Design Essentials - Squares

Jewelry Discussion
1

Was: Diamond cuts technicals

Hi Wayne,

Your response reminded me that I had wanted to point out earlier
that Mother Nature does indeed create squares.

Yes, and as a chemist, I should have remembered your example of salt
crystals, etc. I also pointed out Fibonacci and his numbers, and the
squares with sides the lengths of those numbers, when put together,
create the spirals found in nature - the arrangement of sunflower
seeds on those huge happy looking flowers and on the shells of such
creatures as the nautilus, etc.

We’re all inspired by the world around us and everything, even
manmade, originally came from mother nature.

Helen
UK

2 
I'm having trouble thinking of an example of a naturally occurring
round shape, though. Spheres, yes, but what has a round planar
surface in Nature?

Wayne - just being esoteric at this point - strictly speaking there
is neither square nor circle in the universe that we know of (you
know this, just discussion), because they are two dimensional and
the universe is three dimensional. In the spirit of it’s meaning to
design, though, a sphere can give one knowlege of the circle, as a
cube can give one knowlege of the square. The shapes are based on
those two dimensional concepts. But there are discs here and there -
some flowers approach it, and we used to pick up crinoid-fossil
segments that were fairly perfect discs. Intellegence tends to try
to bring order out of disorder, too, so you could say that some
animal footprints are close enough, or the section of a tree trunk,
that a human would see it as “circular”, speaking to the evolution of
geometry and design. And thanks to Helen for the Fibonacci number -
I was familiar with the concept, but never knew the name or saw it in
depth, before.

3

As I said before, use of the square requires special circumstances.
Few cases that you mention, even if they were true and the are not,
would not buttress your argument; but I will address them one by
one.

Take one look at Fibonacci if you don't think that squares exist
in nature. Put together squares with sides the length of the
Fibonacci numbers and you come up with the spirals found in nature.

Fibonacci numbers or Fibonacci Series, properly understood, is the
best argument against using square. The basis for Fibonacci Series is
the sqr(5) or geometrically it is the ratio of a diagonal of a
rectangle 2 X 1 to it’s small side. It is exactly why your assertion
that "Put together squares with sides the length of the Fibonacci

numbers and you come up with the spirals found in nature

is nonsensical. Spiral construction involves rectangles with long
and short sides relating to each other in the Golden Ratio, not
squares. As a result of sub-divisions, there are squares present on
illustrations, but they are incidental to the process. This also
addresses Wayne point on salt crystals and similar manifestations of
square in Nature. All the natural processes of growth involves
Fibonacci Series. One way to understand it is when any step in the
process is the result of previous steps and relates to them in a
pattern. Due to an irrational nature of sqr(5) the equality, which is
a necessary property of a square, cannot be achieved, and therefore
nature cannot make square things. We should not confuse that squarish
and square are different concepts. The true shape of a crystal is
it’s unit cell and not outward appearance. After all, Wayne as a
gemologist, should appreciate the fact that in a crystal with unit
cell having property of square, the cleavage, or parting would be
impossible, and we know it is not the case.

Squares in architecture? The first architect who probably comes to
mind for anyone would be Frank Lloyd Wright. He was very fond of
the square and used it to form the basis of many of his building
designs.

Which of his works do you refer to? If you can be more specific, I
can address the point then. I am familiar this his works and I cannot
find justification for your statement. As a general case architects
do not employ square, unless they absolutely must.

Also look at the pyramids of Egypt. You may have to be in a
helicopter to see it, but they are square from the top.

Pyramid example does not make your point, because Pyramid is a
special case in itself. One of the properties of square is convey the
sense of serenity.( I call it dullness ) Since a pyramid is a place
of
an eternal rest, the square is very appropriate. By the same token, a
lot of the tablets on a cemetery head stones are also squares for the
same reason.

My experience of design education was quite the opposite and John's
point about "sticks, cheese, astronomy, mud" was that a true
designer can materialise a design given any starting point. For me,
that summed up a good designer.

