Ever wondered what four dimensions really mean? Discover why knots can’t exist in 4D space — and how mathematicians use cubes and clever analogies to understand higher dimensions.

Mathematicians say knots cannot exist in four-dimensional space because the extra dimension allows a rope to move around itself and untangle, revealing surprising insights into geometry and topology.

Color-changing fibers are helping scientists to understand, for the first time, the exact ways some knots hold tighter than others. In 2018, researchers developed pressure-sensitive fibers in part to ...

MIT researchers develop a mathematical model to predict a knot’s stability with the help of color-changing fibers. Photo by Joseph Sandt Knots are some of the oldest and most-used technologies that ...

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the ...

Researchers wanted to understand precisely how blackworms execute tangling and ultrafast untangling movements for a myriad of biological functions. They researched the topology of the tangles. Their ...

Mathematicians have studied knots for centuries, but a new material is showing why some knots are better than others. One sunny day last summer, Mathias Kolle, a professor at the Massachusetts ...

Editor's Note: This article was provided by Inside Science. The original is here. (Inside Science) – Knots are everywhere, from laces of shoes to stitches that seal cuts. Sailors and others have known ...

Consider the plight of a gardener struggling with a recalcitrant tangle of garden hose. Sometimes, no amount of pulling or twisting unsnarls the coils. At other times, the tangles readily come apart, ...

From bow ties and shoelaces to sailing boats and climbing ropes, knots are not only very useful for our daily lives, but for mathematics too. Researchers have reported a new mathematical operation to ...

You may not have heard of knot theory. But take it from Bill Menasco, a knot theorist of 35 years: This field of mathematics, rich in aesthetic beauty and intellectual challenges, has come a long way ...

We can tie knots in three dimensions because one-dimensional ropes “catch on each other”. This is why a long rope wound around itself, if done right, won’t come apart. We trust knots with our lives ...