Quadratic Bezier Curve and Parabola

Quadratic Bezier Curve and Parabola
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2016-06-11 20:22
This example demonstrates the geometric relationship between a quadratic Bezier curve and a parabola through curve stitching. It involves core mathematical concepts such as parabola, upper and lower sum (Riemann sum), curve sketching, linear functions, geometry, and arithmetic mean. The construction uses GeoGebra commands Locus, Line, Sequence, and objects like A, B, C, t, P, loc1, g, h, list1. It is suitable for high school mathematics education and learning, helping to understand the geometric representation and calculation methods of curves and functions.

GeoGebra Commands & Parameters

  1. Locus(P, t) → loc1
  2. Line(A, B) → g
  3. Line(B, C) → h
  4. Sequence(Line[(k * A) + ((1 - k) * B), (k * B) + ((1 - k) * C)], k, -5, 5, 0.05) → list1