Comments on: A Quick Intuition For Parametric Equations https://betterexplained.com/articles/a-quick-intuition-for-parametric-equations/ Math lessons that click Fri, 11 Dec 2020 06:38:41 +0000 hourly 1 By: Jacob https://betterexplained.com/articles/a-quick-intuition-for-parametric-equations/#comment-345851 Thu, 26 Jul 2018 12:27:00 +0000 http://betterexplained.com/?p=3734#comment-345851 If the idea was to explain the needs for using parametric equations, I think the explanation is a little bit short. For instance, there is a different in the solutions of the following two equations 1) y = 5x + 3 and 2) x^2 + y^2 = r^2. The following explanation comes from the calculus II notes by Paul Dawkins (http://tutorial.math.lamar.edu):
In the first equation, there is a one to one relationship between the variable y and x that falls in the definition of a function. In the second equation (not a function), however, solving ‘y’ as a function of ‘x’ would result in dealing with two separate equations due to the square root operation that requires plus or minus. Therefore, the curve of the second equation would require two separate equations, one equation for points on the upper have plane (y1 = (+) sqrt(r^2 – x^2)) and another equation for the points located in the lower have plane (y2 = (-) sqrt(r^2 – x^2)).
To avoid dealing with two functions for different parts of the curve represented by the second equation, it is better to deal with two parametric equations (x = r cos(p) & y = r sin(p)) representing all points of the second equation and the curve. There should be no need to deal with parametric equations if the second equation would have accounted for all points (x,y) of the curve it represents.
On the other hand, I am not completely sure the two equations above were meant to represent a set of parametric equations or two different functions of the temperature variable. If the intent is to plot Ice cream as a function of Sunscreen, then we should have a system of parametric equations.

Thank you,
Jacob

]]> By: janis https://betterexplained.com/articles/a-quick-intuition-for-parametric-equations/#comment-334369 Thu, 26 Jan 2017 14:21:30 +0000 http://betterexplained.com/?p=3734#comment-334369 This is fantastic! Thanks so much. Easy to follow.

]]> By: Bob https://betterexplained.com/articles/a-quick-intuition-for-parametric-equations/#comment-333639 Sat, 17 Sep 2016 01:57:08 +0000 http://betterexplained.com/?p=3734#comment-333639 In reply to Eric V.

Eric V,

A few folks have asked me what “causes” voltage and current. Thanks for the explanation.

]]> By: Prof__Lee https://betterexplained.com/articles/a-quick-intuition-for-parametric-equations/#comment-333246 Tue, 26 Jul 2016 13:51:10 +0000 http://betterexplained.com/?p=3734#comment-333246 Beautifully explained! I particularly like the video! Thanks so much!

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