The idea of a tangent line is central to many aspects of mathematics. In geometry, we study when a line rests on another figure at just one point, the point of tangency. In calculus, the slope of the line tangent to a curve at a point becomes the “derivative” of that curve at that point. One can even think of tangencies in more than one dimension. Imagine an (x,y) plane drawn on a table with a three dimensional object resting on it. One can therefore find a point of tangency in the x direction, and also one in the y direction.
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