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Dynamic Visualization of Continuity and Pythagorean Theorem

Dynamic Visualization of Continuity and Pythagorean Theorem
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2017-06-14 17:37
FunctionSequenceCoordinate GeometryCalculusComplex Number
This GeoGebra example dynamically visualizes the relationship between continuous functions and the Pythagorean theorem using randomly generated points, sequences, and table text. Core concepts include continuity, the Pythagorean theorem, calculus fundamentals, and complex number geometry. Construction employs commands like Random, Sequence, TableText, Line, and objects such as rises, runs, and input boxes to enable real-time parameter adjustment via buttons and text fields. Ideal for high school calculus introduction, analytic geometry exercises, or complex number exploration, it helps students intuitively grasp the geometric meaning of function changes and distance formulas.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → n_1
  2. Random(-20, 20) → n
  3. Random(-10, 10) → m
  4. Line(B, A) → a
  5. Textfield(deltax) → InputBox1
  6. Textfield(deltay) → InputBox2
  7. Textfield(b) → InputBox3
  8. Sequence(((deltax * i), b + (deltay * i)), i, -20, 20) → list1
  9. Sequence(Segment[A + ((deltax * (i + 1)), (deltay * i)), A + ((deltax * (i + 1)), (deltay * (i + 1)))], i, -20, 20) → rises
  10. Sequence(Segment[A + ((deltax * i), (deltay * i)), A + ((deltax * (i + 1)), (deltay * i))], i, -20, 20) → runs
  11. TableText({{p, k, l}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}, {A12, B12, C12}, {A13, B13, C13}, {A14, B14, C14}, {A15, B15, C15}, {A16, B16, C16}}, "|_r") → text2