Section 18.1: What is Calculus?

18.1 Outline

  1. What is Calculus?
    1. Calculus is the mathematics of motion and change.
    2. The three main ideas of calculus are limit, derivative, and integral
  2. The Limit: Zeno’s Paradox
    1. Achilles and the tortoise
    2. limit of a sequence
  3. The derivative: the tangent
See the whole entry “Section 18.1: What is Calculus?”

Section 15.4: Conic Sections

15.4 Outline

  1. Introduction
    1. definition
    2. model
  2. Geometric definition of conic sections
    1. parabola
      1. focus
      2. directrix
      3. axis
      4. vertex
    2. ellipse
      1. foci
      2. major axis
      3. center
      4. minor axis
    3. circle
      1. center
      2. radius
    4. hyperbola
      1. transverse axis
      2. center
      3. conjugate axis
  3. Algebraic definition of conic sections
    1. general form
      1. first-degree equation
See the whole entry “Section 15.4: Conic Sections”

Section 8.2: Area

8.2 Outline

  1. Rectangles
    1. define area
    2. define square unit
    3. formulas
      1. rectangle
      2. square
  2. Parallelograms
    1. definition
    2. formula
    3. derivation of formula
  3. Triangles
    1. formula
    2. derivation of formula
  4. Trapezoids
    1. definition
    2. formula
    3. derivation of formula
  5. Circles
    1. formula
    2. derivation of formula
  6. Applications
    1. conversion application
    2. acre definition
    3. conversion of
See the whole entry “Section 8.2: Area”

Section 7.6: Mathematics, Art, and Non-Euclidean Geometries

7.6 Outline

  1. Golden rectangles
    1. definition
    2. divine proportion
    3. tau
  2. Mathematics and art
    1. golden ratios in art
    2. proportions of the human body
    3. spiral constructed using a golden rectangle
  3. Projective geometry
    1. Duccio’s Last Supper
    2. Hogarth’s Perspective Absurdities
    3. false perspective
    4. Masaccio’s The Holy Trinity
See the whole entry “Section 7.6: Mathematics, Art, and Non-Euclidean Geometries”