Geometry is the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space.

     ∆   ∆    Let me say that
              2 points make a line

In geometry, a closed plane figure having three sides and three angles is known as a triangle.  Or an alternative way of thinking about it would be as a three-sided polygon that can be classified by angle, as in an acute triangle, or by side, as in an equilateral triangle. A triangle is formed by connecting each of three points to the other two.  The sum of the interior angles of a triangle is 180 degrees, its area is calculated by multiplying its height by one half of its base.    

     ∆   ∆    3 points make a form
              or shape

In architecture triangular forms provide superior strength, though they can be logistically problematic in terms of furnishing them as spaces.  Rectangles have been by far the most common geometric form for buildings.  Rectangular shapes are easily standardized, most furniture and fixture designs are interchangeable with most rectangularly shaped buildings.  When put into use though, triangles inherently support structures against lateral pressures. Because each side supports the others, a triangle will not deviate from its shape, with the exception of in the event of a broken joint or broken, bent, or extended side.  Rectangular forms on the other hand are extremely dependent on the strength of their joints.

     ∆   ∆    3 points make for a
              strong argument that is
              easy to remember

An example of a triangular shaped building would be The Flatiron Building.  Located in Manhattan, it was designed by Chicago’s Daniel Burnham. The early skyscrapers of New York typically had square or rectangular bases with towers protruding upward.  Conversely, the Flatiron Building is the epitome of the Chicago school.  Designed such that its facade has been divided into the smaller units of base, shaft, and then capital, it is reminiscent of a classical Greek column.  Not unlike many other similarly trianglular-shaped structures, the building takes the name “Flatiron” from its resemblance to the clothes iron as found in extensive use within garment factories of the time.

In geometry a square is defined as a rectangle having all four sides of equal length.  In relation to the discipline of city planning, it can also be an open area or plaza in a city with green space such as Washington Square Park.  Another interpretation of the city square concept would be that of the urban market, such as Haymarket Square in Chicago.

     ∆   ∆    any more than 5 points
               to an argument
               let us say for example 8
               would be anarchy
               and hence subject to derision
               and so let us abide by
               the 3

The present day Brown Building on the campus of NYU also in Manhattan is an example of a typical rectangular building.  It is actually square when seen from above.   The building is located at the northwest corner of Greene Street and Washington Place.  It is located such that nearby to the west lies Washington Square Park, which is actually not a square but more simply a rectangle.  Formerly know as the Asch Building, it was the location of the Triangle Shirtwaist Factory that occupied the 8th, 9th, and 10th floors.

It was not until 1870 that buildings in New York City were first built above five stories, first with the completion of the Equitable Life Assurance Building.  The Equitable Life Assurance Building was the first to feature passenger elevators, and some argue the world’s first skyscraper.  The building was eventually destroyed by fire in 1912, one year after the Triangle Shirtwaist Factory fire.  Prior to 1885 very few buildings were built taller than five stories outside of Manhattan.  It was not until after the Great Chicago Fire necessitated massive reconstruction, that buildings by architects such as William Le Baron Jenney, Louis Sullivan, Daniel Burnham, and others during this period became the basis for the development of the modern skyscraper.

     ∆   ∆    There are 3 points in Chicago that I know well
               enough to leave them behind
               they form a near perfect isosceles triangle

Previous to the late 1800s a number of factors prevented the construction of taller buildings from being profitable.  Due to a number of developments in the late 19th century that proposition inverted itself, the introduction of the passenger elevator being only one.  Primary among them was the increase in real estate prices.  For example, prices in the Chicago Loop increased from $130,000 per quarter acre in 1880 to $900,000 per quarter acre in 1890.  Property in the city centers increased in value as the working population in the cities increased, and as corporations competed for the most centralized locations.  As one might expect, the tallest buildings were constructed within the largest metropolitan centers of New York City and Chicago by virtue of possessing the most expensive property values.  Additionally, companies that planned to construct multi-story buildings bid more for the prime locations and this served to increase prices in these centralized areas.  In this way the prices of real estate and the height of buildings converged in a perfect storm that resulted in each increasing dramatically.

While the Equitable Life Assurance Building is argued by some as the world’s first skyscraper, it is largely accepted that the first modern skyscraper was the Home Insurance Building of Chicago, completed by William Le Baron Jenney in 1885.  The Home Insurance Building was the first building with in excess of five stories to be supported internally and externally by a fireproof steel and iron frame.  One year later and less than a mile from the world’s first modern skyscraper the events of the Haymarket Affair unfolded.

     ∆  ∆     2003 W. Fulton Street  
              my studio
              the location in which
              this piece
              has come into existence  
              to where the green and pink lines
              take me to, from and past
              the Haymarket memorial
              as seen from above
              at speeds unknown

It was in the aftermath of the events of the Haymarket Affair that the prominent businessmen of Chicago placed enormous political pressure on local politicians to have an armory built to protect the neighborhood they all shared.  For fear of a working class revolution, Prairie Avenue, or “Millionaire’s Row” as it was know, would be buffered to the north by the First Regiment Armory at 1552 S. Michigan Avenue.  Daniel Burnham and John Root were commissioned to design the new building.    

