Mathematical Theory of Braids: From Everyday Patterns to Algebraic Structures
By
marysminefnuf
If you only eat one bagel today, this is the bagel.
Summary
This article explores the mathematical concept of braids, explaining how braids can be represented and manipulated mathematically. It discusses braid diagrams, the algebraic structure of braids, and how braids can be composed and decomposed. The content appears to be an educational piece about mathematical braid theory, connecting everyday braiding concepts (like hairstyles and friendship bracelets) to formal mathematical representations and operations.
Key quotes
· 5 pulledWhether in the context of hairstyles, friendship bracelets, or even parachute cords -- most will be familiar with the notion of a braid.
As can be seen in the images above, each braid starts with some number of strands which are repeatedly crossed under/over each other in some way.
We can represent the particular crossings of a braid with a braid diagram like the one shown below.
Note that we typically don't allow the strands of a braid to 'turn back up'.
Of course, other braids will have different patterns and structures.
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