Osculating Circle
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point on the curve is the circle whose center lies on the inner normal line and whose curvature is the same as that of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named circulum osculans (Latin for "kissing circle") by Leibniz. The center and radius of the osc...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point on the curve is the circle whose center lies on the inner normal line and whose curvature is the same as that of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named circulum osculans (Latin for "kissing circle") by Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point. A geometric construction was described by Isaac Newton in his Principia. Imagine a car moving along a curved road on a vast flat plane. Suddenly, at one point along the road, the steering wheel locks in its present position. Thereafter, the car moves in a circle that "kisses" the road at the point of locking. The curvature of the circle is equal to that of the road at that point. That circle is the osculating circle of the road curve at that point.
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