GEOMETRY in NATUREThe DNA of DESIGN

Mark Rosenhaus, CKD

Leonardo Da Vinci’s Vitruvian Man is the familiar icon of proportion. The width of the outstretched arms equals his height (within the square). The chest is 62% of the arms. A perfect star fits within the circle using the same proportions.

The geometry in nature is found in the sequence of Fibonacci Numbers. Find the pattern, then dividing adjacent numbers produces 62%. The Golden Rectangle proportion has the width 62% of its length.

Drawing the Nautilus Golden Rectangle: Begin with a 1x1 square (ACc) , add a smaller (cDd) square 62% of the original square. This will produce a Golden Rectangle, where the width is 62% of it’s length (1:1.62). Add another square (dBe) 62% of the second square, followed by square (efh) which is 62% of the previous square, and so on. Scribe an arc from A - c, then another arc from c - d, then d - e, e - f, f - g and g - h to complete the spiral.

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DNA building block pattern repeats within a square and Golden Rectangle. With the 62% proportion in our DNA, it is obvious we find it so pleasing.

Spiral of the galaxies The spiral of the galaxies is the same swirl as the Nautilus and the side of your fist.

Sunflower spirals in a clockwise direction count 34; counter clockwise, 55 - exactly 62% Fibonacci Numbers. Pineapples count 11 and 17.

Fibonacci proportions of the finger: The first digit is 62% of the second digit, which is 62% of the third. The total length of the first two digits equals the third digit.

Michelangelo’s “David” has a beautiful body. The floor to navel distance is 62% of his height. At birth the navel is in the middle of the body. Boys at 13 years may also have perfect proportions, then between 13 - 17 their proportions will vary until growth stops. My son at 13 had perfect proportions, then his legs grew more and now we say he has long legs.

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Audrey Hepburn – face analysis: A square is formed as the width of her face equals the height from chin to eyebrows. Another square is formed from the corners of her mouth up to the underside of her eyes. A Golden Rectangle is the width of her face, then from chin to the top of her head. Each cheek is 62% of her mouth as is the chin to mouth distance, and from the underside of her eyes to the top of her eyebrows. Most women have nice size cheeks, but a large chin distance makes a long face while the eye area is usually too small. Some women shave, then redraw their eyebrows. A friend with a narrow face pulls her hat down to her eyes and is more attractive because it ‘squares her up’. Drawing diagonal lines through the two squares of her face intersect at the tip of her nose. Scribing an arc from her nose to the corners of her mouth delineates the curve of her lower lip.

Fish Proportions: The main body is a Golden Rectangle, 1.00 unit x 1.618 (1.62) units. The remaining tail section is 1 x 1. The mouth is at 62% of the body height.

Parthenon columns 62% of the height to the peak

Why is a Greek Urn so beautiful? Similar to the face, the width is 62% of the height as are the upper and lower sections 62% of the middle. Good decoration emphasizes form, as provided by the figures. The width of the outer portion of the spout (17.5) is 62% of the inside diameter (11.6).

The three segments of the lower portion (above the base), are in Fibonacci sequence.

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Stonehenge Golden Proportions: The distance from the outer ring to the center stones is 62% of the distance between the center stones. Once again, proportions similar to our mouth-to-cheek distance.

The Space Shuttle’s wingspan and length are 78 feet and 122 feet - a 64% ratio. (62% might have prevented its problems.)

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Previously the portrait was centered on the $10 note. Now, the distance from the right edge to the right eyebrow – which is the focal point – is 62% of the total length of the bill

Empire State Building. The focal point is designed within a square. Generating Lines cross at strategic points to determine location of windows, decoration and change in setbacks. Outside corners of the building guide to the top of the tower. Placement, as well as proportion, create a lasting impression.

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Jan Vermeer balances, locates and sizes the chandelier with well placed objects. Generating lines through the stool leg, the painter’s right leg and the easel direct the viewer to the edges of the chandelier.

The Cathedral of Notre Dame is designed within a Golden Rectangle. A square defines the lower portion. The size and placement of the rosette is tangent to the diagonals of the square and the larger Golden Rectangle. The bottom of the rosette is at the midpoint of the square – just as the eye is on a face.

27x15 + 27x27 = 27”x42” 42”x42” 27”x42” The glass doors form a square with Golden Rectangles on each side that

are divided into a double door square and a horizontal Golden Rectangle. When the owners were told these are the same proportions as the Taj Mahal, they were awestruck, understanding the importance this relationship brings to their kitchen.

My first Golden Proportion kitchen.Each upper cabinet is a Golden Rectangle (G.R.) They are different sizes, yet the same proportion. (See the dimensions, above.) The entire group fits within a G.R. The middle cabinet along with the shelf is a square and forms a G.R. with the cabinet to its right. Diagonal lines cross in the center of the middle cabinet – right where the eye wants to go – confirming correct proportions.

Locating hardware: The space between the knobs is 62% of the width of the drawer. From the bottom of the drawer to the knob is 62% of the height - the same proportions as your face. Handles are located along the diagonal from the knob to the opposite lower corner. This is connect-the-dots for adults, similar to stars in a constellation. Creating familiar patterns is comforting for a more pleasing design.