I will reiterate that design is a process of reducing the complexity
until the only elements that remain are absolutely essential to the
expressing the main idea, and therefore is limiting in its nature.
Work of Frank Lloyd Wright is a testament to that.

Leonid Surpin.

4

Good points, John. We DO try to place order on the chaos, don’t we?
It’s what mathematics is all about, conceptual describing, not
factual representation.

And then we have opinions on what is “pleasing”, an emotional
reaction to a visual perception.

Concerning simple geometric shapes, most folks seem to have strong
preferences between a circle or a square…I could never decide. In
my stone cutting, left to my own devices, I like cushions that are
squares with rounded corners! I don’t know why, it’s just my
favorite shape.

Maybe it’s the Tao at work!
Wayne

5

Leonard,

Fibonacci numbers or Fibonacci Series, properly understood, is the
best argument against using square. The basis for Fibonacci Series
is the sqr(5) or geometrically it is the ratio of a diagonal of a
rectangle 2 X 1 to it's small side. It is exactly why your
assertion that "Put together squares with sides the length of the
Fibonacci is nonsensical. Spiral construction involves rectangles
with long and short sides relating to each other in the Golden
Ratio, not squares. As a result of sub-divisions, there are squares
present on illustrations, but they are incidental to the process.
This also addresses Wayne point on salt crystals and similar
manifestations of square in Nature. All the natural processes of
growth involves Fibonacci Series. One way to understand it is when
any step in the process is the result of previous steps and relates
to them in a pattern. Due to an irrational nature of sqr(5) the
equality, which is a necessary property of a square, cannot be
achieved, and therefore nature cannot make square things. We should
not confuse that squarish and square are different concepts. The
true shape of a crystal is it's unit cell and not outward
appearance. After all, Wayne as a gemologist, should appreciate the
fact that in a crystal with unit cell having property of square,
the cleavage, or parting would be impossible, and we know it is not
the case.

This is very misleading. While it is true that a Fibonacci series
can be constructed using expressions relating to the Golden Ratio,
this is by no means a mathematically exclusive definition of a
Fibonacci series, merely one way to express such a series.

I am sure you are familiar with a Fibonacci tiling, the classic way
to express creation of a Fibonacci spiral. Such a tiling creates a
Fibonacci spiral when arcs connecting the opposite corners of
squares are connected. The shapes that do this are SQUARE, not
squarish and not rectangular or any other shape.

Fibonacci expressions can also be found in certain right triangle
relationships, reciprocal sum relationships, in an examination of
the divisibility of prime numbers, and, yes, in an examination of
the Golden Ratio, as well as many other places, although some of the
commonly-given examples in Nature are suspect.

In its purest form, spiral growth of a crystal results in the
simplest possible geometry allowed by such growth, which is a
square, growing outward in spiral form from a center or near-center.
It SHOULD be a circle, but that doesn’t happen. This is not
precisely how mineral crystals in the isometric system form, but it
is certainly a close approximate description. The outward appearance
is a square.

Of course, no true cubic unit cell could cleave, but mineral
crystals are NOT unit cells, they are, as you know, geometric
combinations of unit cells, and the cleavage takes place along the
natural planes of weakness represented by the weak edge-edge
attractions among these unit cells.

Yours is a specious argument based on Helen’s unfortunate poor
choice of words which you called “nonsensical”. I’d rather attribute
her phrasing to shortcomings in the mode of communication and
perhaps even the absence of a good mathematical grasp of Fibonacci
relationships. I understood her intention, and with your obvious
command of the subject, I think you must have, too.

But, your argument that the Fibonacci series is the “best argument
against using the square” is, shall we say, selective…and not
exclusively true.

Please, there is no need to offer an argument based on Binet’s
closed-form solution and its relation to the “Golden” ratio. Keppler
also long ago pointed out that the limits of consecutive quotients
approach the “Golden” ratio and that these examples are Fibonacci
recursives. I understand these completely, but they are not
exclusive arguments or definitions, they are simply descriptions of
relationships.

