This shows the outdoor monument "Dodecahedron", and the four interior works "Theorem", and "Circle, Square, Triangle".
Pythagoras
2003 Commission of Salt Lake City Corporation
Pioneer Police Precinct Building, 1040 West 700 South, Salt Lake City, Utah
2003 Commission of Salt Lake City Corporation
Pioneer Police Precinct Building, 1040 West 700 South, Salt Lake City, Utah
The long wall displaying Triagle, Circle, and Square.
The production of this work was done entirely in-studio by myself and a few fellow artists. All design, bronze casting, wood work, steel work, and installation were completed by my tiny team at the University of Utah facilities and the studio of David Eddy, with a special thanks for woodworking to Shawn Porter and stainless steel production to Larry Wheeler. The project spanned great effort over the course of eight months.
Pythagoras relates the ideals of societal law with the governing mathematics of natural law through the formal language of geometric shape. The works are based upon the complexities of the ancient Mayan calendar whose form is a complex mathematical dialogue on what Western culture understands as the Fibonacci Sequence. The geometric proportions employed within this calendar accurately describe the mathematical principles underlying the motion of celestial bodies. The structure of such an advanced portrayal relies upon geometric expression foundational to mathematics – Phi, the proportional ratio of 1.618. Phi also serves as the mathematical base for the Golden Mean, the central tenant of beauty in Hellenic art and architecture, and the recursiveFibonacci Sequence (1,1,2,3,5,8,13…), a pattern which describes the ordering structure of many organic, celestial, and geometric systems.
As cultures become aware of the mathematic principles which govern underlying harmonies in nature,they determine a conception of Natural Law. This Natural Law is also capable of describing the laws of societal order. The Hellenic mathematician and philosopher Pythagoras explored this idea extensively. In demonstrating that ideal mathematical forms also have physical expressions in the natural world, he postulated how human societies can also exhibit aspects of such ordered expression.
Within the Mayan calendar, Phi is expressed through the symmetries of the pentagram. In Pythagoras, these geometric relationships inform the design of the interior relief work, while the dodecahedron (the resultant twelve-sided form created when pentagrams are joined in three dimensional space) governs the structure of the exterior form.
The interior works relate the ideals of Natural and Societal Law while the exterior form relates the application of these laws. All of the works connect to one another conceptually and formally – unifying the interior and exterior of the building. There are four interior works of cast bronze and a variety of contrasting woods. One work hangs within the lobby, with three related works installed along the major hallway. The exterior sculpture is a fully dimensional cast bronze and stainless steel form derived from the same shapes as the interior bronze forms.
The three works installed along the hallway – Circle, Square,and Triangle – are seven foot diameter circles. Each is composed of an inner circle, three feet in diameter, and a two foot wide outer ring. The inner circle is a convex form of cast bronze. The bronze form examines one ofthe three geometric design shapes – the circle, the square, or the triangle. Its composition references the harmonies of Natural Law as described by the underlying mathematical symmetries of Phi within the Mayan calendar. The varying low-relief wooden forms within the outer ring are derived from the corresponding interior bronze shape. In example, Square: the inner bronze circle extrapolates square shapes latent within the structure of the Mayan calendar, while the outer ring is filled with an arrangement of varying sized squares in an effect similar to a sunburst.
Theorem, the fourth interior sculpture hangs in the lobby facing the three hallway forms. This sculpture has two concentric wooden rings surrounding an inner bronze circle form that is created in the same manner as the other interior pieces. This inner bronze circle is an amalgamation and balance of the square, circle, and triangle. The inner wooden ring is patterned with a sunburst of triangles made from a variety of woods. The triangles are incorporated into a geometric pattern that moves in a counter-clockwise progression as the triangles are transformed into squares (the progression can also be read from clockwise,with the squares transforming to triangles). The outermost ring is evenly bisected into five equal parts of a pentagram, with each section described by a distinctive wood type.
Outside the building near the Jordan River is the twenty foot tall sculpture: a seven foot diameter dodecahedron elevated to a total height of twenty four feet above ground by a central pole and five smaller supporting poles arrayed as apentagram. The form consists of twelve stainless steel hoops forming the dodecahedron (three feet in diameter each) with twelve bronze cast forms radiating within the hoops. These bronze castings are three reproduced sets of the four interior cast shapes – the Circle, Square, Triangle, and Theorem. The geometric patterns of the interior works become dynamic shapes within the exterior piece. Casting effects of flashing intentionally distort the bronze forms. A number of the twelve bronze elements are without defect, while others begin to lose cohesion.These distortions communicate the exercise of law; the difficulties and ambiguities of application. This composition provides a relationship between Pythagoras and the on-site officers’ memorial, commemorating the dedication and personal cost of an officer’s duty.