Generating lines locate and size objects.Generating lines locate and size the keystone, the window and angle of the door crown.

The pantry width is 62% of the star cabinet, which is 62% of the hood space. The top of the hood is half the bottom width. The curve of the hood leads to the corner of the counter top. A line drawn from the top corner of the hood passes through the star cabinet knobs, then diagonally across the lower pantry door to the counter top. The bottom of the star cut out is the midpoint of the door – similar to the eye on a face.

Schematic of previous kitchen.

Piet Mondrian perfectly places shapes with the visual strength of color guiding the viewer around the canvas. Starting with the red square, step down the two black shapes then up the blue and finally to the yellow which completes the spiral.

The tail’s spiral follows the curve of the Nautilus seashell.

The wall composition is a Golden Rectangle. The spiral follows the same pattern of the Nautilus seashell. The main portion fits in the Golden Proportion left door.

The spiral is a wrought iron rod raised ½” off the doors.

Bathroom and shower wall tile arrangements based on Whirling Squares of Fibonacci Numbers: 1, 2, 3, 5, 8, 13, 21.

Three Dimensional ‘Mondrian’: A spiral pattern similar to the Nautilus seashell begins with sliding glass doors, up a Golden Rectangle, across a double square lift up door, continuing to a larger double square and ending with a smaller square half the height of the large square.

The curve and circle are reminiscent of a Joan Miro painting. The entire cabinet is a square. The swerved doors are within a Golden Rectangle. The center of the circle aligns with the intersection of the upper and lower curves.

“The spiral movement of the composition begins with the focal area cabinets recessed with three frosted glass panes the same proportion as the door. They lead to the increased depth double square horizontal lift-up doors; across to the Golden Rectangle; down to the horizontal cabinet and wind around to the final square and knob as the period.

Left to right: The pantry doors are a double square, followed by a Golden Rectangle, two small squares then a Golden Rectangle above the tambour. The bases are all squares. The spiral thrust of the composition adds vitality and movement to the design.

The original definition of symmetry was the balance of harmony and proportion based on weight and mass. A ballerina in the arabesque position is balanced at the center of gravity of the sacrum, upheld by the tip of her toe and one outstretched leg; she moves and the beauty of the moment is gone. The modern definition has regressed into the idea of axial (or mirror) symmetry – a vertical line with two items equidistant from each side. This works with small objects or only minimal time to understand the design. On a large scale it is monotonous.

Notice the difference where the photos are cropped. In the left picture, his hand points directly to the corner. Not so in the upper photo. His arm to hers slides to the lower corner as the curve of his leg to her chest guides to the upper left. We are, at first, attracted to his face in the center of the picture which gazes at hers. Though their bodies are not centered, the picture is balanced as you feel their vitality and movement.The upper photo… static.

The diagonal offset provides vitality and movement as it leads to the ceiling cut out and hood. The knobs and handles emphasize the diagonal. If the arch continued as a circle, it would touch at the corners of the cabinet near the middle knob and handle.

Generating lines help locate, size and compose a wall grouping that culminates at the focal point. Furniture is located in relation to the length of the wall. Accessories are proportional to the furniture. The arrangement peaks at 62% of the width of the wall.

Mies Van Der Rohe. The chair is designed within a square. The proportions of the back and seat are also squares. Arcs from the corner and mid point determine the curves.

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Where do you find inspiration? Robie House, Frank Lloyd Wright horizontals and overhangs.Half the width of the eave is at the left edge of the peaked roof.The distance from the left end of the eave to the peak of the roof is 62% of the eave.

Falling Water. Dynamic, spiral movement of the square fireplace moving to the right to the double square stone wall, up either square block, then across the horizontal lines and back down the small stone wall.

Frank Lloyd Wright inspired eaves, recesses and multiple levels.The thrust of the composition is from the heavier pantry to the open shelf. The cabinets follow the proportions of the finger. The open shelf is 62% of the angled louvered doors, which is 62% of the triple door cabinet. The shelves and angled cabinet equal the width of the glass cabinet. The pantry upper door is a square which fits into the Golden Rectangle lower door.

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The upper cabinets are sculpted in a 1-2-3, 62% Fibonacci sequence: 18”, 30”, 48”.

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3-2-1, 62% sequence of the upper doors.

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Diagonal lines go through key points of the design as shown by the dots on corners of the cabinets. The curve of the top cabinet hits two other corners to confirm exact diameter.

The cabinets are arranged in groups similar to instruments in an orchestra for stronger visual continuity. (Wood, steel and blue glass.) The upper and lower glass doors are proportional to the face, as the width of the wood area is 62% of the glass. The upper door is a square that fits into the lower Golden Rectangle.

Three glass squares and a glass Golden Rectangle surround the horizontal lift up doors.

Mark Rosenhaus, CKD

243 West 72nd StreetNew York, NY 10023

Phone: 212-579-4598Fax: 212-579-4599

Rosenhausdesign.com Rosenhausdesign@aol.com

ROSENHAUS DESIGN GROUP