One of the classic algebraic TESTS for a Fibonacci number demands the
use a perfect square, as well. It says that a positive integer z is a
Fibonacci number ONLY if the expression 5z(squared) + 4 or
5z(squared)-4 is a perfect square. Not a geometric square, of course,
but an algebraic square. Easy to play games with math and semantics,
isn’t it!

Wayne

6

Pyramid example does not make your point, because Pyramid is a
special case in itself. One of the properties of square is convey
the sense of serenity

Gee, thanks Leonid…now I know why I call my 40x40 foot SQUARE
(designed by an architect) home “Serenity Home” Never thought of it
as dull though.

Lainie

7

Leonid,

With all due respect, all you seem to be doing is nit-picking. People
can look at the work of Fibonacci and go away and design something
based on rectangles. They might also use your design ethos of "
process of reducing the complexity until the only elements that
remain are absolutely essential to the expressing the main idea" and
take the SQUARE as a basis for their design.

We are all different and given John’s examples of “sticks, cheese,
astronomy or mud” all of us will be inspired differently, and thank
God for that, that he made us all different or it would be a very
dull (or should I say square) world!

Which of his works do you refer to? If you can be more specific, I
can address the point then.

As one example I was referring to his Price Tower sometimes known as
Prairie Skyscraper. I quote: “Beginning with a rotated square
divided into four quadrants, Wright developed the pin-wheel geometry
of the Price Tower, which generated everything from the building’s
floor plans and construction details to its elevations and ornament.”
I rest my case on the Frank Lloyd Wright issue but if you dig deep
enough into his work you’ll find that he actually liked the square.

Pyramid example does not make your point, because Pyramid is a
special case in itself. One of the properties of square is convey
the sense of serenity.( I call it dullness ) Since a pyramid is a
place of an eternal rest, the square is very appropriate. By the
same token, a lot of the tablets on a cemetery head stones are
also squares for the same reason.

Leonid, you’re at risk of sounding square yourself. Any time an
example doesn’t suit your purposes you call it a special case in
itself. You really are “squareist”. Is it just the square or do you
have prejudices against any other shapes? There are therapists for
such behaviours you know.

I think your design education has left you damaged or certainly
limited, but that’s what you say design is. I prefer to take a bit
more of an open-minded approach to both design and life in general
and think it’s healthier to be like that.

I respect you as one of the “big” guys on Orchid and am sure you
make beautiful jewellery but perhaps you should put a sign on your
door saying “squares not allowed” and make it simpler for everyone
wanting princess cut diamonds to go and find another jeweller.

Helen
UK

8 
And thanks to Helen for the Fibonacci number - I was familiar with
the concept, but never knew the name or saw it in depth, before.

My pleasure John. From my scientific background and love of all
things natural, I used Fibonacci’s theories a lot when doing garden
design (in between teaching science and jewellery making!). And
thanks to this thread, it’s rekindled my interest in such things. So
like some of my garden designs, I may find my jewellery taking on
elements from my chemistry/biology days (such as DNA helices) and or
Fibonacci’s numbers and other nature inspiring ideas.

While this princess cut “debate” did seem a bit of a rant for a
while, I think such discussions can often come round to some useful
design ideas. Long live Orchid!

Helen
UK

9 
Put together squares with sides the length of the Fibonacci
numbers and you come up with the spirals found in nature is
nonsensical. Spiral construction involves rectangles with long and
short sides relating to each other in the Golden Ratio, not
squares.

Read it again, you missed something.

The true shape of a crystal is it's unit cell and not outward
appearance.

Huh?

mind for anyone would be Frank Lloyd Wright. He was very fond of
the square and used it to form the basis of many of his building
designs. Which of his works do you refer to? 

  "That early kindergarten experience with the straight line;
  the flat plane; the square; the triangle; the circle! If I
  wanted more, the square modified by the triangle gave the
  hexagon, the circle modified by the straight line would give
  the octagon. Adding thickness, getting 'sculpture' thereby,
  the square became the cube, the triangle the tetrahedron, the
  circle the sphere." 

