Symmetry

Hey guys,

Can you please help me .

My question is "Why symmetry leads to stability?"

#Symmetry

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

This is a totally wide open, undefined question, but I'll answer it anyway! Let's say that "tendency to change" is some function of some parameter, $f\left(x\right)$ . If, for some value $x$ , there is a symmetry about it, i.e., $f\left( x-\Delta x \right) =f\left( x+\Delta x \right)$ , then it's a extremum, and so it could either be a point of stability or instability. Like a bowl, which could be inverted. Even when it's inverted, it doesn't necessarily mean it'll move---it first has to be knocked off center. The point is, at the extremum, there is no "tendency to change".

Michael Mendrin - 5 years, 8 months ago

Where? In what situation? Unless you give us some more detail, any answers will probably be too general to be useful.

Raj Magesh - 5 years, 8 months ago

Sure. Think of a boat in water. Boats are usually symmetrical along the center vertical plane.

Michael Mendrin - 5 years, 8 months ago

Thank u guys

Rithik Sharma - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$