Archive for symmetry

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1873 – Lie Groups

Topology is the study of how spaces are shaped and connected without worrying about distances. Some properties of spaces are preserved even when the space is being stretched and deformed. Often, the space that is being studied is called a manifold. A line and a circle are simple one dimensional topological manifolds. A plane and […]

1887 – E8

In 1887, Willhelm Killing came up with a classification scheme for Lie algebras. The designation E-8 was eventually applied to an exceptional, simple Lie algegra and the associated Lie group of rank 8 and dimension 248. This is one of the most complex objects known to mankind. Mathematicians Map E8 – [aimath.org] Mathematicians have mapped […]

Quasicrystals

Quasicrystals seem to exist in a state somewhere between glass (disordered atoms) and crystals (ordered atoms) and show qualities of symmetry that were thought impossible. Quasicrystals – [bbc.co.uk] Quasicrystals are interesting quirks of solid-state physics. It used to be thought that the atoms in solid materials1 were either totally ordered (crystalline) or totally disordered (glasses), […]

5-fold Crystal Symmetry

5-fold Crystal Symmetry

Corannulene is a hydrocarbon molecule (C20 H10) that is formed from a cyclopentane ring (C5 H10) surrounded by five benzen (C6 H6) rings. Its curved geodesic surface puts it in the company of fullerenes including buckballs and nanotubes and for this reason the bowl shaped molecule is often called a “buckybowl”. Because of the five […]

1885 – Weyl – bio

Born near Hamburg, Germany in 1885, Hermann Weyl was a mathematician whose work had a strong influence on both physics and number theory. He worked on combining general relativity and the laws of electromagnetism. He worked with Lie algebras, symmetry and created the first version of gauge theory which attempted to describe both electromagnetic and […]

1882 – Noether – bio

Born in Erlangen, Bavaria, Germany in 1882, Emmy Noether was a mathematician who laid the groundwork for the idea of symmetry in mathematics and physics. She studied the works of Hilbert, Klein and Minkowski and was peer with Hermann Weyl. Noether’s theorem – in 1915, she proved a relationship between symmetries in physics and conservations […]

1811 – Galois – bio

Evariste Galois was born in Bourge-la-Reine, France in 1811. His major contribution is known as Galois Theory, which he discovered while trying to find roots for polynomial equations. He was studying permutations of roots and realized that symmetries found in the roots can explain their solvability. This laid the foundation for what is now known […]