Herter Brothers Cabinet

by

Michael S. Schneider

M.Ed. Mathematics

Cabinet for Oliver Ames, Boston, c1883

Gift, in honor of the 75th Anniversary

of The American Wing, 1999 (1999.79), from

Robert L. and Ann R. Fromer, and Margot Johnson Inc.

"Time alters fashions and frequently obliterates the works of art and ingenuity,

but that which is founded on Geometry & real Science, will remain unalterable."

-- Thomas Sheraton, *The Cabinet-Maker and Upholsterer's Drawing-Book *(London, 1791)

During the late nineteenth century (1864 to 1906), Herter Brothers, the New York firm of the German-born brothers Gustave and Christian Herter, was arguably the leading cabinetmaking and decorating firm in the United States. Their work was in great demand by the most affluent clients of this opulent era. This rare cabinet, made for Oliver Ames of Boston, an industrialist and governor of Massachusetts from 1886 to1888, is made of painted and gilded maple wood, glass, brass and silk velvet.

Herter Brothers furniture is one of the many places I look to in order to learn geometry from masters. They seem to have been educated in classical geometry, and I'm awed to see how they applied its harmonious patterns to their designs. But analyzing photographic images of art can be deceptive without knowing the object's actual dimensions. One sign that a classical pattern *is* present is the existence of a consistent theme. In this cabinet, the theme is the "square root of two", the interplay of the square with the "root-two rectangle" which emerges from it. While the numerical value of the square root of two is approximately 1.4142... to 1, we don't need to use numbers at all to understand it. We can see it geometrically, and can replicate it using a compass and straightedge.

To understand the cabinet's whole design, we start most simply, with a square. The diagonal of a square, which is always 1.4142... times the length of the side of the square, can help it to reach beyond itself to become a larger rectangle. Simply put, the diagonal of a square becomes the side of a "root-two rectangle" (i.e., for those who are numerically interested: the long and short sides of this entire rectangle relate as 1.4142... to 1. The size of every element of the cabinet's design can be calculated from this single fact).

is then repeated, creating "root-two rectangles" from the square like fountains in three directions.

reveals the overall rectangle by which the cabinet appears to have been designed.

(To it's friends and admirers, this rectangle is known numerically

as the "1.29288... rectangle" because that's the ratio of its width to its height.)

that the arc made from one side of the square, centered at its corner,

crosses the square's diagonal at a point which subdivides the square

into two smaller "root-two rectangles" overlapping at right angles within the square.

as being formed by the overlapping of two such squares.

can easily be discovered by continuing to apply the root-two theme.

Now we call upon two horizontal root-two rectangles overlapping from the central square.

shows us the limits of the cabinet's central windows and frames (below left).

Replicating this construction below itself

reveals the design of the lower central part of the cabinet (below right).

But notice how it leads us

These are the subtle skills of a master designer

who knows how to weave necessary differences into sublime harmonies.

We saw how the side panels came about as extensions from the original central square

in the process of creating root-two rectangles.

But now it's useful to know that a root-two rectangle's excess section beyond the square

is itself a smaller square plus a root-two rectangle (below left).

This red rectangle is a smaller, turned model of the whole root-two rectangle.

The important idea to a designer is that the part models the whole.

to be made of a square whose (blue) diagonals swing the (red) arcs.

They have been called asymmetrical due to their unusual stance.

But an understanding of geometry reveals that they are truly symmetric in the classic sense.

While today "symmetry" often refers to a kind of mirror-image equal reflection,

the Greek definition of "symmetry" was that parts and whole shared "alike measure".

The parts are in accord with all other parts and with the whole at once.

Wholeness and harmonious accord, traits of what is Good and True,

were once required for art, crafts and architecture to be considered truly Beautiful

and healthy for the soul to gaze at.

Many philosophers of antiquity, and whole civilizations including Egypt, China and India,

knew that exposing people, especially children, to harmony in all its forms helps create harmonious people and societies.

about the diagonal and arc of a square crossing to subdivide a square into overlapping root-two rectangles.

in the root-two rectangle whose square generated the rectangle of the lowest golden panels,

the curtain of unsymmetry is pulled away to reveal how the lower shelf and its vertical support are integral

with the root-two theme which has cast a unified, benificent spell over the entire design.

I'll leave them for you to discover. There's usually more than one way to find each.

But I assure you that you'll only need to know about squares,

and the "root-two rectangles" which sprout from their diagonals.

Perhaps you'd like to construct from scratch the whole geometric plan?

Start with a square and it's diagonal will show you where to go.

Perhaps you can explore and develop the symmetry further than the great Herter Brothers did.

For its excellence, their work was, and remains, admired and very expensive.

But you can explore for yourself the time-tested root-two theme behind it,

whose true root is the eternal Truth of mathematics,

and for no charge at all.

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

or want to learn how,

consider these workbook companions to

"A Beginner's Guide To Constructing The Universe"

of Nature and Art

Michael S. Schneider

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.

Click here to learn about these Activity Books

and see their Tables Of Contents.

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