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e and Natural Logarithm

e and Natural Logarithm
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2017-10-18 22:07
FunctionTrigonometryCalculus
This example demonstrates the properties of the natural logarithm and the base e. Key mathematical concepts include logarithmic functions and their properties. Using GeoGebra commands such as Mirror, Tangent, and Slope, the graph of the logarithmic function and its related properties are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Mirror(P, a) → P'
  2. Tangent(P, f) → c
  3. Slope(c) → m
  4. Tangent(P', g) → d
  5. Circle(P', 1) → h
  6. OrthogonalLine(P', xAxis) → i
  7. Intersect(h, i, 2) → A
  8. OrthogonalLine(A, i) → j
  9. Intersect(d, j) → B
  10. Polygon(P', A, B) → poly1, b_1, p', a_1

AI Drawing Prompt Reference

Draw the graph of a natural logarithm function and its related properties. First, create the mirror image of the function, then find the point symmetric to the mirror image about the x-axis and draw a line perpendicular to the x-axis through this point. Next, draw a unit circle centered at the mirror image point and find its intersections with the perpendicular line. Then, draw a line perpendicular to the line connecting the mirror image point and the intersection point. Finally, connect the mirror image point, the intersection point, and the point where this line intersects the tangent of the logarithmic function to form a polygon, showcasing the tangent, normal, and related geometric properties of the logarithmic function.
The prompt above was compiled from the original drawing commands and is for reference only.