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Linear Function to Cone Open Middle Example

Linear Function to Cone Open Middle Example
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2022-05-20 23:20
FunctionCoordinate GeometrySolid GeometryGraphing
This example demonstrates how to generate a cone geometric model using a linear function, exploring the correlation between functions and solid shapes. Core math concepts include linear functions, cone volume, analytical geometry, and 3D surface construction. Construction highlights involve GeoGebra commands like Textfield, Surface, If, Mode, Sequence, CountIf, Max, Intersect, Segment, Angle, and objects such as j, g, f, d, a, b, c. Suitable for high school and above learners to understand the transformation between function graphs and spatial geometry, and parametric design.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox1
  2. Textfield(b) → InputBox2
  3. Textfield(c) → InputBox3
  4. Textfield(d) → InputBox4
  5. Textfield(f) → InputBox5
  6. Textfield(g) → InputBox6
  7. Surface(h, α, xAxis) → e
  8. Textfield(j) → InputBox7
  9. If(correct, "√", "X") → text4
  10. Mode(l1) → l2
  11. Sequence(CountIf[x ≟ i, l1], i, 0, 9, 1) → l3, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
  12. CountIf(x > 1, l3) → l
  13. CountIf(x ≥ 3, l3) → k
  14. Max(l3) → m
  15. Intersect(xAxis, yAxis) → D
  16. Segment(B, D) → p
  17. Segment(B, F) → n
  18. Angle(F, E, D) → β

AI Drawing Prompt Reference

Create a 3D cone model guided by a linear function. Start with coordinate axes and place key points that define the cone’s reference geometry, then draw connecting segments between these points to establish the construction. Build the cone-like surface using a parameterized surface definition, where the linear-function inputs control the cone opening and side shape. Add text input fields for the parameters and include a small status text that shows √ or X based on a correctness condition. Conclude by marking an angle formed by two characteristic elements around the reference direction to indicate the cone opening relationship.
The prompt above was compiled from the original drawing commands and is for reference only.