Euclid at Christmas

"All I want for Christmas are these badass Euclidian sculptures"

by

Robert T. Gonzalez

December 3rd, 2013

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From London-based "paper engineer" (paper engineer!) Helen Friel comes this creative collection of colorful folding geometric designs. The name of the collection? "Here's looking at Euclid." GEOMETRY PUNS! We must have these.

The paper sculpture collection takes its inspiration (and color scheme) from mathematician Oliver Byrne's The Elements of Euclid, a book' whose subtitle reads:"In which coloured diagrams and symbols are used instead of letters for the greater ease of learners."

Friedel explains why she drew on Byrne's Elements in a recent interview with ROCKPAPERINK:

    The books were published in 1847 but the colors and clean lines could be from today. Byrne also simplified Euclid's proofs by using color instead of letters and numbers. It's a more visual and intriguing way to describe the geometry. I love anything that simplifies. I find it very appealing!

    The colors came directly from Byrne's illustrations. The primary colors are really lovely, bright and very reminiscent of Mondrian. Byrne was definitely ahead of his time [Ed. Note: It's true; Byrne's illustrations are absolutely beautiful, and unmistakably modern]. He was a bit of an eccentric.

Below are a few examples of Friedel's sculptures juxtaposed with their 19th Century counterparts. As far as I can tell, the actual templates for these structures are not available for purchase (the process behind their creation actually looks rather involved); their likeness, however, is available in the form of some pretty snazzy business cards..., which you can pick up  here .

Deceased--Channa Horwitz

Channa Horwitz
May 21st 1932 to April 29th, 2013

"Channa Horwitz dies at 80; artist known for geometric paintings, drawings"

The L.A. native's approach was distinguished by its unusual combination of conceptual complexity and visual dynamism, even sensuality.

by

Holly Myers

May 3rd, 2013

Los Angeles Times

Channa Horwitz, an artist known for her dizzyingly intricate geometric drawings and paintings based on complex predetermined systems, died Monday of complications from Crohn's disease at St. John's Health Center in Santa Monica. She was 80.

In 1968, while still a student, Horwitz proposed a project for the Los Angeles County Museum of Art's seminal exhibition "Art and Technology" that would have involved collaborating with engineers to suspend eight large, free-floating Plexiglas beams within the space of a magnetic field, accompanied by eight beams of light that would fluctuate in intensity depending on the position of the beams.

The project was not accepted — curator Maurice Tuchman later stated, according to the artist, that he did not believe women should be allowed to work with such industrial elements — but the drawing that Horwitz produced to graph the sequences of the light beams' movements became the basis for a series that she would pursue throughout her life. She called it Sonakinatography.

As she wrote in the magazine Flash Art in 1976: "I have created a visual philosophy by working with deductive logic. I had a need to control and compose time as I had controlled and composed two-dimensional drawings and paintings. To do this, I chose a graph as the basis for the visual description of time. I gave the graph a value: one inch became one beat or pulse in time. Using this graph, I made compositions that depicted rhythm visually."

Horwitz's approach was distinguished by its unusual combination of conceptual complexity and visual dynamism, even sensuality. Times art critic Christopher Knight described her works in a 2012 review as "patterned Minimalist drawings that breathe, pulsate and visually warp in most un-Minimalist ways. One colored dot follows another on big gridded sheets of graph paper. Systemic logic, which sustains industrial and digital societies, visually pops and fizzes, becoming a bountiful ritual chant."

Horwitz was born Channa Helene Shapiro in Boyle Heights on May 21, 1932, the first of two daughters. Her father, Louis Shapiro, was a self-taught electrician who developed and manufactured a line of blow-dryers used for pet grooming, founding the company Edemco. She began drawing at a young age.

After marrying and while raising three children, she took classes at Art Center School in Los Angeles (now Art Center College of Design) and Cal State Northridge. In 1972 she received a bachelor's degree from CalArts, where she studied with the renowned performance artist Allen Kaprow, participating in many of his "happenings." She created a happening of her own in 1971, transforming a staircase at the school into a grid of numbered and colored squares corresponding to one of her Sonakinatography drawings, arranging for dancers to move between them in a series of eight choreographed motions — a form of cross-media translation that she undertook on numerous occasions thereafter, often in collaboration with other artists.