     ∆  ∆     2000 S. Michigan Avenue
              my home
              its location a block and a half
              from Millionaire’s Row
              a street I walk nightly
              those homes that have
              not long since been razed
              are celebrated for their

Burham went on to co-author the Plan of Chicago with Edward H. Bennett.  Famous for being influential on the burgeoning discipline of city planning, even though it was never fully realized, the portions that were implemented none the less revitalized the city center.  Burnham’s plan called for numerous buildings to be sited in the city’s Grant Park despite legal restrictions that prohibited it.  A Chicago businessman fought the legality of placing the buildings within the park, despite near unanimous dissent, and won.  The one exception for which the business man consented was for the Art Institute of Chicago.

     ∆ ∆       111 S. Michigan Avenue
              my place of employment
              at the center of the city
              where north divides from south
              where I pace the classrooms
              on the 12th floor and below
              my labor the dissemination
              of information

Burnham died in 1912, one year after the 8th, 9th, and 10th floors of the Asch Building went up in flames.

     ∆  ∆     even {we} want the labor to be hidden
             even {we} want the labor to be silent
        even {we} want finished polished pretense

Scientific management, prevalent around the end of the 19th century and reaching its peak in the early 20th century was a designed system for the examination of the increased efficiency of labor.  The movement was the brainchild of Frederick Winslow Taylor.  The application of Taylor’s ideas were often times problematic.  His ideas were dependent upon intense managerial control.  By nature this required a higher percentage of mangers to workers than had previously been necessary.  Perhaps the greatest failing of Taylorism was its lack of consideration for humanistic elements at play in the workplace.  Often times there was no way to differentiate asinine micro management from well meaning detail oriented quality control, resulting in personal conflicts between workers and managers that later inflated to tensions between blue an white collar classes.

     ∆  ∆     while {we} speak with marbles
              in our mouths

In retrospect, Taylorism can be seen as the logical conclusion to the idea of the division of labor.  Conditions that were prevalent at the time, and the consequences of this managerial approach, were the simultaneous de-skilling of the employee and dehumanization of the workplace.  Left in the hands of fervent capitalists, Taylor’s scientific management principles were applied in abusive fashion with disastrous results, such as the Triangle Shirtwaist Factory fire of 1911.  

One of the aspects most critiqued within Taylorism was that once a time-and-motion study had been conducted on a particular task, the workers performing the task had little to no recourse other than to perform the task as prescribed.  Predictably this led to wide spread resentment among the working population.

     ∆ ∆      us one hundred hues of proletariat
              n’s, a’s, er’s
              the indelible marks that betray our class
              and exclude us from the conversation    

Despite its obvious weaknesses, and by this point largely antiquated notions, scientific management is still relevant in today’s marketplace.  Though originally Taylor sought to simply improve working methodology, the process engineering he developed has a tendency to build skill into the equipment or process rather than that of the worker.  The end result has direct implications to the practice of successfully off shoring work away from increasing concentrations of skilled workers toward destitute populations without skills, but regardless are able to perform the necessary task at a much lower cost to the corporation.

     ∆  ∆     The time will come when our silence will be more powerful than the voices you strangle today.

One concept that was developed using time-motion studies stemming from Taylorist principles, the kitchen work triangle, is an attempt to design the structure of the major work centers of the kitchen in the most efficient fashion.  The major work centers in this case are the stove, sink and refrigerator.  These three points and the lines that form between them define the triangle.  The concept was developed with the aim of reducing costs by arriving at a standardization of construction by the University of Illinois School of Architecture.  The studies were based on a one person kitchen where one individual performed all of the duties.  These included cooking, canning, ironing, and of course serving the family meals.  More recently the National Kitchen and Bath Association attempted to promote an updated multiple rectangle approach to design.  The concept was based on the proliferation of the microwave and the growing reality that the structure of the American family had shifted from one person as cook to multiple individuals sharing those duties.  The new design approach quickly floundered.

     ∆  ∆     I only see death
              at any speed
              it is still expiration

The kitchen cabinet industry, having experienced incredible growth over the last two decades with the exception of the recent economic downturn, has capitalized on the standardization of customization.  For example, the cabinet samples used in this work were created in a factory that specializes in high end custom kitchen cabinetry.  The company in question accumulated $120 million in sales in the fiscal year 2010.

Most installations of kitchen cabinets utilize the use of crown moulding to disguise any gaps or inconsistencies.  Crown moulding has a long history and was employed by the ancient Greeks in any number of ways.  One fundamental way was to divide large spaces into much smaller visual units.  Perhaps more directly they used crown moulding to hide any imperfections that might present themselves at the point where the ceiling and walls or supports come into contact.  Crown moulding has a direct relationship to that of the cornice and also capital, which in turn has been a direct influence to many of the building facades associated with the Chicago school.  The relationship in discussion is exhibited in such landmark structures as the Flatiron Building.  

     ∆  ∆     I see head stones
              {we} know everyone views
              everything differently

Ancient Greek mathematicians viewed geometry as their crown jewel having explored and expanded the discipline like no other known to them.  Perhaps their greatest achievement was removing from the methodology of geometry the trial and error approach in favor of logical deduction.  Also, their cognizance of geometry as the study of eternal forms or abstractions coupled with the development of the idea of the axiomatic method confirm their view.  Among the discoveries by the ancient Greeks that are still central to students education today is Pythagoras’ theorem.  In addition to this basic principle Pythagoras and his students brought to light the notion of incommensurable lengths and irrational numbers.

     ∆ ∆      where you see a crown
              I see headstones on a mantle
              It depends upon the angle
              yet from where I stand
              they clearly become urns of Asches

Change of any variable quantity, in mathematics and the sciences is represented with the fourth letter in the Greek alphabet ∆

[WOOD BLOCKS, CROWN MOULDING, INK - performance / sculpture]