Art of Geometry print-at-home books

Treat yourself or someone crafty with the full set of my geometry tutorial books, currently made up of 10 titles.

Learn basic geometry terminology and skills: bisecting a segment or angle, dividing the circle into 4/8, 6/12 and 5/10. An introduction on the tools you need is also included. This primer is meant for the complete beginner, but even an intermediate user may find it handy to have all the basics clearly gathered in one place.

Learn how to divide a circle into unusual numbers using "approximate constructions" (they're so tricky it can't be done any other way). If you started with the divisions in First Steps, this will mean you can divide with every number up to 13, and every multiple thereafter!

Learn one of the basic grids for geometric patterns. The primary Seven-Circle Grid, which generates the Grid of Triangles, is the basis for working with root 3 (√3) patterns, which is another way of saying we are working with 6 and 12 (and other multiples of 3). The grid and its variations are thoroughly covered, yielding a dozen basic and classic patterns along the way.

Learn one of the basic grids for Islamic patterns, particularly associated with North Africa. The primary Grid of Squares, also known as the Nine-Circle Grid, is the basis for working with root 2 (√2) patterns, which is another way of saying we are working with 4 and 8 (and 16 etc). The grid and its variations are thoroughly covered, yielding 10 basic and classic patterns along the way.

This volume completes the foundational grids by introducing a five-fold grid of 5 pentagrams around 1. The Decagram Grid is also introduced in its quality of "mother of Girih", key to the construction of these tiles devised in Central Asia to cover surfaces with complex strapwork.

Learn to inscribe any number of circles inside a circle or a polygon, a basis notably for Gothic rose windows. We’ll look at two basic constructions that we can use with any polygon or any number of circles inside a circle, and then construct a full-fledged triskele window with its tracery.

Learn to construct an eight-lobed oculus (rosette window) from Chartres and a root 3 window pattern from the Great Umeyyad Mosque, each with the additional dimension of tracery.

“The Heavenly City is a geometer’s name for the traditional diagram that represents the order of the universe and the numerical code that underlies it. [It] contains the numbers, measures, shapes, proportions, and musical harmonies that are constant in nature.” — Jon Michell, How the World Is Made: The Story of Creation According to Sacred Geometry.

This diagram was discovered by geometer John Michell in the 1970s. The reason it is called the Heavenly City, and also New Jerusalem, is that it was reconstructed from the detailed description of St John’s vision in Revelations, where an angel showed him “the perfect pattern of creation”. He described it as a city with, among other things, three gates on each of its four walls (full description in Revelation 21:9-14). The result is the unusual feature of 12 circles arranged in 4 groups of 3, rather than being equally distributed around the perimeter.

There is more than one possible route to construct this diagram, and we will work with two:
• The Marriage of 7 and 12 creates a 28-pointed star which generates the 12 moons.
• Drawing Down the Moon introduces the Starcut to derive the size of the Moon from the circle of Earth.

Learn to create a slightly simplified version of one of Chartres cathedral's famous rose windows, also known as "The Glorification of the Virgin". Even with the smallest details left out, this is a complex process not for the faint of heart!

Learn an impressive self-contained motif from a wall carving in Armenia. The highly intricate knotwork is based on 16 circles around a centre. The difficulty here lies in picking out the plaited bands from the numerous construction lines, but the finish is highly satisfying.