Homotopy facts for kids
Homotopies are a cool idea in mathematics, especially in a field called Topology. Imagine you have a super stretchy object. A homotopy is like smoothly changing its shape without tearing or cutting it. All the shapes you can stretch or twist it into are considered "homotopy equivalent."
A famous example is how a coffee cup can be smoothly changed into a donut. To a topologist, these two shapes are actually the same! This is because you can deform one into the other without breaking it.
In topology, a homotopy can also describe how one function can smoothly turn into another. Think of a function as a rule that takes an input and gives an output. A homotopy between two functions, say f and g, is like a continuous movie showing f slowly becoming g.
It's like having a dial that you can turn from 0 to 1. When the dial is at 0, you get function f. As you slowly turn the dial towards 1, the function smoothly changes. When the dial reaches 1, you have function g. This shows how f and g are connected through a continuous transformation.
Images for kids
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The two dashed paths are homotopic. The animation shows how one path can smoothly change into the other without moving its start and end points.
See also
In Spanish: Homotopía para niños