  "These primary forms and figures were the secret of all
  effects... which were ever got into the architecture of the
  world" 

  "Taken East a the age of three to my father's pastorate near
  Boston, for several years I sat at the little kindergarten
  table-top ruled by lines about four inches apart each way
  making four-inch squares; and among other things, played upon
  these 'unit lines' with the square (cube), the circle (sphere)
  and the triangle (tetrahedron or tripod) - these were smooth
  maple wood blocks. Scarlet cardboard triangle(60o-30o) two
  inches on the short side, and one side white, were smooth
  triangular sections with which to come by pattern--design--by
  my own imagination. Eventually I was to construct designs in
  other mediums. But the smooth cardboard triangles and maple
  wood blocks were most important. All are in my fingers to this
  day." 

  "Also German papers, glazed and matte, beautiful soft color
  qualities, were another one of the 'gifts'--cut into sheets
  about 12 inches each way, these squares were slitted to be
  woven into gay colorful checkerings as fancy might dictate.
  Thus color sense awakened. There were also ingenious
  'constructions' to be made with straight, slender, pointed
  sticks like toothpicks or jack-straws, dried peas for
  joinings, etc., etc. The virtue of all this lay in the
  awakening of the child-mind to rhythmic structure in Nature --
  giving the child a sense of innate cause-and-effect otherwise
  far beyond child-comprehension. I soon became susceptible to
  constructive pattern evolving in everything I saw. I learned
  to 'see' this way and when I did, I did not care to draw
  casual incidentals to Nature. I wanted to design."

all quotes by Frank Lloyd Wright They inspired Wright, who would
remember them all his life. “Mother found the ‘gifts,’ and what gifts
they were,” he once wrote. “I soon became susceptible to constructive
pattern evolving in everything I saw. I learned to ‘see’ this way,
and when I did, I did not care to draw casual incidentals of Nature.
I wanted to design.” Froebel blocks are deceptively simple. Playing
with them shows how, for example, two rectangles form (or come from)
a
square, which in turn divides into two triangles. Concepts like
proportion and spatial relationships are thus absorbed through
play–and the memory is long-term. Wright use of grids for design is
derived from the method of geometric study developed by the German
philosopher and educator, Frederich Froebel.

http://www.nbm.org/Exhibits/past/2000_1996/Windows_Page.html

Stylistically, the “Taliesin Line” was considered quite conservative
compared to Wright’s initial avant-garde furniture lines, “The
Burberry,” “The Four Square,”

And finally, a simple quote:

The square is probably the best known of the qudrilaterals. It is
defined as having all sides equal, and its interior angles all right
angles (90). From this it follows that the opposite sides are also
parallel.

A square is simply a specific case of a regular polygon, in this
case with 4 sides. All the facts and properties described for
regular polygons apply to a square. See Regular polygons.

Or is it, as one lone, single person would have us believe, the root
of all evil?

The most important lesson of all to know in life is the rule of
holes: Whenever you find yourself in the bottom of a deep, deep
hole, STOP DIGGING!

10

Please see the on my website on the golden rectangle -
made of decreasing squares - defining a Fibonici series - the perfect
spiral.

