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

~Plato





The Ewers Architecture logo is the arc that transforms a square into a Golden Section. The Golden Section has been used extensively by architects, musicians, artists, and mathematicians over the centuries. Ewers Architecture uses the arc to remind us that a simple form such as this can have powerful implications and symbolism.

The Golden Section can be constructed from a simple square, as shown in the diagrams at the right. Note that the solid black arc created in Step Two is the Ewers Architecture logo.




A (very) SHORT HISTORY
The Golden Section has been referred to as the Divine Proportion, the Golden Rectangle, or the Fibonacci Sequence (after Leonardo Fibonacci of Pisa who pioneered some of the early mathematical phenomena and its connection with nature). This proportion has been demonstrated in the Greek architecture of the Parthenon, the Renaissance architecture of Leon Battista Alberti’s Santa Maria Novella in Florence, and used extensively by Le Corbusier in his quest for modular designs of modern architecture.




MATHEMATICAL IMPLICATIONS
The Golden Section is more than just a simple rectangle. The proportions represented are a simple, yet mesmerizing, mathematical sequence.

Encarta Encyclopedia describes the proportion as, 'a geometric proportion in which a line is divided so that the ratio of the length of the longer line segment (A) to the length of the entire line (C) is equal to the ratio of the length of the shorter line segment (B) to the length of the longer line segment (A)." Mathematically written, this would read: A/C = B/A

Part of the mathematical beauty lies in the geometric demonstration above, where the line segment B can be constructed from the square created by line segment A, using a simple arc.

Another piece of the mathematical wonder lies in how this form may be subdivided into more of its own proportions. The rectangle which is added to a square in order to make the Golden Section is a Golden Section in itself. This proportion may then be interpolated or extrapolated an infinite number of times, always creating another rectangle of the same proportion. This is only the beginning of the mathematical calculations. The formulas and interpretations have meaning for pentagons, dodecahedrons and beyond.

The Golden Section is a simple tool that may be used to enhance the meaning and beauty of an architectural work. Most of all, though, the Golden Section reminds us that proportions are important to all works of art, and that we must always learn from the masters of the past.

EWERS ARCHITECTURE LOGO

step one

STEP ONE...

Draw a simple square.


step two

STEP TWO...

Using a line from the midpoint of one side of the square to an opposite corner as the radius, construct an arc that will define the extents of the new rectangle.


step three

STEP THREE...

Using the endpoints of the arc, complete the rectangle.


step four

STEP FOUR...

This is the proportion recognized since antiquity as the Golden Section.



golden section proportions

MATHEMATICAL PROPORTIONS