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December 23rd, 2017, 10:30 AM  #1 
Newbie Joined: Dec 2017 From: Sweden Posts: 2 Thanks: 0  Implicit function to determine the shape of an egg
Hi all, I was wondering how people determine functions that are representative of oval shapes. I am using the implicit functions: ((9y^2)/16a^2)+((x^2)/((a^2)(1(y/10a)))=1 and ((x^2)+(y^2))^2=(ax^3)+(ab)xy^2 This extends beyond my knowledge of calculus. Could someone tell me about implicit functions, and the process by which people can come up with such equations? How do people find the parameters, and the exponents of each variable? What happens when you change the parameters, for example if you change a from 3 to 9 in the first function? Any help would be appreciated. Last edited by skipjack; December 23rd, 2017 at 02:55 PM. 
December 23rd, 2017, 08:33 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
The first equation has more opening parentheses than closing parentheses. What was intended?

December 23rd, 2017, 09:32 PM  #3 
Senior Member Joined: Aug 2012 Posts: 2,342 Thanks: 731  
December 26th, 2017, 02:40 AM  #4 
Newbie Joined: Dec 2017 From: Sweden Posts: 2 Thanks: 0  
December 26th, 2017, 06:31 AM  #5 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
Yes, the parentheses are out of balance in the first equation. We must guess what your intention is. Is it $\dfrac{9y^2}{16a^2} + \dfrac{x^2}{a^2 \left ( 1  \dfrac{y}{10a} \right ) } = 1.$ Moreover, "oval" implies to me a symmetric figure in the plane whereas "eggshape" implies to me a nonsymmetric figure in either the plane or space. By analogy with other formulas, yours appears to be derived from some geometric description. Do you have such a description? 
December 29th, 2017, 07:53 AM  #6  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
 
December 29th, 2017, 10:24 AM  #7 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  @Country Boy Defining what words mean today by their etymologies is not a reliable practice. "Fee" is derived from a word meaning "cattle," but the word "fee" today does not mean anything close to "cattle." Many people would describe certain symmetric shapes as ovals. It is a bit hard to answer how a set of functions were derived without knowing a more precise definition that was given.


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determine, egg, function, implicit, shape 
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