Editing Inversive geometry (section)

{{Short description|Study of angle-preserving transformations}}
{{Other uses|Point reflection}}
In [[geometry]], '''inversive geometry''' is the study of ''inversion'', a transformation of the [[Euclidean plane]] that maps [[circle]]s or [[Line (geometry)|lines]] to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied. Inversion seems to have been discovered by a number of people contemporaneously, including [[Jakob Steiner|Steiner]] (1824), [[Adolphe Quetelet|Quetelet]] (1825), [[Giusto Bellavitis|Bellavitis]] (1836), [[John William Stubbs|Stubbs]] and [[John Kells Ingram|Ingram]] (1842–3) and [[William Thomson, 1st Baron Kelvin|Kelvin]] (1845).<ref>''[http://files.eric.ed.gov/fulltext/ED100648.pdf Curves and Their Properties]'' by Robert C. Yates, National Council of Teachers of Mathematics, Inc., Washington, D.C., p. 127: "Geometrical inversion seems to be due to Jakob Steiner who indicated a knowledge of the subject in 1824. He was closely followed by Adolphe Quetelet (1825) who gave some examples. Apparently independently discovered by Giusto Bellavitis in 1836, by Stubbs and Ingram in 1842–3, and by Lord Kelvin in 1845.)"</ref>

The concept of inversion can be [[#In higher dimensions|generalized to higher-dimensional spaces]].