Eastwood, Michael2015-12-130044-8753http://hdl.handle.net/1885/76526The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.Copyright Information: © Masaryk University, 2014 http://www.maths.soton.ac.uk/EMIS/journals/AM/ The journal website states it supports an open access policy. (As of 1/9/2015).201410.5817/AM2014-5-2652016-02-24