MathPlotAI Logo MathPlotAI

Functions Rectangle in Semi Circle

Functions Rectangle in Semi Circle
Loading the math board and drawing, please wait…
2018-11-24 03:07
FunctionCoordinate GeometryCalculusGeometric ConstructionGraphing
This example demonstrates the process of drawing a function rectangle within a semicircle, highlighting geometric and analytical concepts. It involves curve sketching, tangent lines, orthogonal lines, and key GeoGebra commands like Semicircle, Segment, OrthogonalLine, Intersect, Polygon, Midpoint, CircleSector, Angle, Point, and Vector. Core math concepts include functions, derivatives, and coordinate geometry. Suitable for high school and above, particularly for calculus and geometry instruction.

GeoGebra Commands & Parameters

  1. Semicircle(A, B) → c
  2. Segment(A, B) → f
  3. OrthogonalLine(C1, f) → g
  4. OrthogonalLine(C2, f) → h
  5. Intersect(c, g, 1) → C
  6. Intersect(c, h, 1) → D
  7. Polygon(C1, C2, D, C) → q1, c1, c2, d, c_1
  8. Midpoint(A, B) → E
  9. CircleSector(E, B, A) → e
  10. Polygon(E, C1, C) → t1, c_2, e_1, i
  11. Angle(E, C1, C) → α
  12. Point(e) → F
  13. Point(e) → G
  14. Midpoint(F, C1) → H
  15. Midpoint(C2, G) → I
  16. Vector(H - (0, 0.7), C1 - (0, 0.7)) → u
  17. Vector(H - (0, 0.7), F - (0, 0.7)) → v
  18. Midpoint(C1, E) → J
  19. Vector(J - (0, 0.7), C1 - (0, 0.7)) → w
  20. Vector(E - (1, 1.5), F - (0, 1.5)) → k
  21. Vector(E - (-1, 1.5), G - (0, 1.5)) → j
  22. Vector(J - (0, 0.7), E - (0, 0.7)) → b