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Area Differential

Area Differential
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2016-07-06 20:25
FunctionCalculusDerivative
This example illustrates the concept of area differential. It involves key mathematical concepts such as area, derivatives, and functions. Using GeoGebra commands like Line, Point, Polygon, Locus, and Derivative, the example constructs the graphs of functions f and g and demonstrates their loci using the Locus command. Suitable for high school mathematics education and learning calculus concepts.

GeoGebra Commands & Parameters

  1. Line(a, xAxis) → h
  2. Point(h) → A
  3. Sequence(CurveCartesian[x(a + (r * t) + ((ί * r) * k)), y(a + (r * t) + ((ί * r) * k)), t, -1, 1], k, -1, 1, 2 / n) → list1
  4. Sequence(CurveCartesian[x(a - (r * k) + ((ί * r) * t)), y(a - (r * k) + ((ί * r) * t)), t, -1, 1], k, -1, 1, 2 / n) → list2
  5. Point({list1, list2}) → B
  6. Sequence(CurveCartesian[x((a + (r * t) + ((ί * r) * k))^(2)), y((a + (r * t) + ((ί * r) * k))^(2)), t, -1, 1], k, -1, 1, 2 / n) → list3
  7. Sequence(CurveCartesian[x((a - (r * k) + ((ί * r) * t))^(2)), y((a - (r * k) + ((ί * r) * t))^(2)), t, -1, 1], k, -1, 1, 2 / n) → list4
  8. Polygon(B, B', 4) → poly1, i, j, k, l, C, D
  9. Point(poly1) → E
  10. Locus(z_2, E) → loc1
  11. Derivative(f, x) → xu
  12. Derivative(f, y) → xv
  13. Derivative(g, x) → yu
  14. Derivative(g, y) → yv
  15. Sequence((x(Element[list5, i]) + (ί * y(Element[list5, i])))^(2), i, 1, 16) → list6
  16. Polygon(list6) → poly2