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December 23rd, 2017, 11:30 AM   #1
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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)+(a-b)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 03:55 PM.
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December 23rd, 2017, 09:33 PM   #2
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The first equation has more opening parentheses than closing parentheses. What was intended?
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December 23rd, 2017, 10:32 PM   #3
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Quote:
Originally Posted by skipjack View Post
The first equation has more opening parentheses than closing parentheses. What was intended?
A broken egg.
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December 26th, 2017, 03:40 AM   #4
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Quote:
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The first equation has more opening parentheses than closing parentheses. What was intended?
Sorry, I always have trouble with parentheses. Is the equation unclear?
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December 26th, 2017, 07:31 AM   #5
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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 "egg-shape" implies to me a non-symmetric 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?
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December 29th, 2017, 08:53 AM   #6
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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 "egg-shape" implies to me a non-symmetric 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?
An ellipse is symmetric. An "oval" is "egg-shaped" The word "oval" comes from the Latin "ovum", "egg".
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December 29th, 2017, 11:24 AM   #7
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An ellipse is symmetric. An "oval" is "egg-shaped" The word "oval" comes from the Latin "ovum", "egg".
@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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