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equiangular spiral

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A curve whose equation in polar coordinates is r=ae, where a (>0) and k are constants. Let O be the origin and P be any point on the curve. The curve derives its name from the property that the angle α between OP and the tangent at P is constant. In fact, k=cot α. The equation can be written r=+b, and the curve is also called the logarithmic spiral. Animations of related curves, and an interactive manipulative of the spiral in Geometer's Sketchpad.

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