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);...
[read more]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)
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
COMPLETE the three Projectivity Drawings
FINAL FORM:
Perspectivity and Dual
Projectivity and Dual
Dual Pappus Theorem
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
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)
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...
[read more]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...
[read more]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.
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...
[read more]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:...
[read more]Proportions and Dimensional Analysis HW #5 (1-9)
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)
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)
DRAW three additional Star Shadow drawings (put best one on top).
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!
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...
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"“An approach to the secrets of space from the standpoint of artistic and imaginative insights.” - Lawrence Edwards
The 11th Grade Projective Geometry block is a challenging, highly imaginative, synthetic approach to geometry, stretching the limits of our traditional “Euclidean” worldview. Through various geometric constructions first...