ARTi
The mathematical definition of a closed loop
Chapter 1

The basic anatomy of a shoelace knot

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Answer

Chapter 2

The topology of mathematical knots

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Answer

Chapter 3

The lacing grid optimization

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Answer

Chapter 4

The physics of the walking impact

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YOUR GOAL

Master of The math of shoelaces

Ch 2 · The topology of mathematical knots
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Tangle Trick Magic
BETA

dash Weave the colorful laces to discover the surprising math that keeps your shoes tied.

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dash Mathematical Knot Topology

Fuse those shoelace ends! (Glue 'em tight!) / That's a true math knot! (You got it right!)

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dash Lord Kelvin and his atomic vortex theory

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Lord Kelvin and his atomic vortex theory

dash An early theory proposed that chemical elements were microscopic knots.

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Classifying knots by their minimum crossing numbers

dash Knots are classified by the minimum number of times they cross.

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Fun Fact

Knotted molecules: Chemists have successfully synthesized molecular knots, creating the tightest knot ever tied in 2017 using just 192 atoms.

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Glossary
knot theory (noun)
The mathematical study of closed, three-dimensional loops and how they deform without being cut or self-intersecting. In 1876, Peter Guthrie Tait tabulated these mathematical loops, distinguishing secure reef knots from weak granny knots.

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Gossip

Would you study molecular DNA knots?

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Quiz

Why do scientists study the mathematical knots formed by DNA strands?

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dash Classifying knots by their minimum crossing numbers

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Gossip

Do you find abstract math fun?

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Quiz

Which biological enzymes cut and untangle knots in human DNA strands?

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dash The mathematical definition of a closed loop

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Quiz

How many basic Reidemeister moves are used to change a knot diagram without changing the knot itself?

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dash How biology knots DNA to pack genes

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Quiz

In topology, what does it mean if two knots are considered equivalent?

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Quiz

What is the name of the simplest mathematical knot with zero crossings?

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Quiz

What is a mathematical knot, unlike a real-life shoelace knot?

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Quiz

What did physicist Lord Kelvin believe chemical atoms were made of in 1867?

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Quiz

What is the name of the simplest mathematical knot, which has exactly three crossings?

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