1. Geometry and Trigonometry
1. Point, Tuples, and Vectors
2. Lines
1. Equation of a 2d line
2. Angle between two lines
3. Perpendicular to a Line at a Point
4. Equation of line between two points
5. Tangent Line to a Curve
6. Tangent Line less Calculus
7. Vector Notation of a Line
1. Method 1
2. Method 2
8. Intersection of two line segments
9. Distance from a Point to a Line
10. General Solution Distance to a Line
11. Short Distance from Line to Origin
12. Slopes Only
13. Parallel Lines
14. Polynomial Lines
3. Functions
4. Parametric Equations
1. Implicit functions
2. Parameters
3. Completing the square
4. Derivative of Parametric Equations
5. Basic Trigonometry
1. More Definitions
2. Common Unit Circle Angles
3. Law of Sines
4. Periodic Functions
5. Periodic time functions
6. Polygon Interior Sequence Derivation
1. n-gon Starting at any point
7. Polygon Exterior Sequence Derivation
8. Derivation of Pi
6. Polar Coordinates
7. Bézier Curves
1. Triangles
1. Definitions
2. Area Formula for Triangle
3. Heron's Theorem
4. 30 60 90 Triangles
5. Isosceles Triangles
6. Ceva's Theorem
7. Special Names
8. Pythagorean Triangles (Triples)
9. Triangle with known sides
10. Regular Polygon
2. Circles
1. Unit Circle
2. Derive Area inside a Circle
3. Parametrization of a Circle
4. Three points make a Circle
5. Three points make a Circle - Method 2
6. Graphing a circle
7. Sector Area of a Circle
8. Lateral Area of a Cone
9. Frustum of a Cone
10. 2d Circle Intersections
11. Axes tangent Circles
12. Tangent to Circle from line slope
13. Uniform Size Tangent Circles
14. Tangent Circle to Two Circles
15. Descartes Circle Theorem
16. Lotfollah Dome
3. Cycloid
1. Conic Rotation
1. Axes Rotation Point Rotation
2. Conic Rotation
3. Rectify the Conic
4. Derive Rotation Angle
5. Matrix Rectification
2. Ellipse
1. Cartesian Derivation
2. Polar Ellipse Derivation
3. Eccentricity
4. Parametric form for the ellipse
5. Standard Equation of Ellipse
6. Algorithm to rotate an ellipse
7. Area of an ellipse
8. Chart of Ellipse Equations
3. Hyperbola
1. Parabola
1. Basics
2. Nomenclature
3. Parabola:Vertex at (h,k)
4. Solving a Rotated Parabola
5. Parametric Rotation
6. Parametrize any Parabola
7. Vertex of a Parametric Parabola
8. Standard Parametric Form
10. Vertex Summary
11. Tangent between parabolas
2. Conic with Five Points
1. Reserved
1. Trigonometry Identities
2. Euler's Formula
3. Cubic Equation
4. Arc Length
5. Catenary Curve
1. Short Derivation
2. Detail Derivation
3. Common Catenary Examples
4. Summary
5. Catenary Approximation