Symmetry in Mathematics
- Geometric shapes can be symmetric through reflectional, rotational, translational, or helical symmetry.
- Symmetry in logic refers to the property of a relation being the same in both directions.
- Symmetric logical connectives include 'and', 'or', and 'if and only if'.
- Symmetry exists in various mathematical structures, such as even and odd functions, symmetric groups, symmetric matrices, and Galois groups.
- Symmetry is seen in symmetric probability distributions and as skewness in statistics.
Symmetry in Science and Nature
- Symmetry in physics refers to invariance or lack of change under any transformation.
- Many laws of nature originate from symmetries.
- Noether's theorem states that for every continuous mathematical symmetry, there is a corresponding conserved quantity.
- Wigner's classification states that the symmetries of the laws of physics determine the properties of particles.
- Symmetry is observed in continuous and discrete symmetries of spacetime, internal symmetries of particles, and supersymmetry.
Symmetry in Biology and Chemistry
- Bilateral animals exhibit symmetry with respect to the sagittal plane.
- Plants and sessile animals often have radial or rotational symmetry.
- Symmetry changes in biology correspond to the appearance of new parts and dynamics.
- Symmetry is important in chemistry for understanding interactions between molecules and quantum chemistry.
Symmetry in Psychology and Neuroscience
- Humans and animals have special sensitivity to reflection symmetry.
- Bilateral symmetry is a key factor in perceptual grouping.
- Symmetry detection is fast, efficient, and robust to perturbations.
Symmetry in Social Interactions, Arts, and Architecture
- Symmetrical interactions include reciprocity, empathy, dialogue, and respect.
- Asymmetrical interactions may convey superiority or specialness.
- Symmetry is used in various art forms and architecture, such as visual arts, ceramics, textiles, and building design.
Symmetry Data Sources