Art Works by Stephen J Luecking
Bridges Mathematics and the Arts
The sculptor creates spherical polyhedrons whose interiors are hollowed to form an alternate poly... more The sculptor creates spherical polyhedrons whose interiors are hollowed to form an alternate polyhedron nested within the larger external polyhedron. The polyhedrons are all variations on Platonic, Archimedean,
Catalan and Kepler-Poinsot solids. Sculptures comprise the repetition of a single, block-like module whose simple geometry belies the complexity of the finished work. Environmental versions of this series use blocks
that may serve as seating and contain hollows in which children may nestle
2011 Axis Mundi belongs to a category of sun dials known as scaphes. Scaphe dials take their name... more 2011 Axis Mundi belongs to a category of sun dials known as scaphes. Scaphe dials take their name from the Greek word for ship-scaphos. Typically these dials are shallow bowls, unlike hemispheriums, which possess the full depth of a half sphere. The scaphe dial functions much like a cross between a horizontal dial and a hemispherium. Like the hemispherium its bowl shape reflects the arc of the heavens and like the horizontal dial its lines take the form of elegant curves. Cast in the image of a vessel, the scaphe dial suggests a receptacle for catching and gathering the light.
Portfolio of early sculpture.
Papers by Stephen J Luecking
The architect Antonio Gaudi created visionary imagery from often profoundly mathematical forms. A... more The architect Antonio Gaudi created visionary imagery from often profoundly mathematical forms. A sculpture in the garden of his home in Parc Guell ,Barcelona, embeds the Platonic solids and uses these to represent the heavens in the same cosmographic spirit as that of Johannes Kepler in his Harmonices Mundi.
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, 2013
As a group, the artists educated near the turn of the 19 th and 20 th centuries possessed greater... more As a group, the artists educated near the turn of the 19 th and 20 th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then emphasized the use of manipulatives, i.e., visual and interactive aids thought to better fix the student's acquisition of mathematical skills. This visual training in mathematics significantly affected the early development of abstraction in art. This paper presents examples of this visual mathematics education and samples its effects on the development of abstract art in the first decades of the 20th century.
Computer modeling permits the creation and editing of mathematical surfaces with only an intuitiv... more Computer modeling permits the creation and editing of mathematical surfaces with only an intuitive understanding of such forms. B-splines used in most commercial modeling packages permit the approximation of a wide variety of mathematical surfaces. Such programs may contain tools for aiding in the production of these surfaces as physical sculptures. We outline some techniques for non-mathematical designers and sculptors to produce these objects with conventional modeling.
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, 2012
Periodic minimal surfaces are doubly curved and so problematic to create from paper, a material m... more Periodic minimal surfaces are doubly curved and so problematic to create from paper, a material more amenable to developable surfaces. However, breaking the curvature into polygonal facets can visually approximate these surfaces. Furthermore, repeating and alternately inverting a single fundamental patch will tile periodic surfaces. This patch may be triangulated and unfolded into patterns for the modeler to print and fold into a number of non-planar tiles for constructing the surface. In the case of a lined periodic minimal surface, like the Schwarz D-Surface, the straight lines crisscrossing the surfaces define the boundaries of the fundamental patch as non-planar polygons. As demonstrated in this paper, such saddle polygons are relatively simple to fabricate and then to join into a representation of the surface.
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture, 2011
The circadian and annual geometry of the sun's rays will simplify into what is termed the shadow ... more The circadian and annual geometry of the sun's rays will simplify into what is termed the shadow planes model for sundial projection. The author employs this model within a 3-D modeling program to design a series of non-traditional sundials derived from toroidal surfaces. These include the standard torus, as well as one eccentric torus: the horn cyclide.
Journal of humanistic mathematics, Jul 1, 2019
As a group, the artists educated near the turn of the 19 th and 20 th centuries possessed greater... more As a group, the artists educated near the turn of the 19 th and 20 th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then stressed the use of manipulatives, i.e., visual and interactive aids thought to better fix the student's acquisition of mathematical skills. This visual training, especially in geometry, significantly affected the early development of abstraction in art. This paper presents examples of this visual mathematics education and samples its effects on the development of abstract art in the first decades of the 20 th century.
Journal of Mathematics and the Arts, Jun 1, 2010
The author offers the geometric and aesthetic rationale as to why Russian artist Kasimir Malevich... more The author offers the geometric and aesthetic rationale as to why Russian artist Kasimir Malevich subtitled five of his paintings as ‘Colored Masses in the Fourth Dimension’, even though they seemingly do not differ significantly from his other works with titles such as ‘Self Portrait in Two Dimensions’. In explaining Malevich's titling, art historians have, in the main, credited the influence of theosophical concepts of a fourth dimension as proffered by Ouspensky on the artist's desire to project a ‘feeling’ of higher dimension. The author asserts instead that Malevich's paintings could be viewed as actual visualizations of a 4-D geometry and that his notions about geometry in art rely far more on Nikolai Lobachevsky's concept of pangeometry.
