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Geometric Construction Example by Martin Flashman

Geometric Construction Example by Martin Flashman
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2017-02-15 00:45
FunctionSequenceGeometric Construction
In collections Mapping Diagrams: From AB to C&DE, Resource
This example demonstrates the basic principles of geometric construction, involving core math concepts such as random variables, logic, and constructions. Using GeoGebra commands like Point, Vector, Textfield, etc., users can intuitively understand the key points of geometric construction. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_1
  2. Vector(A_1, B) → u
  3. Textfield(f) → inputBox1
  4. Sequence((0, k), k, -3, 3) → SourcePtsMD
  5. Sequence((k, f(k)), k, -3, 3) → ExpGraphpts
  6. Vector(A_1, B_2) → v
  7. Sequence(Vector[(0, k), (2, (y_{zoom} * f(k)))], k, -3, 3) → ExpMD
  8. Sequence((2, (y_{zoom} * f(k))), k, -3, 3) → ExpTargPts
  9. Sequence(Vector[(2, k), (4, (y_{zoom} * f(k)))], k, -3, 3) → InvLogMD
  10. Sequence((base^(k) + 1, (2 * k)), k, -2, 3) → logGraphpts
  11. Sequence(Vector[(0, base^(k) + 1), (2, (y_{zoom} * g(base^(k) + 1)))], k, -3, 3) → logMD

AI Drawing Prompt Reference

On a coordinate plane, start with a point on the y-axis and draw a vector pointing right to another point. Place an input box for a function nearby. Along the y-axis, mark points from -3 to 3 at equal intervals, and for each, compute the function value to create corresponding points. Connect each y-axis point to its function-value point with a vector, showing a mapping. Then map these function values to points on the vertical line x=2, and further to points on x=4, illustrating a logarithmic transformation. Additionally, plot an exponential curve, and draw vectors from y-axis points representing exponential values to points on x=2, demonstrating the inverse relationship between exponential and logarithmic functions. The whole figure shows geometric constructions of function mappings and transformations.
The prompt above was compiled from the original drawing commands and is for reference only.