areas

sonom, Apr 5, 2014

Table of Contents

  1. formulas
    1. area of a triangle (sas)
    2. area of a rectangle
    3. area of a rectangle-1
    4. area of a parallelogram
    5. area of a triangle
    6. area of a triangle-2
    7. area of an equilateral triangle
    8. area of a trapezoid
    9. area of a kite
    10. find the area
    11. regular polygons
    12. Brahmagupta's formula
    13. area of a circle
    14. measurements in a circle
    15. find the area-1
    16. Area of Circles (3)
  2. ratios
    1. pythagorean and galileo's law
    2. areas of similar triangles
    3. ratio of areas-1
    4. ratio of areas-2
  3. calculus
    1. area of a circle-1
    2. minimum area
    3. minimum area (line)
    4. maximum area (angle)
    5. napier's inequality
    6. a property of the hyperbola
    7. area between a curve and x-axis
    8. area between two curves
    9. area of an ellipse
    10. an extrema problem-2
    11. an extrema problem-3
    12. the bell curve
  4. themes from the history of mathematics
    1. the lune of Hippocrates
    2. the lunes of Alhazen
    3. generalization (pappus) of pythagorean
    4. archimedes' arbelos
    5. archimedes' "salinon"
    6. ptolemy's theorems
    7. yin-yang
    8. Garfield's proof for pythagorean theorem
    9. vivianni's theorem
    10. a Reuleaux triangle
    11. sierpinski triangles
    12. Koch snowflake
    13. pyth-proof7
  5. miscellaneous
    1. areas inside a parallelogram
    2. areas inside a trapezoid
    3. square vs rhombus
    4. areas-3
    5. rolling circle squares itself
    6. the famous "1/5" square
    7. the famous "1/7" triangle
    8. a math trick-1
    9. a math trick-2
    10. an identity-2
    11. an identity...
    12. squaring a rectangle
    13. pythagorean (verification)
    14. square-rectangle paradox
    15. isosceles triangle paradox
    16. geometric mean theorem
    17. Water Triangle
    18. fraction multiplication
    19. comparing fractions
    20. subtraction of proper fractions

1.

formulas

  • 1. area of a triangle (sas)
  • 2. area of a rectangle
  • 3. area of a rectangle-1
  • 4. area of a parallelogram
  • 5. area of a triangle
  • 6. area of a triangle-2
  • 7. area of an equilateral triangle
  • 8. area of a trapezoid
  • 9. area of a kite
  • 10. find the area
  • 11. regular polygons
  • 12. Brahmagupta's formula
  • 13. area of a circle
  • 14. measurements in a circle
  • 15. find the area-1
  • 16. Area of Circles (3)

1.1.

area of a triangle (sas)

area of a triangle (sas)
– sonom

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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2.

ratios

  • 1. pythagorean and galileo's law
  • 2. areas of similar triangles
  • 3. ratio of areas-1
  • 4. ratio of areas-2

2.1.

pythagorean and galileo's law

pythagorean and galileo's law
– sonom

2.2.

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2.3.

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2.4.

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3.

calculus

  • 1. area of a circle-1
  • 2. minimum area
  • 3. minimum area (line)
  • 4. maximum area (angle)
  • 5. napier's inequality
  • 6. a property of the hyperbola
  • 7. area between a curve and x-axis
  • 8. area between two curves
  • 9. area of an ellipse
  • 10. an extrema problem-2
  • 11. an extrema problem-3
  • 12. the bell curve

3.1.

area of a circle-1

area of a circle-1
– sonom

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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4.

themes from the history of mathematics

  • 1. the lune of Hippocrates
  • 2. the lunes of Alhazen
  • 3. generalization (pappus) of pythagorean
  • 4. archimedes' arbelos
  • 5. archimedes' "salinon"
  • 6. ptolemy's theorems
  • 7. yin-yang
  • 8. Garfield's proof for pythagorean theorem
  • 9. vivianni's theorem
  • 10. a Reuleaux triangle
  • 11. sierpinski triangles
  • 12. Koch snowflake
  • 13. pyth-proof7

4.1.

the lune of Hippocrates

the lune of Hippocrates
– sonom

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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5.

miscellaneous

  • 1. areas inside a parallelogram
  • 2. areas inside a trapezoid
  • 3. square vs rhombus
  • 4. areas-3
  • 5. rolling circle squares itself
  • 6. the famous "1/5" square
  • 7. the famous "1/7" triangle
  • 8. a math trick-1
  • 9. a math trick-2
  • 10. an identity-2
  • 11. an identity...
  • 12. squaring a rectangle
  • 13. pythagorean (verification)
  • 14. square-rectangle paradox
  • 15. isosceles triangle paradox
  • 16. geometric mean theorem
  • 17. Water Triangle
  • 18. fraction multiplication
  • 19. comparing fractions
  • 20. subtraction of proper fractions

5.1.

areas inside a parallelogram

areas inside a parallelogram
– sonom

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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5.14.

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5.15.

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5.16.

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5.17.

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5.18.

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5.19.

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5.20.

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