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• W826121872 abstract "Although I am a non-mathematician my artwork originates with the aesthetic intuition of geometric form. It bears a relation to the natural world and the mathematical coherence found in natural forms. When we look at nature we see patterns. We discover the rhythms of life and see motion in form. Patterns are my metaphor for the structure and hidden formal order of our natural world As a mosaic artist I make tessellated sculptures and approach the concept of infinit¥ through my art. I construct my universe through surface division and hyperbolic geometry. The structure and patterns of my hyperbolic sculptures may be analyzed mathematically. Yet, as visual art objects they stand on their own merit and can be appreciated by general audiences. 1. Description of Hyperbolic Sculptures 1.1 Infinity. The notion of infinity has fascinated me. It suggests timelessness. In my hyperbolic sculptures infinity is metaphorically represented by repeating patterns and regular tessellations, which decrease. in size at the bounding edge. In hyperbolic geometry the concept of infinite smallness is contained within the finite circle. There is a reduction in size of the arcs from the larger center to the smaller arc leading from the center to the outer edge. The idea is that of constant diminution. The' distance is not measured uniformly over the whole ,unit disc and therefore the figures are said to be congruent. The interior arcs mark an angle and cross each other in ever-smaller distances. [1] On the hyperbolic plane the arcs of the circles cut the circle and are orthogonal to the bounding edge. They are perpendicular to the unit disc including diameters. Its circumference represents infinity, beyond that is absolute nothingness. [2] The circles have a constant curvature and are not concentric. The smaller. their diameter, the closer their centers are to the bounding rim.disc. They suggest a sequence towards the infinitesimal at the circumference. The curvature of the 3D-mosaic sculpture is hyperbolic (meaning concave) and consists of a tiled pattern surface division. (Figure 1, Figure 2) 1.2 Time. The concept of time is represented metaphorically. It is implicit in the subtractive process of cutting away to obtain modules and then piecing these modules together to form a surface pattem. The mosaic surface is composed of units that combine to resemble pixels on a computer screen. It is a part to whole relationship. One becomes aware of the energy and time expended in cutting and piecing together the tiling pattern from point to segment, to shape. The" @default.
• W826121872 created "2016-06-24" @default.
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• W826121872 date "2003-01-01" @default.
• W826121872 modified "2023-09-27" @default.
• W826121872 title "Geometric Mosaic Tiling on Hyperbolic Sculptures" @default.
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