Lesson plan
Implicit curve
of the surface z=\sin(x+y)-\cos(xy)+1 In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation x^2+y^2=1 . In general, every implicit curve is defined by an equation of the form : F(x,y)=0 for some function F of two variables. Hence an implicit curve can be considered as the set of zeros of a function of two variables. Implicit means that the equation is not expressed as a solution for either x in terms of y or vice versa. If F(x,y) is a polynomial in two variables, the corresponding curve is called an algebraic curve, and specific methods are available for studying it. Plane curves can be represented in Cartesian coordinates (x, y coordinates) by any of three methods, one of which is the implicit equation given above. The graph of a function is usually described by an equation y=f(x) in which the functional form is explicitly stated; this is called an explicit representation. The third essential description of a curve is the parametric one, where the x- and y-coordinates of curve points are represented by two functions both of whose functional forms are explicitly stated, and which are dependent on a common parameter t.…
Article summary
of the surface z=\sin(x+y)-\cos(xy)+1 In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation x^2+y^2=1 . In general, every implicit curve is defined by an equation of the form : F(x,y)=0 for some function F of two variables. Hence an implicit curve can be considered as the set of zeros of a function of two variables. Implicit means that the equation is not expressed as a solution for either x in terms of y or vice versa. If F(x,y) is a polynomial in two variables, the corresponding curve is called an algebraic curve, and specific methods are available for studying it. Plane curves can be represented in Cartesian coordinates (x, y coordinates) by any of three methods, one of which is the implicit equation given above. The graph of a function is usually described by an equation y=f(x) in which the functional form is explicitly stated; this is called an explicit representation. The third essential description of a curve is the parametric one, where the x- and y-coordinates of curve points are represented by two functions both of whose functional forms are explicitly stated, and which are dependent on a common parameter t.…
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.