We introduce the important technology of defining, and computing the tangent line to an algebraic curve at a point lying on it. We start with a discussion on bi polynumbers, which are two dimensional arrays that are equivalent to polynomials in two variables, but without us having to fret about what a "variable" actually is.
Then we introduce algebraic curves associated to bi polynumbers, discuss the thorny issue of when we can find points lying on such, and then investigate how to define a tangent line should we have a point on a curve.
The trick is to start with an important special case-- we introduce the idea of a grounded algebraic curve. For this defining tangents is easy -- we just truncate the bi polynumber. For the more general case, we have to do some judicious translation.
education film Bi Polynumbers and Tangents to Algebraic Curves | Algebraic Calculus One | Wild Egg | |
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