Vector Methods

Table of Contents

• Algebra and Elementary Geometry

  • Vector Decomposition
  • Vector Methods: Point to line
  • Tool: Altitude of a triangle
  • Vectors: Angle Bisector
  • Circle Through Three Points
  • Vectors: Incircle
  • Vector Algebra: Inequalities in the plane
  • Convex Quadrilateral 1 (quiet)
  • Convex Quadrilateral 2 (loud)
  • Centroid of a triangle
  • Centroid of a polygon
  • Complex Algebra: Rotation

• Intersection Machine

  • Line, Ray, Segment intersection
  • Intersect Line and Circle
  • Intersect Line and Ellipse
  • Intersect two circles
  • Polygon self-intersection, 1
  • Intersect Polygon and Ray
  • Intersect Polygon and Line
  • Intersect Polygon and Segment
  • Polygon Self-Intersection 2
  • Intersect View Rectangle

• Collision

  • Collision: Circle and Rectangle

• Orientation

  • Orientation 1: Binary sign
  • Orientation: Circle
  • Parent, Child
  • Translation, Scale, Rotation
  • Tool: Circular Arc
  • Signed angle

• From 100 Great Problems

  • 40a. Triangulation from 3 known points
  • 52. Astroid, Rolling Circle
  • 31b. Monge's Problem: Vector Solution
  • Pole and Polar 2
  • Tangent circles, differential

• Light

  • Reflect a Ray of light, 1
  • One-sided reflection
  • Reflect a lamp
  • Two Mirrors
  • Refract a ray (Snell's Law)
  • A ray in a corner (between two lines)

• Conic Sections & More

  • Parabola from Four Tangents, 2
  • Bézier Parabola
  • Vectors: Parabola from Three Points (Focus and Directrix)
  • Vector Parabola 3D
  • Ellipse: Foci from parametric equation
  • Parabola: Vertex and (Focus or Point on arc)

• The Tangent Circle Problem

  • Mutually Exterior & Tangent Circles, 2
  • Reflection: Line about a Circle
  • Reflection: Circle about a Circle
  • Circle Reflection: Metric Space
  • Arbelos 1c: Vector Reduction

• Supplement: Zeros of trigonometric polynomials

  • Trigonometric Polynomial, 1
  • Trigonometric Polynomial, 2
  • Approximate the function cos(x)