1. Geometry and Trigonometry
    1. Point, Tuples, and Vectors
      1. The Distance Formula
      2. The Dot Product
      3. Summary
    2. Lines
      1. Equation of a 2d line
        1. General Linear Form
        2. Slope Intercept Form
        3. Point Slope Form
        4. Intercept Intercept Form
        5. Slope
        6. Atan2
      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
      1. Injective, Surjective, Bijective
      2. Inverse Functions
    4. Parametric Equations
      1. Implicit functions
      2. Parameters
      3. Completing the square
        1. Intuitive understanding for completing the square
        2. Derive vertex form
        3. Didactic Method to complete the square
        4. Factoring with the Quadratic Formula
      4. Derivative of Parametric Equations
    5. Basic Trigonometry
      1. More Definitions
      2. Common Unit Circle Angles
        1. Unit Vectors "Lite"
      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
      1. Convert to Polar
      2. Polar Ellipse
      3. Polar Line
      4. Convert From Polar
      5. Convert Polar to Parametric
    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
          1. Acute Triangle
          2. Median
          3. Centroid
          4. Circumcenter
          5. Orthocenter
          6. Incenter
        8. Pythagorean Triangles (Triples)
        9. Triangle with known sides
        10. Regular Polygon
          1. Constructing the 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
          1. Geometric Mean
        8. Lateral Area of a Cone
        9. Frustum of a Cone
        10. 2d Circle Intersections
          1. The easy intersection
          2. Intersect by Rotation Translation
          3. Intersect using vectors
        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
          1. Center of the 4th Circle
          2. Apollonius Circles
        16. Lotfollah Dome
      3. Cycloid
        1. Conic Rotation
          1. Axes Rotation Point Rotation
            1. Equation 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
            1. Elliptic Center
            2. Translation
            3. General Conic Form
          6. Algorithm to rotate an ellipse
          7. Area of an ellipse
          8. Chart of Ellipse Equations
        3. Hyperbola
          1. Parabola
            1. Basics
            2. Nomenclature
              1. Vertex Finding
              2. Focal Length
            3. Parabola:Vertex at (h,k)
              1. Vertical Aligned Vertex Equation
              2. Symbolic Algebra 1
              3. Symbolic Algebra 2
              4. Parabola Derivation, Open right
            4. Solving a Rotated Parabola
              1. Rotation
              2. Solve Without Rotation
            5. Parametric Rotation
            6. Parametrize any Parabola
            7. Vertex of a Parametric Parabola
              1. Rotation Angle of a Parametric Parabola
            8. Standard Parametric Form
            9. Quadratic Bézier
              1. Vertex of Bézier Parabola
            10. Vertex Summary
            11. Tangent between parabolas
          2. Conic with Five Points
            1. Reserved
              1. Trigonometry Identities
                1. Using Trig Identities
                2. Angle Sum Identity Proof
                3. Half Angle Sum Identity
                4. Side length of a Regular n-gon
              2. Euler's Formula
                1. Hyperbolic Functions
                2. Complex to Polar Form
                3. Trig Identities from Euler's Formula
              3. Cubic Equation
                1. De Moivre's Theorem
              4. Arc Length
                1. Derivative and Slope
                2. Mean Value Theorem
                3. Standard Arc Length
                4. Arc Length with Parametric Equations
              5. Catenary Curve
                1. Short Derivation
                2. Detail Derivation
                3. Common Catenary Examples
                  1. Using the Information
                  2. Class 1. Equal attachments
                  3. Class 2. Unequal attachments
                  4. Solved Examples
                4. Summary
                5. Catenary Approximation