Which branch of mathematics is characterized by its focus on the properties of geometric objects that remain unchanged under continuous deformations?
Understand the Problem
The question is asking to identify the branch of mathematics that studies the properties of geometric objects that are preserved under continuous deformations like stretching, bending, twisting, and crumpling, but not tearing or gluing. This field focuses on properties that are invariant under these kinds of transformations.
Answer
Topology
The branch of mathematics characterized by its focus on the properties of geometric objects that remain unchanged under continuous deformations is Topology.
Answer for screen readers
The branch of mathematics characterized by its focus on the properties of geometric objects that remain unchanged under continuous deformations is Topology.
More Information
Topology is sometimes referred to as "rubber-sheet geometry" because it deals with properties that remain unchanged when objects are stretched, twisted, crumpled, or bent without tearing or gluing.
Tips
It is important to remember that topology focuses on properties that remain unchanged under continuous deformations, which exclude cutting or gluing.
Sources
- Topology - Wikipedia - en.wikipedia.org
- Topology - Britannica - britannica.com
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