GEOMETRY in NATURE
The 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.

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

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.
1.62

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 62%
13 had perfect
proportions, then his legs
grew more and now we
say he has long legs.

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.

Fibonacci Flying Formation : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
Count the number of birds in each group.

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

.62 1.00 .62
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.

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.

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

62%
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

100%
62%
.62 1.00 .62

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.

The cabinet above the tambour door is a Golden Rectangle, with an adjacent
square. The angle of the custom hood leads to a corner. The top corner of the
hood begins a diagonal through the corners of the adjacent cabinet and continues
to the end of the counter top.

The Taj Mahal is designed within a square. The entrance is a square with its size
determined by a diagonal from the midpoint at the base up to the outer square. The
distance above the door is 62% of the overall height.

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.

Georges Seurat skillfully positions precisely sized objects around the canvas
to direct the scene. From the center red umbrella the man to its left is looking
tangent to it towards the tree, then down between the seated girls. From the
black umbrella in the upper right, a diagonal goes through those girls as the
dog‟s tail and nose are exactly on the line.

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.

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

Empire State Building.
The focal point is
designed within a square. 1.00
Generating Lines cross at
strategic points to
determine location of
windows, decoration and
change in setbacks.
Outside corners of the .38
building guide to the top of
the tower. Placement, as
well as proportion, create
a lasting impression. .62

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 has direction.

The beauty of gracefulness in line, form and movement. It is not axial
symmetry, yet it is balanced. There is a beginning and an end, with no repeats.

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.

Dynamic Symmetry’s
greatest values produce
equilibrium with the
vitality and movement of
a see-saw. The
outstretched arm is
balanced by the mass of
the hat. His fingers
counter balance the
direction he faces.

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.

The full kitchen showing
generating lines determining
cabinet proportions around
the microwave and air
conditioner grill cover.
Similar lines as Notre Dame.

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.

Full view of the kitchen showing 6” backsplash turning the corner, then becoming full
height at the sink, supporting the glass cabinet to emphasize the double level ceiling.

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.

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.

Dynamic symmetry is an ‘X’ formed by the thrust of his arms
towards her legs, then his left toe to her elbow to the upper right.

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.

Enjoy!

The balanced body replicates the graphic. Or, is the pattern derived from the body?
The optical illusion is actually vertical.

Golden Rectangles and a square whirl in balance - as on a see-saw.

Back wall spiral composition: The glass inserts are in proportion to the door as
eyes and mouth are to a face. They guide your view upward to the horizontal lift up
doors then across to the Golden Rectangle and down. A double square over the
cooktop leads to the single square to complete the arrangement.

Proportional layout using squares, double squares and Golden Rectangles

Hardware placement: The drawer handle is not centered on the height of the drawer.
It is 62% of its height up from the bottom. The knobs are aligned with the ends of the
handle and the lower corner of the door. Creating patterns adds vitality to the design.

100%
62%
50%
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.

More Frank Lloyd Wright horizontals, multiple levels and recesses.

18” 30” 48”
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.

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

30”
55” 48”
34”
21”
The Golden Proportion kitchen cabinets continue into the dining room with a square
open space and Golden Rectangle glass cabinet. Together they form a larger Golden
Rectangle. Even the base cabinets are 30” and 48” Golden Proportion.

55”
34”
21”
3-2-1, 62% sequence
of the upper doors.

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 four squares are set in the cabinet as eyes on a face. The bottom of the
cut out is at the midpoint of the door. The space on each side of the cut out
is 62% of the opening. The top upper doors are all squares.

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.

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.

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.

Whirling cabinets of varying
depths create movement in
this 10 foot high space. The
horizontal doors are double
squares, the pair of doors
form a single square, the
vertical cabinet is a Golden
Rectangle.

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.

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

Two pairs of doors each form squares followed by a Golden Rectangle. The horizontal
cabinets form an ‘L’ shape with the glass pantry. The entire arrangement completes a
spiral viewed either clockwise or counter clockwise.

Van Gogh energizes the night sky creating movement to enliven the painting.

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.

Future Reality: Cirque de Cuisine

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 glides 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.

This kitchen is 10’ high and only 6’
wide. The cabinets on the right are
12”deep. Sliding and lift up doors
provide ‘nose clearance’ and allow
more open cabinets than a swinging
door in your face.
Notice that the step arrangement of
doors and open space accent the
height and length of the room and
lead to the ceiling focal point.

This view shows swing up and lift
up doors, along with the pull out
garbage can and step stool.
Notice the relationship of the arch
cabinet and ‘sky light’, including
the three-dimensional curved flue.

The thrust of the design leads to the hood, then out the terrace door to view the Empire
State Building. The diagonal placement of the knobs and handles are evident.

The dynamic quality of this building in Germany by Zaha Hadid has energy similar to the
previous kitchen. Where do you get your inspiration?

What do the statue of ‘David’ and
kitchen cabinets have in common?
The contractor replied:”…………...”.

ROSENHAUS DESIGN GROUP
Mark Rosenhaus, CKD
138 West 72nd Street
New York, NY 10023
Phone: 212-579-4598
Fax: 212-579-4599
Rosenhausdesign.com
Rosenhausdesign@aol.com