Though closely aligned with the work of conceptual and minimalist artists like Sol Lewitt, Mel Bochner and Agnes Martin, Horwitz worked in relative isolation for much of her career, without the public acclaim those artists enjoyed. That tide has shown signs of turning, however. She has had several shows in Germany in recent years, and was featured in the Hammer Museum's biennial Made in L.A. in 2012. In the last few months, she was awarded a Guggenheim Fellowship and invited to participate in this year's Venice Biennale. Her most recent show is up through June 8 at Francois Ghebaly Gallery in Culver City.

Anne Ellegood, senior curator at the Hammer Museum, met Horwitz in 2010 and was drawn to her work immediately. "I am impressed by her commitment to her practice over a very long period of time," she said, "often with little critical, curatorial or commercial recognition. I admire the fact that once she identified a working methodology that both provided her with structure and infinite space for exploration, she stuck with it. She never wavered from her commitment to her work."

Hammer Museum...

In the early 1960s Channa Horwitz (b. 1932 Los Angeles) made a discovery that was crucial for her artwork: by limiting her visual language to simple logical systems and sequences, she could open herself to innumerable possibilities. Her embrace of a rules-based conceptualism gave her an enormous sense of freedom, and she has been making geometric abstract drawings and paintings employing predetermined systems ever since. Seeking to capture time and motion—she dubbed her series of drawings initiated in the 1960s Sonakinatography to reflect her commitment to sona (sound) and kina (movement)—Horwitz lays down her drawings on graph paper, the lines and squares rendered in deep black or the colors of the spectrum to create oftentimes deliriously intricate patterns. The logic of her renderings is quickly usurped by a sense of awe about the great mysteries of life and the inevitable entwining of chance and structure that characterizes daily existence. For all their conceptual rigor, her remarkable drawings undulate with great rhythm and intensity. The selection for Made in L.A. includes examples from Horowitz’s series Sonakinatography, Canon, and Matrix, demonstrating the range of her remarkable output over the past five decades.

Epitrochoids and hypotrochoids=Spirograph

 

Brought to life by Kenner in the late 1960's.

Spirograph [Wikipedia]

Those triangles...the films of Bruce and Katharine Cornwell

Bruce and Katharine Cornwell are primarily known for a series of remarkable animated films on the subject of geometry. Created on the Tektronics 4051 Graphics Terminal, they are brilliant short films, tracing geometric shapes to intriguing music, including the memorable 'Bach meets Third Steam Jazz' musical score in ‘Congruent Triangles.’ Their work, distributed by the defunct International Film Bureau, is now out of distribution.

As a World War II WAC, Katharine Cornwell was involved in investigating the ENIAC computer for bomb survey analysis, which fueled her interest in mathematics. Bruce Cornwell did graphics work for a television station in Madison, WI, where he was also engaged with the local public radio station. The Cornwells were married in 1956. Bruce has stated that his interest in math films was influenced by his seeing Disney’s ‘Donald in Mathmagic Land,’ which prompted his comment "anyone with half a brain and one hand tied behind his back could make a better film."

Like many other makers of quality academic film, the Cornwells found it made better financial sense to have additional careers. Katharine became a consultant specializing in executive compensation, while Bruce taught at Brooklyn Polytechnic. They live in Brooklyn.

Filmography:

For Houghton Mifflin, the Cornwells, in conjunction with Duane W. Bailey, made a series called 'Calculus in Motion,' consisting of eight 3 minute, color, animated, silent 8mm loops. They were available as either Technicolor Magicartridges or Kodak Cassettes. They are: Functions, Limits, Derivatives, Concavity and Points of inflection, Rolle's Theorem and the Mean Value Theorem, The Definite Integral, The Fundamental Theorem, and Taylor Polynomials.

For the Mathematical Association Of America in conjunction with Stanford University, a number of films were produced at the Cornwells' studio for the MAA Calculus series, under various directors. We do not have the names of most of these films, but among them are:

Limit [1965]
Theorem of the Mean Policeman [1966]
Volume of a Solid of Revolution [1965]

Cornwell films distributed by the International Film Bureau [IFB]:

The London Of William Hogarth [1956]
Similar Triangles [1962]
How Do You Count? [1963]
Possibly So, Pythagoras! [1963]
Seven Bridges Of Koenigsberg [1965]
Newton's Equal Areas [1968]
Trio For Three Angles [1968]
Congruent Triangles [1976]
Journey To The Center Of A Triangle [1976]
Circle Circus [1979]
Dragon Fold - and Other Ways to Fill Space [1979]

Here are two examples...