www.judyhoch.com/etc.cfm

Judy Hoch, GG

11

It has become clear that a return to the fundamentals is called for
on this topic. Anyone can argue with what I’m about to write, but Mr.
Pythagoras, Mr. Euclid, and myself will laugh at you. There are four
basic shapes in geometry and by extension, design. There is one - a
straight line. It must be “absolutely” straight, because if it
deviates it will become a circle. This is the point where “absolute”
geometry and design part ways a bit, because design is human and a
bit casual, not mathematical. But a straight line is straight. Then,
if the line deviates from straightness, it will arc around and
eventually find itself again. The line can actually do as it pleases,
but theoretically and conceptually it will double back, find itself
again, and become a circle - a single line which is also a curve.
(I’ll use the mathematical term for curve, because modern graphics
uses “curve” for any line, straight or arced). There is no two line
form - the lines simply form an angle, do not ever meet, and go off
into infinity. Number three is the triangle, the simplest polygon
(many sided) form. Number four is the square. Beyond that is only the
prime numbers, which are much less important to design. The five
sided figure (pentagon) has some value, but 7, 13, and more sides to
poygons are not important to design, though they may be used as
needed. There is also what is known as a “regular” polygon. What this
means is that all sides are equal length, and what it also means,
which is important to design, is that the polygon can be inscribed
inside or outside a circle, which is really just happy coincidence.
So a circle, which is by definition “regular”, has a uniform
diameter. A regular triangle can be represented as a=b=c, and a
square as a=b=c=d. What is most important about this, in design
terms, is that the circle gives us all “curves” - arced lines. The
triangle gives us threes, and the square gives us fours. Again, if
you want the prime numbers, then that is beyond and somewhat unusual,
though the pentagon has a certain appeal. Thus if someone has a
circular center and wishes to surround it with stones, if they are
any designer they will surround it with threes or fours - threes will
give you a stone on the north and south, and a space on the east and
west. Fours will give you a stone on N,S,E and W. Threes give you
sixes, twelves, fifteens, eighteens. Fours give you eights, also
twelves, sixteens and twenties. When you put fours around a center,
you are making a square. Yes, there is a 16 sided polygon, whatever
the Greek for it is. That is found by splitting each side of the
square in 4 parts - the square is the “Mother”, if you will. When you
put threes around a center, you are making a triangle. The same is
true if it is inside the circle (circumscribed). If one is to put
eight elements, or sixteen around a circular center, it is far easier
and more efficient to think of that as two or four squares rotated at
some angle around the center than to try to deal with a sixteen sided
polygon, and the same is true with the triangle. When one enters into
3d graphics, they will find two primitive shapes - the sphere and the
cube. There are other shapes, such as the torus, which are really
just time saving features - so as to not have to make a torus from a
sphere every time. For a person to say that the square is of no
importance or usefullness is, quite frankly, to say that they are
profoundly ignorant about geometry and design, and I for one find
that, on a public forum involving many students and novices,
bordering on flaming. The square is not simply important, it is at
the core of geometry and design - a fundamental part of human
consciousness.

http://www.donivanandmaggiora.com

12

I love your piece (of jewellery) based on the Fibonacci series Judy.
It’s beautiful.

Helen
UK

13

Wayne,

I am not sure that I can respond to all points in your post due to
time limitation, but to distill the argument to one central issue is
whether or not Fibonacci Series is an argument towards the use of the
square as a first choice in a design, or the last one necessitated
only by special circumstances.

We kind of have waltzed in a very important subject not only in
Jewellery Design, but in Art, and Mathematics, and many other related
areas. So a detailed explanation is in order, and at the end I will
address the construction of the spiral.

Fibonacci discovered the sequence while trying to answer a very
mundane question: “How many rabbits a farmer can expect in a year
starting just with one pair of rabbits”. He realized that the
sequence
representing increase in population will be as follows: 1, 1, 2, 3,
5,
8, 13,…, infinity. To understand the sequence one has to note that
every number in the sequence is the sum of 2 preceding numbers except
the first two numbers. The reason is that in the beginning a pair of
rabbits would give a birth to one rabbit. Since, this rabbit is to
young to take part in procreation sequence, the original pair would
produce a second rabbit, while the first would be reaching sexual
maturity, so It can participate as well. That is why the first two
members of the sequence is 1, 1.

Fibonacci theorized that all the growth processes in nature are
following the same scheme. It did not take long to connect his
discovery to the works of Pythagorians. They found out that taking
the
length of the diagonal of rectangle with dimensions 2 X 1, adding
this
length to the length of the short side and dividing the sum by 2, the
resulting length would relate to the length of the short side in the
most pleasing manner. In math terms 1/2( 1 + sqrt(5) ). The reason
for sqrt(5) is the diagonal of 2 x 1 rectangle, is also a hypotenuse
of a right triangle with sides 2 and 1, and the hypotenuse^2 = 2^2 +
1^2 ( by Pythagorus Theorem ) This is also known as Golden Ratio.
Numerically it = 1.618 approximately.

