Nexus Network Journal

, Volume 19, Issue 1, pp 179–203 | Cite as

Marriages of Incommensurables: ϕ-Related Ratios Joined with √2 and √3

  • Mark A. Reynolds
Geometer's Angle


In his “Marriages of Incommensurables: Phi Related Ratios Joined with the Square Roots of Two and Three”, artist and geometer Mark A. Reynolds has found two ratios from the golden section family that generate relationships with the square roots of two and three. He includes the grids and procedures necessary for producing these ratios. For him, the significance of the constructions is that they join together ratios from two different groups of rectangles: the golden section family and the square root rectangle progression, two systems that are usually incompatible with each other. In these constructions and grids, the square root of the golden section and the golden section squared are related mathematically to the square roots of two and three, respectively, in ways that he believes have not been seen before. Reynolds calls this series of constructions, “marriages of incommensurables”, and the two he presents here are part of a larger group he has been working on for some time.


Geometry Geometrical constructions Incommensurables Irrationals Square roots Phi-related ratios 


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Copyright information

© Kim Williams Books, Turin 2016

Authors and Affiliations

  1. 1.Mill ValleyUSA

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