The hottest Symmetry Substack posts right now

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A polynomial with Rubik’s cube symmetry

A Piece of the Pi: mathematics explained • 78 implied HN points • 25 Nov 24
🔬 Science Mathematics Symmetry Group Theory
  1. Rubik’s Cube has a huge number of ways it can be scrambled, around 43 quintillion, which shows its interesting symmetry in math. It can be thought of as not just a puzzle, but a complex mathematical object.
  2. There are specific rules about how the pieces of the Rubik’s Cube can be rearranged, which creates a lot of interesting patterns and symmetries. This helps mathematicians understand how groups of movements relate to each other.
  3. Recent research has shown that it's possible to find polynomials that have the same symmetries as the Rubik’s Cube. This connects the world of puzzles to deeper mathematical concepts, making it a fun area to explore.

On Certain Asymmetries

The Ruffian • 319 implied HN points • 21 Oct 23
🌍 World Politics Israel Hamas Conflict Symmetry Media
  1. Many commentators focus on Israel's strategy in the conflict, but few ask about Hamas' endgame, which involves the elimination of Jews.
  2. The Israel-Hamas conflict showcases different objectives, with Israel aiming to secure its borders while Hamas seeks to destroy Israel completely.
  3. There is an asymmetry in the way Western leftists address the conflict, often failing to condemn Hamas's actions and aims explicitly, which is necessary for credible criticism of Israel's actions.

How Researchers found Gods Number[Technique Tuesdays]

Technology Made Simple • 139 implied HN points • 22 Nov 23
🔬 Science Math Programming Combinatorics Symmetry Simulation
  1. God's Algorithm aims for the fewest moves possible in combinatorial games like Rubik's Cube.
  2. Researchers found God's Number for Rubik's Cube using techniques like partitioning, symmetry, and dropping optimality.
  3. Key strategies used were dividing the problem into smaller parts, leveraging symmetry to reduce work, and focusing on finding solutions within 20 moves instead of the best possible solution.

Picturing symmetry

A Piece of the Pi: mathematics explained • 24 implied HN points • 04 Mar 24
🔬 Science Symmetry Mathematics Group Theory
  1. The order in which symmetries are applied can significantly affect the final result, as shown through reflections and rotations of a square.
  2. Using Cayley graphs can help visualize and calculate products of symmetries.
  3. In symmetry operations, combining reflections and rotations follows specific rules, similar to adding odd and even numbers. Grouping rotations and reflections can simplify understanding complex symmetries.
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Edge colourings and Archimedean lattices

A Piece of the Pi: mathematics explained • 24 implied HN points • 18 Feb 24
🔬 Science Mathematics Graphs Symmetry
  1. Edge colorings of graphs are not just recreational, but have practical applications in quantum technology.
  2. Graphs can be colored either by edges or by vertices, with different requirements for each coloring approach.
  3. Vizing's Theorem states that a graph can be edge colored with either the maximum degree or the maximum degree plus one colors.

Pyritohedral symmetry

A Piece of the Pi: mathematics explained • 24 implied HN points • 11 Feb 24
🔬 Science Symmetry
  1. Pyritohedral symmetry is a unique type of symmetry displayed by certain crystal structures, like pyrite crystals, which have irregular pentagonal faces forming an irregular dodecahedron.
  2. Pyritohedral symmetry involves various rotations and axes of rotational symmetry, represented by colorful lines highlighting vertices and edges. This symmetry forms a group known as A_4.
  3. Complex crystals like the Holmium-Magnesium-Zinc quasicrystal exhibit even more intricate symmetries, such as those of a regular dodecahedron, represented by larger rotational symmetry groups like A_5.

Group Theory Application Webinar Reminder

Quantum Formalism • 19 implied HN points • 23 Mar 22
🔬 Science Group Theory Applications Webinar Symmetry
  1. Don't miss the Group Theory application webinar today at 5pm GMT with Owen Tanner from Glasgow University.
  2. Register for Lecture 03 on the abstract notion of a 'zero element' at [https://www.crowdcast.io/e/group-theory-lecture-03](https://www.crowdcast.io/e/group-theory-lecture-03).
  3. Join the Discord community at [https://discord.gg/SPcmcsXMD2](https://discord.gg/SPcmcsXMD2) for group study sessions and interactions.

Influential Mathematicians: Sophus Lie

Quantum Formalism • 19 implied HN points • 13 Aug 20
🔬 Science Mathematics Quantum Mechanics Symmetry Geometry Algebra
  1. Sophus Lie was a Norwegian mathematician who made significant contributions to mathematics, developing the theory of continuous transformation groups that later led to Lie groups and Lie algebras.
  2. Lie Groups and Lie Algebras, named after Sophus Lie, are essential in the Hilbert space formalism of quantum mechanics, specifically in understanding symmetry and operators in quantum systems.
  3. Although Sophus Lie did not directly contribute to quantum formalism, his mathematical work has had a profound influence on areas of mathematics that are crucial to understanding quantum mechanics.