Geometric Construction 4

Let A,B,C,D be four points on a circle. Construct four circles S1, S2, S3, S4 so that S1 is tangent to S2  at A, S2 is tangent to S3  at B, S3 is tangent to S4 at C, S4 is tangent to S1  at D.

1.gif (9078 bytes)

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Construct the graph of the quadratic polynomial given by a tangent, the point of contact and a second point of the graph.

2.gif (11836 bytes)

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Let A,B,C,D be four points on the graph of a quadratic polynomial. Construct four quadratic polynomials with graphs S1, S2, S3, S4 so that S1 is tangent to S2  at A, S2 is tangent to S3  at B, S3 is tangent to S4 at C, S4 is tangent to S1  at D.

3.gif (12869 bytes)

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Construct the parabola given by two tangents and points of contact.

4-1.gif (13280 bytes)

4-2.gif (14684 bytes)

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Construct the common tangents of a parabola and its directrix.

5.gif (10369 bytes)

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Construct the graph of the cubic polynomial p with p(a), p'(a), p(b), p'(b) given.

hermite.gif (10066 bytes)

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Construct the cubic spline passing through four points.

7.gif (9668 bytes)

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Construct an animation displaying two tangential parabolas, one stationary one moving.

8.gif (7935 bytes)