A Tale of Knots & Games
Allison Henrich, Ph.D.
Seattle University
April 27, 2014
Allison Henrich, Ph.D. A Tale of Knots & Games
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The history and significance of knots in various fields such as art, accounting, sailing, chemistry, biology, and physics. It defines knots and links mathematically and explains knot diagrams. The document also mentions the story of the Gordian knot and Alexander the Great's attempt to untie it.
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A Tale of Knots & Games
Allison Henrich, Ph.D.
Seattle University
April 27, 2014
What is a knot?
Ancient knots in art
While celtic knots began to appear in history around 450 AD...
Ancient knots in art
While celtic knots began to appear in history around 450 AD...
...knots have been appearing in art since at least 2200 BC.
The story of the Gordian knot
A knot that was impossibly difficult to untie was tied to an oxcart belonging to Gordias.
An oracle proclaimed that the man who untied the knot would become king of Asia.
The story of the Gordian knot
A knot that was impossibly difficult to untie was tied to an oxcart belonging to Gordias.
An oracle proclaimed that the man who untied the knot would become king of Asia.
In 330 BC, Alexander the Great famously tried to untie the knot.
Knots and Incan accounting
The Inca empire in fourteenth century South America used knots (quipu) for accounting.
Out to sea!
Knots have been put to use for fishing and sailing for as long as we can remember.
Knots and chemistry
One of the first times knot theory appeared as a subject of scientific study was in 1860. Lord Kelvin, in an attempt to reconcile several competing atomic theories, proposed that atoms had a knotted structure.
Knots and chemistry
One of the first times knot theory appeared as a subject of scientific study was in 1860. Lord Kelvin, in an attempt to reconcile several competing atomic theories, proposed that atoms had a knotted structure.
Lord Kelvin and a scientist named Peter Tait set out to classify knots. This classification was meant to aid in the classification of atoms.
Recent history
More recently, knots have played a central role in the following disciplines. (^1) Physics (quantum field theory, statistical mechanics)
Recent history
More recently, knots have played a central role in the following disciplines. (^1) Physics (quantum field theory, statistical mechanics) (^2) Chemistry (properties of molecules)
What is a knot?
Definition (A Mathematical Notion) A knot is a circle that doesn’t intersect itself sitting in space.
What is a knot?
Definition (A Mathematical Notion) A knot is a circle that doesn’t intersect itself sitting in space.
Intuitively, we say that two knots are equivalent if we can get from one to the other by bending, stretching, and rotating as long as we don’t break or cut the knot anywhere.