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GeoGebra Example: Angles, LCM, GCD, Curve Sketching, Multiplication, Orthocenter

GeoGebra Example: Angles, LCM, GCD, Curve Sketching, Multiplication, Orthocenter
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2017-02-15 05:50
AngleVectorFunctionTrigonometryGeometric Construction
This example demonstrates the construction of geometric figures and phenomena involving angles, LCM and GCD, curve sketching, multiplication, and orthocenter using GeoGebra. The core mathematical concepts include angle calculations, least common multiple and greatest common divisor, function curve plotting, vector multiplication, and properties of the orthocenter in triangles. The construction utilizes commands such as Point, Vector, Textfield, Sequence, Intersect, and Segment. It is suitable for high school mathematics education and learning, helping to understand geometric constructions and algebraic applications.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_1
  2. Vector(A_1, B) → u
  3. Textfield(f) → inputBox1
  4. Vector(A_1, B_2) → v
  5. Sequence((f(k), k), k, -3, 3) → logGraphpts
  6. Vector(B_2, A_2) → w
  7. Intersect(f, b, (3.9999999990043906, 19.99999999820455)) → D
  8. Vector(x_*, C_1) → z
  9. Segment(D, X) → j
  10. Sequence((k, f(k)), k, 2, 20, 2) → ExpGraphpts
  11. Sequence(Vector[(0, k), (2, f(k))], k, 2, 20, 2) → ExpMD
  12. Sequence((2, f(k)), k, 2, 20, 2) → ExpTargPts_1
  13. Sequence(Vector[(2, k), (4, f(k))], k, 2, 20, 2) → InvLogMD_1
  14. Sequence((0, k), k, 2, 20, 2) → SourcePtsMD_1
  15. Sequence(Vector[(0, f(k)), (2, g(f(k)))], k, 2, 20, 2) → logMD

AI Drawing Prompt Reference

Draw a coordinate plane with a function curve. Place a point on the vertical axis and construct two vectors from it to different locations, forming a triangle. Mark the intersection of the curve with a line, and connect that point to another reference point with a segment. Along the curve, sample points at integer steps from negative to positive values, and also draw vectors from equally spaced points on the vertical axis to corresponding curve points, as well as vectors from equally spaced points on the horizontal axis to higher curve points, illustrating mapping and transformation. The figure includes the curve, points, vectors, and segments, highlighting angles, multiplication, and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.