Projective Geometry

Homework Wednesday April 25

Wednesday, April 25, 2012

For Friday:

FINAL FORM Growth Measure (2 drawings) and Step Measure (2 drawings)

FINAL MORNING LESSON BOOK due! 

STUDY for Final Exam on Friday!

Morning Lesson Book Items So Far

Wednesday, April 25, 2012

- The Three Big Questions Essay

- Star Shadow Construction

- Circle Shadow Construction

- Kepler's Propellor Thought Experiment Explained

- Implications of Projective Geometry (Choice Two) Essay

- Perspecting the point at infinity into view

- Quadrangle with automatic point D construction

- Quadrangle Net

- 3 points on one...

Homework Tuesday April 24

Tuesday, April 24, 2012

Complete the set of three Linewise Conic drawings, and explain the movement from one to the next, and the significance of each one.

Morning Lesson Book Items So Far

Monday, April 23, 2012

- The Three Big Questions Essay

- Star Shadow Construction

- Circle Shadow Construction

- Kepler's Propellor Thought Experiment Explained

- Implications of Projective Geometry (Choice Two) Essay

- Perspecting the point at infinity into view

- Quadrangle with automatic point D construction

- Quadrangle Net

- 3 points on one...

Homework Monday April 23

Monday, April 23, 2012

COMPLETE One more Linewise Conics (in which line y moves to infinity)  Templates attached

Put into FINAL FORM Pascal's Theorem, and Pascal Dual Theorem

Put into FINAL FORM the Pointwise Conic

Homework Friday April 20

Monday, April 23, 2012

COMPLETE One more projectivity map (this one is dual to the first).  Template attached.

Homework Thursday April 19

Thursday, April 19, 2012

PRACTICE At least 4 Pascal Dual Theorem examples

FINAL FORM At least one Pascal Theorem

COMPLETE One "Projectivity Map" (We will call it something else later!)  Template attached

Homework Wednesday April 18

Wednesday, April 18, 2012

PRACTICE at least 4 Pascal Theorem examples (attached templates for the conic sections)

ADD the simpler wording for Desargues Theorem to your Final Form

MAKE edits or changes to any of your final forms that you need to correct

Homework Tuesday April 17

Tuesday, April 17, 2012

FINAL FORM Desargues Theorem: 1) Include the written theorem, the construction, how it can be proven by interpreting it as a 3-dimensional construction, and the special properties of the Desargues Theorem.  2) Do a second Desargues construction with one pair of sides parallel

PUZZLE:  What is the deal with the Pappus Theorem, the...

Morning Lesson Book Items So Far

Monday, April 16, 2012

- The Three Big Questions Essay

- Star Shadow Construction

- Circle Shadow Construction

- Kepler's Propellor Thought Experiment Explained

- Implications of Projective Geometry (Choice Two) Essay

- Perspecting the point at infinity into view

- Quadrangle with automatic point D construction

- Quadrangle Net

- 3 points on one...

Homework Monday April 16

Monday, April 16, 2012

FINAL FORM COLLECTION tomorrow!

DRAW at least three successful Desargues' Theorem constructions.

DUALIZE the Pappu's Theorem Construction.  Write the dual theorem and demonstrate it.

Homework Thursday April 5

Thursday, April 5, 2012

STUDY Review Sheet for quiz on Monday April 16 (Attached)

FINAL FORM Pappus with one pair and also with two pairs of parallel sides (two drawings, each with an explanation of the significance of the results for the reality of the point at inifinity and the line at inifinity

DRAW Two kinds of Projectivity (the normal one and the dual...

Homework Wednesday April 4

Wednesday, April 4, 2012

FINAL FORM Projective Triangle in Motion & What is lost and left when Euclidean Geometry becomes Projective Geometry?

FINAL FORM Cross Ratio is preserved under a projectivity (demo drawing and explanation.  Include class results and computer results)

Homework Tuesday April 3

Tuesday, April 3, 2012

FINAL FORM Pappus' Theorem (write the theorem, demonstrate drawing)

FINAL FORM Cross Ratio of Projectie Quad equals 1

FINAL FORM 3 pts one one line to 3 pts on another line in one projectivity (attached doc to help you with this one)

Morning Lesson Book Items So Far

Tuesday, April 3, 2012

- The Three Big Questions Essay

- Star Shadow Construction

- Circle Shadow Construction

- Kepler's Propellor Thought Experiment Explained

- Implications of Projective Geometry (Choice Two) Essay

- Perspecting the point at infinity into view

- Quadrangle with automatic point D construction

- Quadrangle Net

- 3 points on one...

Homework Monday April 2

Monday, April 2, 2012

FINAL FORM Collection tomorrow

WORK TO UNDERSTAND How 3 pts on one line can be connected to three points on another line with one projectivity

CALCULATE the Cross Ratio of a Projective Quadrangle

DRAW At least 3 Pappus Theorem Constructions

Homework Friday March 30

Friday, March 30, 2012

DRAW a Quadrangle Net according to the instructions.  Fill the page and color it with two contrasting colors.

FINAL FORM Kepler's Propellor Thought Experiment

FINAL FORM Perspecting the Point at Infinity into View

PUZZLE over how to get from three random points on one random line to three more random points on another random line,...

Homework Thursday March 29

Thursday, March 29, 2012

FINAL FORM Thoughts on Three Questions Essay

ROUGH DRAFT: Implications of Choice 2: (1) Descrition of Euclid's Axioms, and where they came from, (2) Special discussion of the 5th postulate. What is it's significance?  Why did Euclid include it?  What case was he excluding?  What did mathematicians do afterward due to their discomfort...

Homework Wednesday March 28

Wednesday, March 28, 2012

ROUGH DRAFT Kepler's Propeller Thought Experiment (include the drawing, description of the situation, description of the movements [of the line and of the point of intersection] and describe The Choice that this leads a person to about the parallel position!

FINAL FORM a Shadow Drawing with a circle casting the shadow

THINK about the...

Homework Tuesday March 26

Tuesday, March 27, 2012

FINAL FORM Star Shadow Drawing construction (use shading to emphasize the relevant planes)

WRITE Your thoughts on the three Big Questions from class

DRAW A shadow construction w/ a circle as the shadow caster (this will require you to choose your own points to project on the circle and then to use your drawing skills to smoothly...

Homework Monday March 26

Tuesday, March 27, 2012

READ Syllabus, come with questions tomorrow

DRAW at least three Star Shadow Constructions to master the technique (instructions attached below)

PONDER your participation in constructing your reality!

First Day of Class March 26 2012

Sunday, March 25, 2012

Here attached is the syllabus.