Parabolic Segment: Archimedes Insight
Creation of this resource was inspired from watching Steven Strogatz 's "The Beauty of Calculus" lecture (specifically, 43:35 - 51:42) he delivered at Yale University.
This GeoGebra applet dynamically illustrates one interesting fact Archimedes discovered as he was using triangles in his attempt to calculate the area of a parabolic segment (i.e. area bounded by a parabola and any secant line drawn through it) by method of exhaustion.
LARGE POINTS are MOVEABLE at any time.
The unlabeled slider (upper right) adjusts the parabola's vertical stretch.
Note:
Segments and/or lines of same style-type (color, style) that appear parallel ARE PARALLEL.