html,

http://hotmath.com/games.html,

http://www.hanssoft.com/html/games.html, and

http://snowflakes.lookandfeel.com/

Katelin: http://www.saltire.com/gallery.html

Kimberly: http://www.mathsnet.net/dynamic/pythagoras/index.html and

http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html#cns

Sasha: http://mathforum.org/alejandre/applet.polyhedra.html

Spencer: http://www.cut-the-knot.org/pythagoras/FaultyPythPWW.shtml and

http://www.math.wichita.edu/~richardson/behold.html

Sketchpad Shortest Distance Paths

Image of Shortest Distance Paths

Sketchpad Equidistant 1

Image of Equidistant 1

Sketchpad Equidistant 2

Image of Equidistant 2

Sketchpad Euclid's 5th Postulate

Image of Euclid's 5th Postulate

From the Sketchpad 4 folder, open up Sketchpad/Samples/Sketches/Investigations/ Poincare Disk.gsp.

Show that the existence part of Playfair's axiom works: Create a hyperbolic segment by constructing a parallel via perpendiculars. Measure the alternate interior angles on both sides to see that they are not congruent. Hence the uniqueness part of Playfair's does not hold, and in fact, we can create infinitely many parallels through a given point to a given line. In addition, our proof of the sum being 180 degrees will also fail because the alternate interior angles are not congruent on both sides.

Then discuss the Hyperbolic Parallel Axiom: If m is a line and A is a point not on m, then there exist exactly two noncollinear halflines AB and AC which do not intersect m and such that a third halfline AD intersects m if and only if AD is between AB and AC.

Investigate the Pythagorean Theorem in hyperbolic geometry.

Discuss the model of hyperbolic geometry using hexagons and heptagons - a hyperbolic soccer ball.

1) Name

2) Something that will help us remember them

3) Something that you both have in common other than this course or your interest in mathematics

Next discuss how can we tell the earth is round without technology?

Mention the related problem on Project 2 for Friday [Wallace and West Roads to Geometry 1.1 8].

Where is North?

Begin the Geometry of the Earth Project. Groups choose their top three problems and turn these in to Dr. Sarah. Next, read through the handout.

Induction versus deduction. An introduction to minesweeper games as an axiomatic system.

Axiom 1) Each square is a number or a mine.

Axiom 2) A numbered square represents the number of neighboring mines in the blocks immediately above, below, left, right, or diagonally touching.

Examine game 1. Students are called on in random order to state and then prove something about a specific square in game 2. History of Euclid's elements and the societal context of philosophy and debate within Greek society. Go to the computer lab in 205. Intro to Geometric Constructions. Begin Euclid's Proposition 1. Time at the end of class to work on Project 1.

Go over an application - a proof that the perpendicular bisectors are concurrent.

Build a right triangle in Sketchpad and investigate the Pythagorean Theorem.

Go to Applications/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp

Go through Behold Pythagoras!, Puzzled Pythagoras, and then Shear Pythagoras. Click on Contents to get to the other Sketches.

Return to the classroom.

Go through Euclid's proof. Discuss Sibley