Back to Fibonacci. Let’s take 3 (third member of the series and
multiply it by 1.618 ( golden ratio )

3 * 1.618 = 4.854 - slightly under to 5 which is the fourth member
of the sequence

5 * 1.618 = 8.090 - slightly over 8 which is the fifth member of the
sequence

8 * 1.618 = 12.994 - slightly under 13 which is the six member of
the sequence If we continue this process to infinity ( forever ), it
would become obvious that the larger the members of Fibonacci
Sequence
become, the ratio will get closer and closer to the value of Golden
Ratio of 1.618. So these 2 concepts are very closely connected. In
essence they are manifestation of the same phenomena which is knows
as
self-similarity, and studied under the umbrella of Fractal Geometry.

Spiral construction: Draw 2 perpendiculars. ( lines intersecting at
90 degrees ). We should get 4 vectors ( lines for simplicity ). Let’s
label them as A, B, C, and D starting with horizontal left of center
and proceeding clock-wise.

Mark the distance of 3 on vector A, distance of 5 on vector B,
distance of 8 on vector C, and distance of 13 on vector D. Connect
these point with a curved line and you have your spiral. The process
can be continued, if desired, by marking distances corresponding to
the values of sequential members of Fibonacci Sequence. The next
number would be 21 marked on vector A and so on. Or we can a kind of
formal definition that a spiral is a curve, where points of
intersection of the curve and perpendiculars originated in the center
of the curve, represent vectors the magnitudes of which, taken in
sequence, relate to each other as consecutive members of the
Fibonacci
Sequence, starting with smallest and proceeding clock-wise, or
counter-clockwise, depending on the direction of the spiral.

Why on many illustrations of the process the squares are used? The
reason is that curved line mathematically represented as equation of
second degree, and since square is geometrical representation of a
number raised to second power, it manifest it’s presence, but is not
it integral to the process.

To say that squares have anything to do with spiral construction,
would be akin to saying that diamond mining is ultimately based on
the use of hammers, since diamond bearing rock is crushed by hammers
( or similar tools ) to reveal their presence. Squares, in spiral
construction, serve exactly the same purpose as hammers in diamond
mining. As we can extract diamonds without the use of hammers, we can
construct spirals without the use of squares. Squares, in spiral
construction, are as important as egg shells in preparation of an
omelet. Do you say when served an omelet in a restaurant that egg
shells were excellent ? I hope not.

In conclusion:

Square represent things which are static. The length is exactly
matches the width; no interplay between it’s elements; it is a
mathematical abstraction and symbolizes absence of movement.
Fibonacci Sequence is mathematical model of growth. It allows us to
understand how things are evolving in nature, it is the very dynamism
of everything around us, and therefore the two are diametrically
opposed. The conflation of these 2 concepts under the thesis of
"Fibonacci Sequence based on square" is truly nonsensical position. I
cannot even believe that I have to argue that point.

Leonid Surpin.

14

I dunno, whole lotta theoretical, perhaps heretical jaw jabbing goin
on. I can’t follow some of it but it’s interesting nonetheless.

my feeling is

if it looks good, make it

I wonder if this thread will ‘evolve’ itself back into the What Is
Art Sphinx?

oops, I didn’t just jinx it, did I?

15 
I rest my case on the Frank Lloyd Wright issue but if you dig deep
enough into his work you'll find that he actually liked the
square.

In the spirit of real discussion…I mentioned his Four Square
line, but decided today for general interest to go ahead and post
what it really was. Wright’s Prairie Style Home project was homes
built around a square main room, intended to be affordable,
tract-home style housing sold through Sears. He also designed a line
of furniture and accessories to accent the Prairie Style, called the
Four Square line, which name was later changed by Henredon Heritage,
the manufacturers, to The Taliesan Collection, the name of Wright’s
estate and workshop. This is all, of course, history. A good page to
see accessories in this line is here:

http://www.fitzdecarts.com/flw_metalware_+_ceramics.htm

and at the bottom is a button for more, which goes to a few more
pieces. The lighting page especially has some good examples.

16 
With all due respect, all you seem to be doing is nit-picking.

See my post to Wayne addressing this issue.

