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Length vs. Temperature - Square Root Simulation

Length vs. Temperature - Square Root Simulation
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2017-10-17 02:50
FunctionGeometric Construction
This example demonstrates the simulation of the relationship between length and temperature using a square root function. It involves core mathematical concepts such as square root functions, geometric constructions, and data simulation. Key GeoGebra commands like Polygon, Textfield, Segment, If, Point, and Mirror are used to create dynamic visualizations, with sliders to simulate temperature changes and observe length variations. Suitable for high school mathematics education, focusing on function graphs, geometric transformations, and data visualization.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Textfield(cmin) → InputBox1
  3. Textfield(cmax) → InputBox2
  4. Textfield(a) → InputBox3
  5. Textfield(outputmin) → InputBox4
  6. Textfield(outputmax) → InputBox5
  7. Segment(E, F) → j
  8. Textfield(a) → InputBox3_1
  9. Textfield(outputmin) → InputBox4_1
  10. Textfield(outputmax) → InputBox5_1
  11. Segment(E_1, F_1) → j_1
  12. Polygon(A_1, B_1, 4) → poly1_1, f_1, g_1, h_1, i_1, C_1, D_1
  13. If(ZeroToOne < 37 / 256, 0, 37 / 256 ≤ ZeroToOne ≤ 179 / 256, (48.845 * (ZeroTo256 - 37)^(1 / 3) / 256), ZeroToOne > 179 / 256, 1) → red
  14. If(ZeroToOne < 94 / 256, 255, 94 / 256 ≤ ZeroToOne ≤ 210 / 256, ((-2.198 * (ZeroTo256 - 210))) / 256, ZeroToOne > 210 / 256, 0) → blue
  15. Textfield(lengthmin) → InputBox6
  16. Textfield(lengthmax) → InputBox7
  17. Point(Circle[G, abs(n(a))]) → H
  18. Segment(G, H) → k
  19. Textfield(n) → InputBox8
  20. Mirror(H, G) → H'
  21. Segment(G, H') → l
  22. Point(Circle[I, abs(puzzle(a))]) → J
  23. Segment(I, J) → m
  24. Mirror(J, I) → J'
  25. Segment(I, J') → r