Geometry of the
North Rose Window
of Chartres Cathedral

Michael S. Schneider
M.Ed. Mathematics

"Beauty doth of itself persuade the eyes of men without an orator." -- Shakespeare

Many people are interested in actually seeing how geometry was applied in the art of sacred traditions worldwide.
One fine example involves the north rose window of Chartres Cathedral.
Clearly, it is geometrically designed. But do you know how?

(Artists and architects should)
"... fix their eyes on perfect truth as a perpetual standard of reference,
to be contemplated with the minutest care,
before they proceed to deal with earthly canons about things beautiful."
-- Plato

Here's the flow of the geometric construction, developed from a drawing in The Dimensions Of Paradise, written by my friend John Michell:

First, use one of the various techniques for finding twelve equally-spaced points around a circle.
One simple construction is shown here, which begins by turning a circle and constructing a square around it:

Connect every fifth point as shown to create this dodecagram, or twelve-pointed star.

Twelve small circles nestle within the rays of the star as shown below.

Find the outer point of each of these circles, and connect them to form a smaller dodecagram star, seen here.

While it's not necessary, you may want to erase some of the inner line segments, like this below, within the inner red outline.
Then (below, right) connect points with twelve central lines as shown.

So what size should the circular rose window itself be? Not necessarily the full circle.
Don't try to decide based on human whim but, again, let the geometry itself show you what to do.

"Sacred architecture is not, as our time chooses to see it,
a 'free' art, developed from 'feelings' and 'sentiment',
but it is an art strictly tied by and developed from the laws of geometry."
-- Fredrik Macody Lund

Our wise ancestors understood that mathematics was not a human invention (only the ways to symbolize it are) but it is a discovery, and that shapes and numbers are ambassadors from eternity able to teach us a divine language expressing eternal principles.

"Architecture aims at Eternity; and therefore, is the only thing
incapable of modes and fashions in its principles."
-- Sir Christopher Wren

So, to find the proper size of the circular window itself, connect every fourth point of the large dodecagram star to form an equilateral triangle. The circle constructed within that triangle will show you the window's intended size.

This is enough to reveal the basic scheme of how this rose window was designed.

"The good, of course, is always beautiful,
and the beautiful never lacks proportion."
-- Plato

Of course, the geometry of this window is an integral part of the design of the entire structure, which was composed as an interconnected whole. Using an elevation plan of Chartres, see if you can discover how this construction "extends" to encompass and relate to the building's entire design. I suspect that the whole front is an expanded version of the window.

I've created an animated version of this construction.

Other rose windows were similarly designed using different geometric constructions. The Canticle of the Sun East Rose Window of Grace Cathedral in San Francisco, California, uses this same geometric grid but in a different way. I've created an animated version of its geometric grid (identical, up to a point, with that of Chartres). The Cathedral of St. John The Divine uses a different, but related, grid. I've painted some watercolors using this geometric pattern. This activity may be found in Constructing The Universe Activity Book Volume 2.

With these clues, perhaps you'll be able to discover the geometric constructions underlying the great cathedral rose windows for yourself. Or design your own rose window. Just let the geometry show you what to do.

Images and Text (c) 2003-2008 Michael S. Schneider

For more about the philosophy of sacred art using twelve-fold design symbolism, click here.

To see any of these geometric analyses, click on its name:

The West Rose Window of the Cathedral Of St. John The Divine (NY)

The East Rose Window of Grace Cathedral (SF)

A Herter Brothers Cabinet


If you enjoy doing geometric constructions
or want to learn how,
consider these workbook companions to
"A Beginner's Guide To Constructing The Universe"

Constructing The Universe Activity Books

Create and Explore Geometric Patterns
of Nature and Art

Michael S. Schneider

Ideal for Artists, Craftspeople, Architects, Designers
and anyone who wishes to be inspired
by the relationships of mathematics with nature and human creativity.
Filled with hands-on geometric constructions and activities.
Many Illustrations. Easy To Understand. Self-Paced.

730 pages of hands-on geometric activities!

Available Only Through This Website!
Click here to learn about these Activity Books
and see their Tables Of Contents.


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