Editing Square root of 2 (section)

===Ancient Roman architecture===
In [[ancient Roman architecture]], [[Vitruvius]] describes the use of the square root of 2 progression or ''ad quadratum'' technique. It consists basically in a geometric, rather than arithmetic, method to double a square, in which the diagonal of the original square is equal to the side of the resulting square. Vitruvius attributes the idea to [[Plato]]. The system was employed to build pavements by creating a square [[tangent]] to the corners of the original square at 45 degrees of it. The proportion was also used to design [[Atrium (architecture)|atria]] by giving them a length equal to a diagonal taken from a square, whose sides are equivalent to the intended atrium's width.<ref>{{citation |title=Architecture and Mathematics from Antiquity to the Future: Volume I: Antiquity to the 1500s|last1=Williams|first1=Kim|author1-link=Kim Williams (architect)|last2=Ostwald|first2=Michael|publisher=Birkhäuser|year=2015|isbn=9783319001371|pages=204}}</ref>