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Riemann Surface: (1-z^2)^(1/2)

Riemann Surface: (1-z^2)^(1/2)
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2018-03-15 19:15
FunctionTrigonometryComplex Number
This example demonstrates the Riemann surface of the complex function (1-z^2)^(1/2). Key mathematical concepts include complex numbers, power functions, and Riemann surfaces. Users can dynamically adjust parameters using the Surface command to observe changes in the function's graph. Suitable for high school and above mathematics enthusiasts and students studying complex function theory.

GeoGebra Commands & Parameters

  1. Surface((u * cos(v)), (u * sin(v)), HRe((u * cos(v)), (u * sin(v)), 2, 0), u, 0, 2, v, (-π), π - π / 500) → B0
  2. Surface((u * cos(v)), (u * sin(v)), HRe((u * cos(v)), (u * sin(v)), 2, 1), u, 0, 2, v, (-π), π - π / 500) → B1
  3. Surface((u * cos(v)), (u * sin(v)), HIm((u * cos(v)), (u * sin(v)), 2, 0), u, 0, 2, v, 0, π - π / 500) → C0
  4. Surface((u * cos(v)), (u * sin(v)), HIm((u * cos(v)), (u * sin(v)), 2, 1), u, 0, 2, v, 0, π - π / 500) → C1
  5. Surface((u * cos(v)), (u * sin(v)), HIm((u * cos(v)), (u * sin(v)), 2, 0), u, 0, 2, v, (-π), ((-π)) / 500) → D0
  6. Surface((u * cos(v)), (u * sin(v)), HIm((u * cos(v)), (u * sin(v)), 2, 1), u, 0, 2, v, (-π), ((-π)) / 500) → D1

AI Drawing Prompt Reference

Draw the Riemann surface of the complex function (1-z^2)^(1/2). First, plot the real and imaginary parts of the surface using parameters u and v, where u ranges from 0 to 2 and v ranges from -π to π. Adjust the parameters to observe changes in the function's graph.
The prompt above was compiled from the original drawing commands and is for reference only.