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Proportional Co-Variation: Real Number Multiplication

Proportional Co-Variation: Real Number Multiplication
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2015-02-06 12:28
FunctionCoordinate GeometryCalculusSlider AnimationGraphing
This example demonstrates proportional co-variation extending from natural to real numbers. It involves core math concepts like multiplication, piecewise functions, histograms, differential calculus, correlation, and parabolas. Constructed using GeoGebra commands like Textfield, Max, Segment, it is suitable for high school and above learners/teachers to understand multiplication variation in reals.

GeoGebra Commands & Parameters

  1. Textfield(number_{multiplier}) → input_{multiplier}
  2. Textfield(number_{multiplicand}) → input_{multiplicand}
  3. Max({number_{multiplier}, (-number_{multiplier}), number_{multiplicand}, number_{multiplicand}, number_{product}, (-number_{product})}) → max
  4. Segment(Unit, Multiplier) → s_1
  5. Segment(Multiplicand, Product) → PCV
  6. Segment((0, 0), Unit) → h_1
  7. Segment((0, 0), Multiplicand) → h_2
  8. Segment((0, 0), Multiplier) → h_3
  9. Segment((0, 0), Product) → h_4
  10. Textfield(number_{multiplier}) → Mltplr
  11. Textfield(number_{multiplicand}) → Mltplcnd
  12. Textfield(number_{multiplier}) → input_2
  13. Textfield(number_{multiplicand}) → input_1
  14. Textfield(number_{multiplier}) → inputBox1_1
  15. Textfield(number_{multiplicand}) → inputBox2_1
  16. Textfield(number_{multiplier}) → input_5
  17. Textfield(number_{multiplicand}) → input_3
  18. Textfield(number_{multiplier}) → inputBox1_2
  19. Textfield(number_{multiplicand}) → inputBox2_2
  20. Textfield(number_{multiplier}) → input_6
  21. Textfield(number_{multiplicand}) → input_4
  22. Textfield(number_{multiplier}) → inputBox1_3
  23. Textfield(number_{multiplicand}) → inputBox2_3
  24. Textfield(number_{multiplier}) → input_9
  25. Textfield(number_{multiplicand}) → input_7
  26. Textfield(number_{multiplier}) → inputBox1_4
  27. Textfield(number_{multiplicand}) → inputBox2_4
  28. Textfield(number_{multiplier}) → input_{10}
  29. Textfield(number_{multiplicand}) → input_8
  30. Textfield(number_{multiplier}) → inputBox1_5
  31. Textfield(number_{multiplicand}) → inputBox2_5

AI Drawing Prompt Reference

Create a graph demonstrating proportional co-variation of real number multiplication, featuring two input sliders for multiplier and multiplicand, calculate their product, and draw four line segments from the origin to each value. Connect the multiplier to the product and the multiplicand to the product with two line segments, determine key positions using a max function, and visualize the variation of multiplication in real numbers.
The prompt above was compiled from the original drawing commands and is for reference only.