And so we continue the introduction of Dynamic Symmetry from our understanding of the √2 rectangle.
A compass swing from the diagonal of a √2 will create a √3 rectangle with the ratio of 1:1.732… Diagram 1 & 2
![Constructing a √3 from the diagonal of a √2](http://howartworks.com/wp-content/uploads/2017/10/Root-2-3.jpg)
![√3 relations to the Square](http://howartworks.com/wp-content/uploads/2017/10/Root-3-Origins.jpg)
and will divide into 3 equal and proportional parts. Diagram 3
![Diagram 2: √3 Subdivisions](http://howartworks.com/wp-content/uploads/2017/10/Root-3-Divisions.jpg)
Further, the intersection of 2 circles, with the same radius, fits within the center √3 rectangular subdivision and can be divided by 2 equilateral triangles. The intersection where the circles overlap is called the Vesica Piscis which translates from Latin to Fish Bladder. Diagram 4
![Diagram 3: Vesica Piscis](http://howartworks.com/wp-content/uploads/2017/10/Root-3-Equalateral-Triangles.jpg)
Here are two √3 logarithmic spirals. Diagram 5
![](http://howartworks.com/wp-content/uploads/2017/10/Root-3-Spiral-Round-Final.jpg)
The √3 can also be divided with a square. Placing a square, equal to the short side of the √3, in the center of the √3 rectangle leaves 2 rectangles on either side that can be subdivided by another square and √3 rectangle. Diagram 6
![Diagram 6: √3 Squares](http://howartworks.com/wp-content/uploads/2017/10/Root-3-Squares.jpg)
Finally, the triangle formed from the hypotenuse of the √3 will form an Equilateral triangle when mirrored about the base.* Diagram 7
![Diagram 8: Equilateral Triangle](http://howartworks.com/wp-content/uploads/2017/10/Root-3-Diagonal-Triangle.jpg)
Here are some examples from history. Diagram 8
*1 + 1 = 2 = √4…