All bronze forms also interpret the shield. While the police shield is part of an ancient emblematic tradition symbolizing protective martial application of societal laws, a shield can also be a vehicle for personal and cultural transformation, as personified in the Medicine Shield of Native American cultures. The bronze forms reference the transformational ideal of the Medicine Shield and harmonies of Natural Law as described by the underlying mathematical symmetries of Phi within the Mayan calendar.
Pythagoras is intended to act as a positive agent within the diverse community – investigating and affirming the underlying structure of society. This public work examines the philosophical thought great cultures of the Americas and Europe have invested into their art to represent the abstract concepts foundational to social structure.
Pythagoras relates the ideals of societal law with the governing mathematics of natural law through the formal language of geometric shape. The works are based upon the complexities of the ancient Mayan calendar whose form is a complex mathematical dialogue on what Western culture understands as the Fibonacci Sequence. The geometric proportions employed within this calendar accurately describe the mathematical principles underlying the motion of celestial bodies. The structure of such an advanced portrayal relies upon geometric expression foundational to mathematics – Phi, the proportional ratio of 1.618. Phi also serves as the mathematical base for the Golden Mean, the central tenant of beauty in Hellenic art and architecture, and the recursiveFibonacci Sequence (1,1,2,3,5,8,13…), a pattern which describes the ordering structure of many organic, celestial, and geometric systems.
As cultures become aware of the mathematic principles which govern underlying harmonies in nature,they determine a conception of Natural Law. This Natural Law is also capable of describing the laws of societal order. The Hellenic mathematician and philosopher Pythagoras explored this idea extensively. In demonstrating that ideal mathematical forms also have physical expressions in the natural world, he postulated how human societies can also exhibit aspects of such ordered expression.
Within the Mayan calendar, Phi is expressed through the symmetries of the pentagram. In Pythagoras, these geometric relationships inform the design of the interior relief work, while the dodecahedron (the resultant twelve-sided form created when pentagrams are joined in three dimensional space) governs the structure of the exterior form.
The interior works relate the ideals of Natural and Societal Law while the exterior form relates the application of these laws. All of the works connect to one another conceptually and formally – unifying the interior and exterior of the building. There are four interior works of cast bronze and a variety of contrasting woods. One work hangs within the lobby, with three related works installed along the major hallway. The exterior sculpture is a fully dimensional cast bronze and stainless steel form derived from the same shapes as the interior bronze forms.
The three works installed along the hallway – Circle, Square,and Triangle – are seven foot diameter circles. Each is composed of an inner circle, three feet in diameter, and a two foot wide outer ring. The inner circle is a convex form of cast bronze. The bronze form examines one ofthe three geometric design shapes – the circle, the square, or the triangle. Its composition references the harmonies of Natural Law as described by the underlying mathematical symmetries of Phi within the Mayan calendar. The varying low-relief wooden forms within the outer ring are derived from the corresponding interior bronze shape. In example, Square: the inner bronze circle extrapolates square shapes latent within the structure of the Mayan calendar, while the outer ring is filled with an arrangement of varying sized squares in an effect similar to a sunburst.
Theorem, the fourth interior sculpture hangs in the lobby facing the three hallway forms. This sculpture has two concentric wooden rings surrounding an inner bronze circle form that is created in the same manner as the other interior pieces. This inner bronze circle is an amalgamation and balance of the square, circle, and triangle. The inner wooden ring is patterned with a sunburst of triangles made from a variety of woods. The triangles are incorporated into a geometric pattern that moves in a counter-clockwise progression as the triangles are transformed into squares (the progression can also be read from clockwise,with the squares transforming to triangles). The outermost ring is evenly bisected into five equal parts of a pentagram, with each section described by a distinctive wood type.
