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Sphere Surface Area Mnemonic

Sphere Surface Area Mnemonic
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2015-11-09 17:42
Solid GeometryCalculusGeometric Construction
This example demonstrates the derivation and visualization of the sphere's surface area formula, involving core math concepts like sphere geometry, integral calculus, and geometric construction. Key GeoGebra commands used include Intersect, Point, Circle, Surface, If, Sphere, and Segment for constructing the visual representation, making it suitable for high school students and math enthusiasts studying calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(Segment[(0, 0, -1), (0, 0, 1)]) → A
  3. Circle(O, 1) → c
  4. Surface((cos(u) * cos(v)), (cos(u) * sin(v)), (z(A) * sin(u)), u, 0, 1.5707963267948966, v, -3.141592653589793, 3.141592653589793) → a
  5. If(z(A) ≟ 0, 1, If[abs(z(A)) < 1, 1 + (z(A)^(2) * log((1 + sin(t_1)) / cos(t_1)) / sin(t_1)), 2]) → k_1
  6. Sphere(O, 1) → b
  7. Point(c) → B
  8. Segment(O, B) → r
  9. Segment(O, A) → d