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Rotating a Parabola Around the x-axis

Rotating a Parabola Around the x-axis
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2014-10-29 22:07
FunctionSolid GeometryCalculus
In collections My 3D Collection
This example demonstrates the effect of rotating the parabola f(x) = 4x - x² around the x-axis. Key concepts include rotation, solid geometry, and coordinate geometry. It uses Circle, Point, CircumcircleArc, Surface, Midpoint, Center, etc., in GeoGebra. Suitable for high school math education or learning.

GeoGebra Commands & Parameters

  1. Circle(xAxis, A_1) → c
  2. Point(c) → A
  3. Point(c) → D
  4. CircumcircleArc(A_1, G, A) → d
  5. Surface(t, (f(t) * cos(u)), (f(t) * sin(u)), t, 0, 4, u, 0, d / 3) → a
  6. Midpoint(A, A_1) → C
  7. Center(c) → E
  8. Center(d) → F

AI Drawing Prompt Reference

Draw the solid formed by rotating the parabola f(x) = 4x - x² around the x-axis. First, draw the x-axis and two points A and D on the parabola, then create a circle c through these points. Next, draw a circular arc d on circle c and use point A on the parabola as the starting point to rotate and generate a surface a along arc d. Finally, find the centers E and F of circle c and arc d, as well as the midpoint C of points A and A_1.
The prompt above was compiled from the original drawing commands and is for reference only.