In this video, I present an overview of symmetries in physics, passive vs. active transformations, and how to derive Noether’s theorem from the Euler-Lagrange equations. Different examples are presented in detail to show how the invariance under specific symmetries can be used to construct conserved quantities.

Beautiful weaving of geometry, group theory, and visual art.

Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed. Such a reversal of chirality is commonly seen in helical plant tendrils and telephone handset cords.

Is symmetry informative? The answer is both yes and no. We examine what information and symmetry are and how they are related. Our approach is primarily mathematical, not because mathematics provides the final word, but because it provides an insightful and relatively precise starting point. Information theory treats transformations that messages undergo from source to destination. Symmetries are information that leave some property of interest unchanged. In this respect the studies of information and symmetry can both be regarded as a Quest for the identity transformation.

Archive of http://www.theophys.kth.se/mathphys/SYM/sym_history.html

Improvements in how densely spheres and other shapes can be packed together could lead to advances in materials science, deep space communication and theoretical physics.