KNOT SUM Meaning and
Definition
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The term "knot sum" refers to a mathematical operation that combines two or more distinct knots to create a new, composite knot. It is a fundamental concept in the field of knot theory, which is a branch of topology that studies the properties and characteristics of knots.
To perform a knot sum, two knots are chosen, and a small section of each knot is removed, creating "open ends" on both. The open ends are then matched and smoothly connected, resulting in a new knot formed by joining the remaining sections. This process essentially involves attaching one knot to another by gluing the open ends together.
The resulting knot sum inherits certain qualities from its constituent knots. For example, if the original knots were both prime knots (knots that cannot be decomposed into simpler knots), then the resulting knot sum will also be prime. However, if either of the original knots was composite (made up of two or more simpler knots), the resulting knot sum will also be composite.
Knot sums are valuable tools in knot theory as they allow for the creation of an infinite number of knots from a finite set of base knots. They also provide insights into the classification and structure of knots, as well as their relationships and interactions.
Etymology of KNOT SUM
The term "knot sum" is a mathematical term used in knot theory. As such, its etymology is rooted in mathematics rather than linguistics.
The word "knot" itself originated from Middle English, derived from the Old English word "cnotta" or "cnytt" which meant a fastening or a tie. It has a history dating back to Old Norse, Proto-Germanic, and ultimately to Proto-Indo-European roots.
The term "sum" comes from Latin, derived from the word "summus" meaning "highest" or "topmost". In mathematics, the word "sum" refers to the result of adding numbers or quantities together.
In the context of knot theory, the term "knot sum" refers to a binary operation that combines two knots to form a new knot. This operation involves removing a small piece of each knot and joining their remaining ends together.