Math Horizons, Sep 1, 2017
Bridges: Mathematical Connections in Art, Music, and Science, 2004
Drawing on his own early experiences as a surveyor the author presents an introduction to the his... more Drawing on his own early experiences as a surveyor the author presents an introduction to the history, principles and methods of ancient rope pulling, Le., surveying geometry, as manifested in Megalithic monuments. Concentrating on some likely field teclmiques dating back to Neolithic builders, this paper assesses similarities and contrasts between the focus of class~c geometry on axiomatic proofs and compass and straightedge construction and the propensity of rope pulling toward canonical principles of mensuration and mechanical construction.
3D or CAD modeling programs can provide tools for the beginner to quickly create mathematical mod... more 3D or CAD modeling programs can provide tools for the beginner to quickly create mathematical models known as sliceforms, or, in the terminology of computer graphics, raster surfaces. This tutorial and workshop provides the novice with the tools and procedures for modeling and physically constructing these models using their PC, a printer, craft knife, glue and paperboard.
Journal of Mathematics and the Arts, Sep 1, 2011
tire after the first five or six. I found Chapter 3: ‘Applications of the Pythagorean Theorem’ an... more tire after the first five or six. I found Chapter 3: ‘Applications of the Pythagorean Theorem’ and Chapter 5: ‘The Pythagorean Means’ to be the most interesting, and Chapter 4 ‘Pythagorean Triples and Their Properties’ the least interesting. The sections on ‘Constructing Irrational-Number Lengths’ and ‘The Lunes and the Triangle’ in Chapter 3 were particularly fascinating. The first, because, as the author notes, ‘The Pythagorean Theorem led ancient mathematicians to a dilemma, namely, irrational numbers . . .’ and the second, because a lune is a crescent formed by two circular arcs, which necessarily involves when finding areas, but whose area can be associated with the area of rectangles using the Pythagorean Theorem. The applications to physics of the three Pythagorean means discussed in Chapter 5 are, of course, particularly interesting to me. I do have a quibble with the Afterword, titled, ‘About the Mathematics Work That Led to the 1985 Nobel Prize in Chemistry: Thanks Ultimately to Pythagoras’ contributed by Dr. Herbert A. Hauptman. I found it preachy and tenuously connected to the subject and tone of the rest of the book. This three page essay could have been easily omitted. To conclude, for the most part, I found the book delightful and worth reading, but would caution that it is neither a mathematics book for the artist (too much technical detail) nor is it an art/music book for the mathematically inclined (too little material and not nearly technical enough). This is a book about the Pythagorean Theorem. If that is where your interests lie it is a good read, but if your interests lie solely in mathematics in the arts, then in spite of the two dedicated chapters your best bet is to skip it because I fear you will be disappointed.
Compendium/North American Sundial Society
This paper considers a space based on a mathematical concept called GridField Geometry; with an e... more This paper considers a space based on a mathematical concept called GridField Geometry; with an equivalent version called Polar GridField Geometry. The two geometries are compared in their respective constructions. In the process, a circular curved wave form is introduced in the maintenance of gridfield space symmetry — all defined and illustrated by the inclusion of specific examples.
Golden Star System is an experimental structural system which uses biomimicary to bring together ... more Golden Star System is an experimental structural system which uses biomimicary to bring together the geometric configuration of the Koch Star, the Golden Mean and the rotation of DNA around its centerline. Creating physical models of Golden Star System (figure 1) appeared to be a challenge. This paper introduces a parametric application to generate Golden Star System around a desired curve in Rhino-Grasshopper and presents a detailed process to make the model ready for 3d printing. Figure 1: Plotted Models of Golden Star System This project focused on an experimental system called the Golden Star System. It involves the nexus of the Golden Mean, the Koch Star (Snowflake) and the rotation of DNA around the center of its axis. The hypothesis associated with this design is that the nexus of these components will improve structural load carrying capacity in dynamic loading situations. Tests are currently being planned. The Golden Mean ratio has been studied for millennia and it has been...
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Art Works by Stephen J Luecking
Catalan and Kepler-Poinsot solids. Sculptures comprise the repetition of a single, block-like module whose simple geometry belies the complexity of the finished work. Environmental versions of this series use blocks
that may serve as seating and contain hollows in which children may nestle
Papers by Stephen J Luecking
Catalan and Kepler-Poinsot solids. Sculptures comprise the repetition of a single, block-like module whose simple geometry belies the complexity of the finished work. Environmental versions of this series use blocks
that may serve as seating and contain hollows in which children may nestle