Nicolas Poussin finished painting **‘A Dance to the Music of Time’** in 1636. The aspect ratio of the painting is 1:1.261 (when you average the difference between the imperial and metric measurements). *Plate 1*

A while back we looked at ‘Triumph of Bacchus’ by Michaelina Wautier where we introduced the √ϕ. This is the explanation promised at that time.

You’ll recall from this post that the ϕ aspect ratio is 1:1.618… which continues on infinitely as an irrational number. *Plate 2*

Well, the √ϕ (√1.618…) equals 1.272… which is also an irrational number. The √ϕ Rectangle has an aspect ratio of 1:1.272…

We can construct a √ϕ reciting from a ϕ rectangle by using the base (**1**) as the radius and swinging the compass up (**2**) to the top of the ϕ rectangle and then drawing a perpendicular line down from the intersection of the arc and the top of the ϕ rectangle to the base of the ϕ rectangle (**3**). *Plate 3*

The aspect ratio of this new rectangle (shaded in gray) is the √ϕ or 1:1.272… *Plate 4*

The √ϕ Rectangle has primary diagonals each with two reciprocals. *Plate 5*

Mirroring the diagonal and reciprocals about either centerline will create the following Dynamic Symmetry armature. *Plate 6*

This is the same armature with vertical and horizontal subdivisions. *Plate 7*

One quality of the √ϕ Rectangle is that its subdivisions also have the ϕ proportions in that if the Purple Segment=1 then the Blue Segment=.618… for each of the straight line segments below. Or, A:B = C:D = E:F = G:H. *Plate 8*

Go back and look at **‘Triumph of Bacchus’** before we continue on to **‘A Dance to the Music of Time’** by Poussin.

The idea of beauty does not descend into matter unless this is prepared as carefully as possible. This preparation consists of three things: arrangement, measure, and aspect or form…

-Nicolas Poussin