# Questions tagged [symmetry]

Questions about symmetry, in group theory, geometry or elsewhere in mathematics. See https://en.wikipedia.org/wiki/Symmetry

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### Introduction to quaternion's geometrical intuitions starting from a set of three complex numbers

Introduction Recently I made a question here about the binary-tetrahedral-group and I started by analyzing quaternion-projections in the complex plane and their associated symmetries. Introduction to ...
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### Introduction to the Binary Tetrahedral group and the 24-cell

Context and introduction I was playing with complex number sequences $Z_n=r_n\omega^n=u_n+iv_n$ represented in space and realized that it's always possible to associate up to 48 naturally symmetric ...
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### Difficulty Understanding Notation for the Symmetries in Tiling Patterns

I am starting to learn group theory, and am reading about the symmetries in tiling patterns here. I have a few questions about the examples provided: In figure 9, a vertical line through the red ...
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### Claims about solution of nonlinear differential equation with symmetries

I have a nonlinear ordinary differential equation (of sixth order). If $y(x)$ satisfies the given nonlinear differential equation and its associated boundary conditions, both $y(1-x)$ and $-y(1-x)$ ...
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### Symmetry about half of the domain in nonlinear ODE solutions

Is there a way to predict in advance whether the solution to a sixth-order nonlinear ODE will exhibit symmetry about half of its domain? The ODE is expressed as \$f(x, y', y'', y''', y'''', y''''', y'''...
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