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Archimedes: Quadrature of Parabolic Segment

Area, Parabola
This is an activity showing Archimedes' Quadrature of a Parabolic Segment. See the attached PDF for the math details. Note how the ratio of the areas is constant at 4/3, just as Archimedes said! The sliders h and k control the parabola, while m is the slope of the line cutting off a segment of the parabola. Click and drag the plot area as needed to see the entire triangle.