Word: euclidean
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...hold that the perfection of form and beauty is contained in the sum of all men." He approached the problems of expressing that perfection, even down to the microscopic depiction of a wart. In his Four Books on Human Proportion, he analyzed anatomy with all the rigor of Euclidean geometry. Yet with the pricking of his pens and burins, he tried to capture all the sensual volumes that the Italian sculptors revealed in marble with the deft chipping of their chisels...
...correct. "Fortunately, scientific endeavor does not have to be perfect to yield results. The magnificent structure of dynamics was based on a differential calculus that was, logically, full of holes." Kepler's laws explaining planetary motion were based on calculations now shown to be mere approximations. Even the Euclidean underpinnings of Newton's iron law of gravitation have become only one of the possible systems of geometry...
Mathematics had been partially unshackled from the physical world by the discovery of non-Euclidean geometrics in the nineteenth century, but the publication of Principia Mathematica in 1908 burst the chains. This three-volume monument by Bertrand Russell and Alfred North Whitehead expressed the fundamental concepts of mathematics in terms of still simpler concepts of logic, and showed that mathematics may be viewed as a game of manipulating symbols according to rules. Since mathematicians can adopt any rules they want, the truths proved in mathematics can have no necessary connection with the world outside of mathematics...
Sooty Icing. "To be stopped by a frame's edge was intolerable," says Still in characteristically irascible terms. "A Euclidean prison had to be annihilated." He does not frame his canvases because they do not end where his paint does. Some of his best adventures in paint occur close to the edges, where colorful jigsaw puzzle pieces are chopped off as if they had turned the corner into a new dimension. Other oils seem to spread relentlessly outward and upward like aerial photography of an erupting volcanic landscape...
...nowhere else. Clifford emerges as a superb mathematician even in the company of the nineteenth-century geniuses. He was one of the last to work with equal success on several mathematical fronts, Poincare being perhaps the last who managed it. Clifford spun out the consequences of the new non-Euclidean geometries and of Abelian function theory; he also gripped the prickly legacy of Kantian skepticism and took to the lecture stand with clear thinking on different epistemological questions...