Paralel Çizgilerden Hiperuzaya Geometrinin Öyküsü

Öklid'in Penceresi

Leonard Mlodinow

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Riermann's work on elliptic spaces had an equally profound impact on the world of mathematics. The need to alter postulates other than the parallel postulate was like the fraying of the strands in a rope. Soon, the rope snapped. Only then did mathematicians realize that hanging from it had been not only geometry, but all of mathematics.
That a space could "curve" yet not be curving into anything was a concept that would later prove necessary in Einstein's general theory of relativity. After all, since we cannot step out of our universe to gaze down at our limited three-dimensional realm, only this sort of theorem can give us hope of determining the curvature of our own space.
Reklam
In Critique of Pure Reason, Kant calls Euclidean space "an inevitable necessity of thought." Gauss did not dismiss Kant's work out of hand. He read it first, then dismissed it. In fact, Gauss is said to have read Critique of Pure Reason five times attempting to understand it.
Today, scholars write that "Descartes's mathematical laziness is notorious," but Descartes was not ashamed to be seeking to find an underlying system that would make proving geometric theorems less taxing. That's how he could sleep in every day and still have more impact than any of those more industrious scholars who have criticized him.
Charlemagne was equally proactive in taking care of himself. It is an emblem of the times that, in his quest for long life, he did not employ a bevy of alchemists or gather around him an academy of doctors. Instead, he invented a kind of theological factory, an industry of clergy devoted to his health. In one monastery alone, Charlemagne had 300 monks and 100 clerks praying continuously for him, in three shifts, around the clock. He died anyway.
Taxes were perhaps the first imperative for the development of geometry, for although in theory the Pharaoh owned all land and possessions, in reality temples and even private individuals owned real estate. The government assessed land taxes based on the height of the year's flood and the surface area of the holdings.
Reklam
137 öğeden 141 ile 137 arasındakiler gösteriliyor.