EUCLIDIAN SPACE: HOW TO UNDERSTAND EUCLIDIAN NUMBERS

Even the Non-Euclidians Owe Euclid: The King of Infinite Space: Euclid and His Elements by David Berlinski.
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Booklist: Starred Review “As dazzling as first love” is how Bertrand Russell described his initial encounter with Euclid. As a mathematician who understands what Russell felt, Berlinski guides his readers through the intellectual wonderland that the ancient Greek geometer created in his epoch-making treatise, the Elements. In writing at once geometrically precise and disarmingly conversational, Berlinski explores the imposing edifice that Euclid erected on a foundation of just five deceptively simple axioms.

Each of these axioms receives careful scrutiny, allowing readers to share in the excitement of mapping out the dimensions of an audacious new human enterprise, inscribing sharp boundaries around key concepts yet opening onto the infinite.

Only an author who thinks both mathematically and philosophically could infer—as Berlinski does—the intellectual and even moral substance of the mental perspective that Euclid unfolds. Readers thus come to realize how Euclid’s pioneering thought made possible the rigor of a mathematical proof—and the discipline of a mathematical life.

Even in the revolutionary modern theorizing of non-Euclidian geometers such as Lobachevsky, Bolyai, and Poincaré, readers will discern Euclid’s abiding influence as a visionary who glimpsed the mathematical unities hidden beneath chaotic appearances.

​An impressively concise distillation of the wizardry that transforms points, lines, and planes into sheer genius. --Bryce Christensen --This text refers to the Audio CD edition."