Outside the building near the Jordan River is the twenty foot tall sculpture: a seven foot diameter dodecahedron elevated to a total height of twenty four feet above ground by a central pole and five smaller supporting poles arrayed as apentagram. The form consists of twelve stainless steel hoops forming the dodecahedron (three feet in diameter each) with twelve bronze cast forms radiating within the hoops. These bronze castings are three reproduced sets of the four interior cast shapes – the Circle, Square, Triangle, and Theorem. The geometric patterns of the interior works become dynamic shapes within the exterior piece. Casting effects of flashing intentionally distort the bronze forms. A number of the twelve bronze elements are without defect, while others begin to lose cohesion.These distortions communicate the exercise of law; the difficulties and ambiguities of application. This composition provides a relationship between Pythagoras and the on-site officers’ memorial, commemorating the dedication and personal cost of an officer’s duty.
All bronze forms also interpret the shield. While the police shield is part of an ancient emblematic tradition symbolizing protective martial application of societal laws, a shield can also be a vehicle for personal and cultural transformation, as personified in the Medicine Shield of Native American cultures. The bronze forms reference the transformational ideal of the Medicine Shield and harmonies of Natural Law as described by the underlying mathematical symmetries of Phi within the Mayan calendar.
Pythagoras is intended to act as a positive agent within the diverse community – investigating and affirming the underlying structure of society. This public work examines the philosophical thought great cultures of the Americas and Europe have invested into their art to represent the abstract concepts foundational to social structure.
Each size circle has a corresponding wood media, while the central form is cast bronze.
The wood forms vary in circumference and height, while the central bronze form is a dimensional half-sphere.
The central form for Circle, finding multiple circles within the geometry inherent in the central form of the Mayan calendar. This is the wood original form for the central bronze form. After creating it in wood, it is molded in silicon. A wax form is pulled from the silicon mold, then the wax form is draped over a large half-sphere and slowly warmed to form the wax from a flat form to a dimensional form. The outer bronze ring is a separate sculpture denoting the annual count of the Mayan calendar. The two forms are cast separately in bronze, then welded together. After months spent creating and casting the 4 central bronze forms, it was time to begin the wooden structure.
The bronze element of Circle surrounded by the blank wooden forms. Once all is composed and fit together, veneering of the wood blanks will begin while the bronze form moves on to patina. The wood process will take another few months of long days, seven days a week.
The central form for Square, finding multiple squares within the geometry inherent in the central form of the Mayan calendar.
The red circles are plugs of Bloodwood. This detail shows the small triangle enter the form, where it will transition into a square on the other side, or vice-vera.
This is the central form for Theorem, which contains all three basic shapes of circle, square, and triangle as extrapolated from the central disk of the Mayan calendar.
The central form for Triangle, finding multiple triangles within the geometry inherent in the central form of the Mayan calendar.
The Triangle proved difficult, as veneering the forms altered the fit. It took an extra week to configure for this challenge, before veneering could begin. The amazing wood work relied on the masterful skills of fellow artist Shawn Porter.
The 7' sphere begins at about 14' , the entire piece topping out at about 24', that is about as tall as a two-story house. So it is big!
The structural complexity of the dodecahedron becomes apparent here. 12 stainless steel disks seem to float, with bronze forms floating in their center. Supporting the bronze is a central stainless steel 12-arm form. This form seats 12 pairs of smaller arms that support the bronze forms, allowing the bronze to appear to float free within the surrounding stainless disk. This entire form sleeves atop the massive central pole, which is supported by five angled runs of stainless steel pipe. The support is set deep into the ground in a massive concrete footing, with separate footing for each of the 5 smaller pipes- the sculpture sits in the site drainage at the level of the Jordan river which flows a stones throw to the West. It is made to remain stable in case of flooding or liquifaction of the soils. All of this amazing technical stainless work was done by Larry Wheeler, and undergrad art student who had gained his underwater welding certification during military service.
Each of the 4 types of bronze shapes is cast in sets of three, for a total of 12 bronze forms. A twelve sided circle is the geometric form derived from a pentagon. A pentagon is the base geometric form of all sequences described by Fibonacci. The bronze shapes are cast utlizing my unique crazing method, making each of the 12 forms unique. This form expresses the application of law by individual officers, while the perfect interior forms represent the ideal of law. This form also relates to the monument for officers fallen in the line of duty in the plaza entrance to the building.
The forms are cast, patina-ed, and welded to their stainless steel structures that will fit them into the dodecahedron superstructure.
Here I am with Theorem, the smallest of the interior works- just to give an idea of scale.