Archimedes used these triangles to work out the area under a chord of a parabola.
First sketch a parabola, and set its equation to be a*x^2
Now draw a chord
Put a point on the parabola and specify its location to be (s+t)/2
Create tangents to the parabola at A and B.
Put a point at the intersection of the tangents
Use the Symbolic Panel to get the area of the triangle ABC.
And the triangle ABD
Notice these areas depend only on the value (s-t). Can you use this to create an infinite series for the area between the chord and the parabola?
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