People can look at the work of Fibonacci and go away and design
something based on rectangles. They might also use your design
ethos of " process of reducing the complexity until the only
elements that remain are absolutely essential to the expressing the
main idea" and take the SQUARE as a basis for their design.

We have to retrace steps here. The argument started as having square
as the product of the design process. This somehow degenerated into
notions that square cannot be used as a basis of something. If we get
back to Princess cut, it is a cut which is mass produced. The cutter
have no idea how it will be used. As a special case maybe, as a
mainstay of the design, absolutely not. But to go from this to the
attribution that square cannot be used as a basis for the design is
a fallacy.

We are all different and given John's examples of "sticks, cheese,
astronomy or mud" all of us will be inspired differently, and
thank God for that, that he made us all different or it would be a
very dull (or should I say square) world!

Following this thesis to a logical conclusion, there is no need to
attend any schools, there are no right and wrong, anybody can mix
cheese and astronomy and proclaim himself or herself a designer.

As one example I was referring to his Price Tower sometimes known
as Prairie Skyscraper. I quote: "Beginning with a rotated square
divided into four quadrants, Wright developed the pin-wheel
geometry of the Price Tower, which generated everything from the
building's floor plans and construction details to its elevations
and ornament." I rest my case on the Frank Lloyd Wright issue but if
you dig deep enough into his work you'll find that he actually
liked the square.

As a response to your point I will use the following quote

  "The H.C. Price Company tower, named Price Tower, is the only
  cantilevered skyscraper built by Frank Lloyd Wright and
  inspired by a tree. This innovative building not only changed
  the horizon of the Oklahoma prairie, but also the world of
  architecture."

There is a difference between using something as a basis, versus
been inspired by something, and the resulting shape of this process.

Leonid, you're at risk of sounding square yourself. Any time an
example doesn't suit your purposes you call it a special case in
itself. You really are "squareist". Is it just the square or do
you have prejudices against any other shapes? There are therapists
for such behaviours you know.

My therapist does not want to see me anymore. In his eyes I am well
beyond the point salvation. But to address your point.

In design nothing is cast in stone. There is an expression that
general rule of design is like a necklace strung of special cases.
The problem is that in some circles it has been taken a license to
mix things in any order.

There are ideals of beauty which we strive to achieve. At our best,
we sometime can get pretty close, and may be that is how it should
be. A design starts with the ideal and proceed by taking into account
real world limitations. Designer is judged on his ability to get as
close to the ideal as possible, while juggling all the other
variables. Art is the celebration of beauty. That is the raison
d’etre. Anything else is the special case. Think how one would design
a War Memorial. Beauty takes a back stage in this case. Egyptian
Pyramids are special case as many others, and the ability to
recognize
it, is mandatory for any designer.

I think your design education has left you damaged or certainly
limited, but that's what you say design is.

If someone would only told me that when my professors were around. I
could have taken them to court and got a lot of money out of them.
But it is to late now. Another big one got away.

Leonid Surpin.

17 
left to my own devices, I like cushions that are squares with
rounded corners!

Yeah, Wayne, my Italian wife as a child referred to raviolis as
“mouse pillows”. There’s something of that to a cushion cut, too -
sumptuous, comforting - one of my faves, too.

18

I think I have a problem, I’ll call it time management. Maybe my
problem is just that I don’t like to spend time on the computer, I
just don’t know. If anyone has noticed or of course cares, most of my
replies are short and sweet. My time away from the bench cost me
money and I wonder how so many have the time to write these
manuscripts. Next issue, who is right here, we have two people
trying to win, someone needs to get an expert on Fibonacci and settle
this. Personally I really don’t care because I design what I want,
when I want, and it makes no difference to me if Leonid likes it or
if Fibonacci would have liked it. My customers like it and thats what
pays my bills. They even buy square rings.

