Essential Ideas

Section 8.3: Surface Area, Volume, and Capacity

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8.3 Outline

  1. Dimensions
    1. one-dimensional measurement (length)
    2. two-dimensional measurement (area)
    3. three-dimensional measurement (volume)
  2. Surface area
  3. Volume
    1. formula for a cube
    2. rectangular parallelepiped
  4. Capacity
    1. standard units of capacity
    2. relationship between volume and capacity
      1. U.S.
      2. metric

 

8.3 Essential Ideas

The surface area … See the whole entry

Section 8.2: Area

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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 7.6: Mathematics, Art, and Non-Euclidean Geometries

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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 7.5: Right-Triangle Trigonometry

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7.5 Outline

  1. Pythagorean theorem
  2. Trigonometric ratios
    1. sine
    2. cosine
    3. tangent
  3. Inverse trigonometric ratios
    1. calculator calculating
    2. inverse trigonometric ratios
      1. inverse tangent
      2. inverse cosine
      3. inverse sine
  4. Applications
    1. angle of elevation
    2. angle of depression

 

7.5 Essential Ideas

7.5.1… See the whole entry

Section 7.3: Triangles

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7.3 Outline

  1. Terminology
    1. six parts of a triangle
    2. classifying triangles
      1. by sides
        1. scalene
        2. isosceles
        3. equilateral
      2. by angles
        1. acute
        2. right
        3. obtuse
    3. congruent triangles
      1. construction
      2. corresponding parts
  2. Angles of a triangle
    1. angles in a triangle
    2. exterior angle
    3. exterior angle property
  3. Isosceles triangle
… See the whole entry

Section 7.2: Polygons and Angles

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7.2 Outline

  1. Angles
    1. vertex (pl. vertices)
    2. angle
    3. notation for angles
    4. equal angles
    5. degree
    6. classifications
      1. acute
      2. right
      3. obtuse
      4. straight
    7. congruent angles
    8. complementary angles
    9. supplementary angles
    10. adjacent angles
    11. vertical angles
  2. Polygons
    1. definition
    2. regular polygon
    3. classifications
    4. quadrilateral
      1. classification
      2. trapezoid
      3. parallelogram
      4. rhombus
      5. rectangle
      6. square
… See the whole entry

Section 7.1: Geometry

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7.1 Outline

  1. Greek (Euclidean) geometry
    1. undefined terms
      1. point
      2. line
      3. plane
      4. surface
    2. categories
      1. traditional (Euclidean) geometry
      2. transformational geometry
    3. Euclid’s postulates
      1. postulate
      2. axiom
      3. theorem
      4. five postulates
    4. parallel lines
    5. non-Euclidean geometries
    6. straightedge
    7. line segment
    8. congruent figures
    9. construct a figure
      1. construct a circle
      2. construct
… See the whole entry