Ellipse

Algebraic geometry and the geometry of growth appear to have some things in common. We can identify curves in living forms by those that pertain to the realm of pure mathematics--the parabola, the hyperbola, the ellipse, the spiral, and so forth. But we have to take into account another important factor: the role of nature as sculptor. The curve of the seashell or crab shell--of each seashell and crab shell--is the result of the give and take between biological geometry (replication and the structure of heredity via the DNA helix) and the environment; That is, forces working from within against forces, pressures from without; one kind of physical substance or system against another. It would be difficult to think of living form, except submicroscopic forms (viruses and the like), perhaps, that would serve as a model of mathematical perfection throughout. The surface configuration of most forms would reveal curves of far greater variance, having been sculpted by erosion, by action of wind and water by a process of subtraction in the case of earth formations. Or an erosion pattern would have been built in by nature over perhaps millions of years, as in the forms of most aquatic creatures--fish, shellfish, seals, squids, and the like, their "pre-eroded" surfaces having been designed by nature so as to offer the least resistance to the force and density of water.

These curves--the serpentine lines of flow, the analytic curves or conic sections (hyperbola, parabola, ellipse), the logarithmic spiral, catenary curves, flat curves and banking curves--are the repertory of curves with which the artist-designer works, consciously or not. We discover by analysis that lines and form profiles of particular beauty and strength are those that reveal considerable contrast in the kinds of curves that follow one another, that flow in and out of one another. They consist of deep or slow curves (ellipses or parabolas) and shallow or fast curves (hyperbolas), long and short curves. They flow into one another with an inevitability and naturalness usually absent from the pure curves of mathematics, especially that of the circle.

[Harlan, Calvin. Vision & Invention, An Introduction to Art Fundamentals. Englewood Cliffs, NJ: Prentice-Hall, 1986.]

R  E  F  E  R  E  N  C  E  S 

Ellipsoid n [1721] a surface all plane sections which are elipses or circles

Elliptical adj [GK elleiptikos defective, marked by ellipsis, fr. elleipein] [1656] 1: of, relating to, or shaped like an ellipse 2a: of, relating to, or marked by ellipsis or an ellipsis b [1]: of, relating to, or marked by extreme economy of speech or writing [2]: of or relating to deliberate obscurity [as of literary or conversational style]

Elliptical galaxy n [1948]: a galaxy that has a generally eliptical space, and that has no apparent internal structure or spiral arms -called also elliptical; compare Spiral Galaxy

Ellipticity n [1753]: deviation of an elipse or a spheroid from the form of a circle or a sphere