Back to work
Bill Wismar

19 
In the spirit of real discussion......I mentioned his Four Square
line, but decided today for general interest to go ahead and post
what it really was. Wright's Prairie Style Home project was homes
built around a square main room, intended to be affordable

In a spirit of real discussion…

There is a technique used in debates called “Reductio ad Absurdum”
which is latin for Reduction to Absurd. The ongoing argument about
the square is an excellent illustration of that.

It started with thesis, introduced by me, that square shape is not
the mainstay of a designer repertoire, due to it’s lack of dynamism,
and it’s use should be justified by special requirements of the
design.

There were a few objections to which a response was provided that one
only has to look at all the previous history of Art and Architecture
to see that it is exactly the case.

Was square ever used ? Sure it was. In bereavement jewellery, in
burial plaques, in framing Nature Mort ( still life ) paintings, in
works where emphasis is placed on stability, serenity, and etc.
Square has a property drawing attention to the center, so if that
where the emphasis is desired, it’s use is justified.

But all of those are special cases. Well, I am not sure why, but some
participants just could not accept the evidence, so the thesis was
degenerated to the “square cannot be used at all”

Reductio ad Absurdum at work.

Frank Lloyd Wright name was dragged in. Man probably turning in his
grave by now.

He deserves much better, so I will discuss his Prairie Skyscraper or
Price Tower, since it was used in this debate.

The following was quoted:

Wright first conceived of a cantilever tower based on the geometry
of a rotated square in a 1927 project for St. Mark’s-in-the-Bouwerie.

  1. The term “rotated square” was taken to mean the same as square,
    which is not.

  2. To use geometry of the square is not the same as having a square
    as a final product.

  3. “Cantilever tower based on the geometry of a rotated square”
    refer to the construction and not to the design.

Reductio ad Absurdum at work.

Let’s see what this building was really about. Here is the excerpt
from Architecture and Space:

Price Tower Commentary

"Wright had two major difficulties of a philosophical sort in
designing a skyscraper: first, as a believer in an architecture close
to nature, he had a hard

time justifying a tal, upright, seemingly anti-nature building; and,
second, his obsession with the twin concepts of continuity and
plasticity. a preoccupation that had led him to the sea-shell and the
cocoon as ideal structural prototypes. made it difficult to approach
the design of a tall, multicellular building… He solved this
dilemma
in a characteristic fashion, by going to the one source in nature
which did suggest a way of building a tall structuRe: the form of a
tree.

In structural terms a tree is a vertical beam cantilevered out of the
ground…

To Wright, the cantilever was also the ‘most romantic, most free, of
all principle of construction.’…

By 1929,…Wright had really designed his concrete-and-glass tree
just the way he wanted it:

the vertical service core was the trunk, and all utilities were
contained within this vertical shaft. All floors were cantilevered
out from it, and the exterior skin was simply sheathed in glass and
metal. This project. the famous apartment tower for the vestry of St
Mark’s-in

-the Bouweie in New York. was never built, but Wright returned to the
basic concept again and again; finally, in 1954, in Bartlesville,
Oklahoma, Wright was able to build his St Mark’s tower. twenty-five
years after it was first designed."

. Peter Blake. Frank Lloyd Wright: Architecture and Space. p86-88.

I have underlined pertinent phrases which I include below for
convenience:

as a believer in an architecture close to nature twin concepts of
continuity and plasticity sea-shell and the cocoon as ideal
structural prototypes He solved this dilemma in a characteristic
fashion, by going to the one source in nature which did suggest a way
of building a tall structuRe: the form of a tree.

Hardly a square worshiper! But it did not stop my respected
opponents in this debate, from making him one. And all this was made
possible by using Reductio ad Absurdum. Very powerful technique
indeed.

I would like to suggest, in the interest of real discussion, that the
names of the artists and the architects and the others contributors
to our understanding of the design, should not be used, unless the
user has firm grasp of the subject in general, and the knowledge of
the body of work in particular.

Leonid Surpin.

20 
I cannot even believe that I have to argue that point.

I agree.

Let’s say some folks actually PREFER square shapes over circular
shapes. We all understand that YOU do not, but most of us don’t feel
the need to project some sort of judgement from that position.

I’m pretty much done with this silliness.

Wayne