Math 0025 review topics
Theorems
- Incidence Theorems
- 3-D incidence axioms and theorems (posted)
- Ceva's theorem and its converse (4)
- Desargue's theorem and its dual (7)
- Semi-circle theorem (10)
- Metric Geometry
- Menelaus' theorem (4.2, car-bike-truck)
- Harmonic ratio theorem (4.2)
- Viewing distinace via a square (9)
- Diagonal semi-circle theorem (10)
- Rectangles versus squares (10)
- Cross ratio (11.1)
- Eves' Theorem (11.2)
- Casey's Theorem (11.3)
- Extended space, projecction maps and vanishing points and lines
- Definitions of E^2 and E^3 (5 and
handout )
- Vanishing points (1)
- Properties (5)
- Projection maps
(handout)
- Vanishing lines (1, 5 and handout)
Constructions
- Completion in 1-point perspective (2 - Letter T)
- Adding elements in 1-point perspective (5)
- Subdivision method for copying art - continguous (6)
- Subdivision method for copying art - noncontinguous (8)
- Drawing shadows via Desargue (7)
- Adding elements in 2-point perspective (8)
- Boxes and cubes in 2-point perspective (10)
- Other 3D figures in 2-point perspective (10)
- Vanishing point via cross-ratios (11)
- Casey's angle (11.3)