"The circle in the moon which divides the dark and the
bright portions is least when the cone comprehending both the sun and the moon
has its vertex at our eye."
"Two equal spheres are comprehended by one and the same
cylinder, and two unequal spheres by one and the same cone which has its vertex
in the direction of the lesser sphere; and the straight line drawn through the
centres of the spheres is at right angles to each of the circles in which the
surface of the cylinder, or of the cone, touches the spheres." (Aristarchus of
Samos, "On the Sizes and Distances of the Sun and the Moon", cca. 250 BC)
"Architecture is the masterly, correct and magnificent play of masses brought together in light. Our eyes are made to see forms in light; light and shade reveal these forms; cubes, cones, spheres, cylinders or pyramids are the great primary forms which light reveals to advantage; the image of these is distinct and tangible within us without ambiguity. It is for this reason that these are beautiful forms, the most beautiful forms. Everybody is agreed to that, the child, the savage and the metaphysician." (Charles-Edouard Jeanneret [Le Corbusier], "Towards a New Architecture", 1923)
"Two kinds of sets turn up in geometry. First of all, in geometry we ordinarily talk about the properties of some set of geometric figures. For example, the theorem stating that the diagonals of a parallelogram bisect each other relates to the set of all parallelograms. Secondly, the geometric figures are themselves sets composed of the points occurring within them. We can therefore speak of the set of all points contained within a given circle, of the set of all points within a given cone, etc."
"What is the shape of space? Is it flat, or is it bent? Is
it nicely laid out, or is it warped and shrunken? Is it finite, or is it
infinite? Which of the following does space resemble more: (a) a sheet of
paper, (b) an endless desert, (c) a soap bubble, (d) a doughnut, (e) an Escher
drawing, (f) an ice cream cone, (g) the branches of a tree, or (h) a human
body?" (Rudy Rucker, "The Fourth Dimension: Toward a Geometry of Higher Reality", 1984)
"Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in straight line. [...] Nature exhibits not simply a higher degree but an altogether different level of complexity." (Benoît B Mandelbrot, 1984)
"To a mathematician, an object possesses symmetry if it retains its form after some transformation. A circle, for example, looks the same after any rotation; so a mathematician says that a circle is symmetric, even though a circle is not really a pattern in the conventional sense - something made up from separate, identical bits. Indeed the mathematician generalizes, saying that any object that retains its form when rotated - such as a cylinder, a cone, or a pot thrown on a potter's wheel - has circular symmetry." (Ian Stewart & Martin Golubitsky,"Fearful Symmetry: Is God a Geometer?", 1992)
"Topology is a geometry in which all lengths, angles, and areas can be distorted at will. Thus a triangle can be continuously transformed into a rectangle, the rectangle into a square, the square into a circle, and so on. Similarly, a cube can be transformed into a cylinder, the cylinder into a cone, the cone into a sphere. Because of these continuous transformations, topology is known popularly as 'rubber sheet geometry'. All figures that can be transformed into each other by continuous bending, stretching, and twisting are called 'topologically equivalent'." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)
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