Notes on book design, sacred geometry; good sources

The ancients, perhaps even neolithic man,  medieval and renaissance man, had some knowledge or imagination for geometry and math that could express evolution and gnomonic growth principles of proportion. Mathematically these can be shown in ratios, square roots, and spirals or sequences like the Fibonacci series.

The basis for some of these are addition and multiplication. Multiplication being an advanced form of addition, 4 x 4 = 4+4+4+4, for example. The Golden Proportion and the Golden Section being familiar to some designers as in the golden rectangle. Geometrically these can be drawn in a couple of ways, based on equations like 1=1/a2 + 1/a, named by the Greeks Ø (phi) seeking a division of Unity.

An example of design can be found in early book pages like the Lindisfarne Gospels (c. AD 700) which shows proportions based on the 3,4,5 “Pythagorean” triangle.

the golden rectangle; note the right triangle in the semi-circle, “Theorem of Thales,” expressions of ø (phi) “division into the extreme and mean terms.”

Another geometric drawing can reveal the golden rectangle based on the division of two squares and an arc constructing a rectangle which, when combined with one of the squares creates the golden rectangle. Ø The Golden Proportion is inseparably related to the square root of 5 function and the construct of a pentagon.

The ancients used proportion and the relationship between squares and spirals to express unity and the sacred in their architecture.

The Fibonacci Series is an additive progression in which the two initial terms is added together to form the third term and where any two successive terms to be approximately in relation to one another as 1 : Ø, a form of the Golden Ratio or infinite decimal equivalent. This series has been found to express patterns in nature.

The golden rectangle and similar proportions are what interest me most in book design as seen in many Medieval and Renaissance page designs as discovered and applied by early 20th century designers like Jan Tschichold in theories on proportion and layout using the Golden Section.  He began to practice moving away from the centered typography of earlier periods. He should be noted as becoming the designer for Penguin Books in 1947, and some of his designs for them can still be found.

It isn’t often that we can apply proportions for margins like the ratio 3,4,5 in common book production, but it is nice to understand that when we do there is a noticeable difference to the eye. The ideal of the combined inner margins or gutters equal to the outer margin for instance is similar to the head margin being half of the foot margin, are not often used due to the demand to save paper and costs by fitting copy using other proportions, if any, but having the knowledge of these things can be kept in mind.  I might add that Tschichold didn’t use them strictly by any means, often using off centered grids and the like for illustrated books. Holding to a grid consistently establishes the relationship of text and image areas that will display a noticeable continuity in a design that is unifying and beautiful.

In Tschichold’s time, and up until the early eighties, designs were drawn on paper, often using hand lettering for covers and other displays of type, that the printer had to follow. Until the development of a reliable photographic type, many layouts were done using ‘repros’ from metal type on ‘repro paper,’ that were then pasted up with hot wax, and then photographed to make negatives. These negatives  were then stripped in flats and burned into plates for the off-set press. This is part of the progression from metal type to digital type as we know it today.

It is useful to understand the metal and the geometric foundation of relationships for space and margins when applying our digital software to design books, or in doing other forms of typography. This is not to say that all books be designed a certain way using what seem like obsolete practices. Graphic design and the theoretical are established in publication design and advertising, and they often consider these basic principles. With advertising, sometimes graphic design overshadows book design and book design theories as established by typographic professionals, but most books should never be designed like advertising. There has been a tendency to ‘mix it up’ with advertising typography in books, and some books might actually work with it in some cases. Some advertising uses the theoretical of graphic design and succeeds visually, but using a bunch of type faces and doing something splashy, or without integration just for the sake of doing something wild, without the use of grids or some unifying factors, never helped a book. Whatever the book project might be, annual report, scholarly book, art book, or history book, an integrated concept can be brought forth in the design. Holding to some basics, new or old, some proportions, some unifying plan that recognizes the relationship of pages throughout a book, will decidedly make it elegant and tasteful to read. Reading is what we should keep in mind when designing books .

Methods of Book Design, Hugh Williamson, 3rd edition; (very comprehensive, available from Amazon)
Rudolf Koch; Letterer, Type Designer, Teacher; Oak Knoll Press / The British Library, 2000.
Writing, Illuminating & Lettering, Edward Johnston, Pitman-Taplinger, NY-a pentalic book.
Designing books: practice and theory, Jost Hochuli, Robin Kinross, Hyphen Press, London; (1996).
Sacred Geometry, philosophy and practice, by Robert Lawlor, Thames and Hudson, Art and Imagination Series (1982).
Jan Tschichold: typographer, by Rauri McLean, Godine, (1975, soft cover 1990).

4 thoughts on “Notes on book design, sacred geometry; good sources

  1. Pingback: Interior Designs » Carter exhibit is much more than a geometry lesson

  2. Dear Mathematician,
    In 1937 the state of Montana conducted its first archeological dig “The Hagen Site”. Established as a National Historical Landmark in 1964 (it is presently undeveloped, and for sale).
    The site is unusual due to the pottery and structure excavated at the site. The pottery is extremely advanced with a style that is hard to account for. The structure was built as a stationary building.
    The equation; the lodge has a 16 foot diameter with 12 supporting posts. The front door faces to the sun raise with two posts 6 feet apart, the center has two posts 4 feet apart, the west wall has two post 2 feet apart. Being that the lodge is round, a sacred native symbol; I circled the other two points, the inner and outer circles.
    Now you have your equation; A to B to C, gives you a 15 degree angle (1/24 of 360).
    The three proportional circles are now called out, and all 3 fit with-in the equation.
    Hope you can enjoy this Native American Star geometry as much as I have. This shows they had the Knowledge of Natures structure which is found in all creation. Star Band found at site


  3. Pingback: Djelloul Marbrook’s Brushstrokes and glances « The Line Break

  4. As a small press designer and publisher, it is always an awakening to have someone notice the work as a whole, as well as the nuances and dynamics of the literature. Thank you to The Line Break.


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