# Symmetry

Hey guys,

My question is "Why symmetry leads to stability?"

Note by Rithik Sharma
2 years, 9 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $$\boxed{123}$$

Sort by:

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".

- 2 years, 9 months ago

Thank u guys

- 2 years, 9 months ago

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

- 2 years, 9 months ago

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

- 2 years, 9 months ago