Congruent Triangles

1976



Journey To The Center Of A Triangle

1976

Aesthetics/science

How ancient the relationship is. Such a relationship embraces epistemology, ontology, metaphysics, theology, mythology, and all the real sciences. It can be a codified or individual interpretation passed on by oral tradition, the written word, visual/auditory transmission, and all characteristics of science. Artistic representation of the cosmos can be primitive and crude or spirited in the latest aesthetic movement of sophistication. Aesthetics and the cosmos can be an intensely personal experience. It can be as simple as connecting the stars and recognizing the constellations or a pristine mathematical formula.

I do not intend to strictly limit the aesthetic experience to mathematical or physical explanations/representations but to include the entire visual and auditory spectrum of experiences. Yes, it certainly appears the universe [neutral] to be a "mess", but it is a fine specimen of specific laws of physics--all interacting in the most minute manner. Historical mistakes as you mentioned are true, but day to day advances dispel old notions and revitalized by new notions of a broader sphere of concern. If man lasts long enough, the "mess" may not be so "messy". I really don't want to get into the technical theories and movements of aesthetics, but it is evident that the beauty of the universe is adequately manifested in the visual and auditory--outside Earth and on Earth.

Beyond the potential aesthetics of the mathematics and physics of the universe, there is the problem with visual representations. The question being, how true to reality are those photographs that we see. In the infancy of astronomy, the images were taken by long exposure on photographic glass plates whose emulsion of sensitivity was not necessarily panchromatic. Many of the prints were enhanced in density, contrast, and color. Sometimes for illustrative purposes, the print was at the mercy of many artists. Today we have computer enhanced images. So for those that do experience an aesthetic experience of the cosmos through visual representation, what are they really experiencing? Does it have an ultimate effect on the experiences? How intense is that "pink"? Is it too "dark" or too "light"? Humm...a matter of personal aesthetics I guess. I don't have a problem with what I see for it is pleasing to the eyes--soothing like chocolate ice cream.

Defining art is probably limited to movements within a period of history whereas aesthetics is a bit more elusive. The residue from presentation, discussion, and analysis of materials presented in an aesthetics course was that "art" was a matter of "taste" and was punctuated by a quip from a student from the back of the room: "Ya, good taste and bad taste"--back to square one. The point is, is that the aesthetics is unique and personal.

Do you find experience between aesthetics and the cosmos that have added to your "being" and provided substantial meaning of living your life and understanding your position in the universe? Is there an ultimate art form or is multiplicity preferred?

Articles:

"Aesthetics and Motivations in Arts and Science"

"Chen Ning Yang on Aesthetics and Physics"

"Dying star creates fantasy-like sculpture of gas and dust"

"The Golden Ratio And Aesthetics"

"Whither Santayana's Aesthetics"


Fractals are pretty cool--a marriage of mathematics and geometry and applied to worldly and cosmic experiences.

"Fractal"

"Fractal Geometry"

The Fractal Geometry of Nature by, Benoit B. Mandelbrot

ISBN: 0716711869


Websites:

Essays by F. David Peat

EXPLORING THE ELECTROMAGNETIC SPECTRUM


Images:

Aesthetics does abound in the universe. Granted the following are abstract and highly geometric, but nevertheless for some provide an aesthetic experience. The photos are from the Mars Orbiter Camera (MOC) on the Mars Global Surveyor spacecraft. [Mars Global Surveyor was launched in November 1996 and has been in the Mars orbit since September 1997. It began its primary mapping mission on March 8th, 1999].

"Carbon Dioxide Landscape"

"Dark Mesas of Aram Chao"

"Dunes in Noachis"

"Exhumed Craters"

"Small Dunes in Hellas"

"South Polar Layers"

"Sulci Gordii"


Archived photos


Artists:

Bathsheba Grossman:

Home Page

"gallery: bathsheba grossman"

Carlo H. Séquin:

"SCULPTURE DESIGNS and MATH MODELS"

Kaz Maslanka:

Blog