Projective Geometry

• Brian Gleichauf

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List of Block Book Items

Wednesday, May 15, 2013

Cover and Table of Contents; Thoughts on the Three Questions; Kepler's Propellor; Star Shadow; Circle Shadow; Projective Triangle in Motion; Implications of Projective Geometry; Projective Quadrangle & Harmonic Point; Quadrangle Net; Pappus Packet (Pappus, Pappus w/ x&y paralle, Pappus w/ one pair parallel, Pappus w/ two pairs parallel);...

Homework Wednesday May 15 2013

Wednesday, May 15, 2013

FINAL FORM Pascal Theorem and Dual (Brianchon's Theorem).  For each one, write the theorem and explain the connection to the Pappus Theorem and projectivities.

Read and come with questions from the Study Guide. (attached)

Homework Tuesday May 14 2013

Tuesday, May 14, 2013

FINAL FORM Linewise Conic Drawings 1, 2 & 3 (explain each one)

DRAW Pascal Theorem and Dual (at least three additional of each, four total)

Extra Credit: Pointwise Conic

Homework Monday May 13 2013

Monday, May 13, 2013

COMPLETE the three Projectivity Drawings

FINAL FORM:

Perspectivity and Dual

Projectivity and Dual

Dual Pappus Theorem

Homework Friday May 10 2013

Friday, May 10, 2013

FINAL FORM Pappus Packet (1. general Pappus Theorem, 2. Pappus theorem with x & y parallel, 3. Pappus theorem with one pair of sides parallel, 4. Pappus theorem with two pairs of sides parallel)

ROUGH DRAFT Duality explained

DRAW:

-Cross ratio under projection

-Projectivity Drawing #1

Homework Thursday May 9 2013

Thursday, May 9, 2013

DRAW:

- Perspectivity (both ways)

- Projectivity (both ways)

- Pappus Dual (write the dualized theorem)

FINAL FORM: Perspecting the Point at Infinity into the Page; Challenge Proof (3 pts to 3 pts in projectivity)

Homework Wednesday May 8 2013

Wednesday, May 8, 2013

Quiz Tomorrow (Study Guide attached to this post)

DRAW: Pappus with x & y parallel; Pappus with one pair of opposite sides paralle; Pappus with two pairs of opposite sides parallel.  Give the interpretation for each one, and how this show that the Pappus Theorem is a true projective theorem.  (You will include this with your first...

Homework Tuesday May 7 2013

Tuesday, May 7, 2013

ROUGH DRAFT: Proof: You can get from 3 (randomly chosen) points on a (randomly chosen) line to 3 (randomly chosen) points on another (randomly chosen) line in one projectivity

ROUGH DRAFT: Pappus' Theorem.  Say when this theorem was discovered, and when it was realized to be a projective theorem.  Write the theorem and show a good...

Homework Monday May 6 2103

Monday, May 6, 2013

FINAL FORM COLLECTION this Wednesday

DRAW one really nice quadrilateral net

FINAL FORM Implications of Projective Geometry

CHALLENGE!  Find a proof that three points on one line can be connected to three points on another line in one projectivity.

Review Questions

Monday, May 6, 2013

Upon what basis must a human being base her axioms from which she can draw reasoned conclusions about the nature of space and her geometry?

What implication of Projective Geometry is pointed to when you consider that one set of parallel lines in the projective plane meet at a point at infinity, but another set of parallel lines, not...

Homework Friday May 3

Friday, May 3, 2013

FINAL FORM: Shadow of a Circle drawing.  Include mention of all forms the shadow can take & name this group of curves

CHALLENGE!  Prove that 3 points on one line can connect to 3 points on any other line in only one projectivity!

FINAL FORM: Projective Triangle in Motion

FINAL FORM: Thoughts on the Three Questions

ROUGH DRAFT:...

Homework Thursday May 2 2013

Thursday, May 2, 2013

Proportions and Dimensional Analysis HW #5 (1-9)

Homework Thursday May 2 2013

Thursday, May 2, 2013

RD Implication of the Projective Geometry Choice.  Explain the reasons for each implication

FF Kepler's Propellor and Star Shadow (due at next ML Book collection)

DRAW three projective quad constructions (in each one, locate point B)

Homework Wednesday May 1 2013

Wednesday, May 1, 2013

DRAW a shadow of circle using the same shadow technique as the star.

WRITE your thoughts on the three big questions

RD Projective Triangle in Movement.  Describe the situation.  Caption each picture telling what is happening

PRACTICE Perspectivity and Projectivity (three additional of each one)

Homework Tuesday April 30 2013

Tuesday, April 30, 2013

ROUGH DRAFT (or FINAL FORM, if you think you can skip the rough draft step): Kepler's Propellor thought exercise.  Explain the conditions and describe the motion of point A.  Explain the Two Choices this leads you to!

Homework Monday April 29 2013

Tuesday, April 30, 2013

READ Syllabus (attached to this post)

THINK about the three big questions and the RR tracks

Do you think that there are facets of reality that you are missing due to your preconceptions and sensory biases?

Are you actively involved in constructing the concepts that make up your reality?

Is it possible to experience something...