What is Isometry?
[[File:Congruence triangle.svg|thumb|Isometry in Geometry]] [[File:Congruence en.gif|thumb|Congruence]] [[File:Iso=tra+sim.png|thumb|Rotation and Transformation]] '''Isometry'''<ref>{{Cite web|date=2020-01-21|title=Isometry|url=https://calcworkshop.com/transformations/isometry/|access-date=2023-06-01|website=Calcworkshop|language=en-US}}</ref> is a concept of [[geometry]].<ref>{{Cite web|date=2023-05-14|title=Geometry {{!}} Definition, History, Basics, Branches, & Facts {{!}} Britannica|url=https://www.britannica.com/science/geometry|access-date=2023-06-01|website=www.britannica.com|language=en}}</ref> Isometry means that one shape can be transformed into another, but [[Metric space|metrics]] such as the arrangement of the points in relation to each other stay the same. An isometry is a special way of changing things that makes sure the [[distance]] between every two points stays the same in both places. An isometry is a special kind of function that moves points from one location in space to some other location. Some of these ways include turning objects, reflecting them across an [[Axis of rotation|axis]], [[Translation (geometry)|translating]] them, or not moving them at all. Most [[transformation]] that repeats itself after every two moves can either be a mirror image or a rotation by half. Every [[movement]] in a flat surface can be made by reflecting<ref>{{Cite web|last=Nunes|first=Vitor|title=Isometries: Reflection|url=https://www.matematica.pt/|access-date=2023-06-01|website=matematica.pt|language=en}}</ref> it at most three times. Every small group of transformations has at least one point that doesn't move.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Isometry|url=https://mathworld.wolfram.com/|access-date=2023-06-01|website=mathworld.wolfram.com|language=en}}</ref> To be an isometry, a [[Function (mathematics)|function]] needs to keep the distances between all points in both places the same. The distance from x to y is the same as the distance from f(x) to f(y).<ref>{{Cite web|title=Isometries Pr