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Geometri
A couple decades after the discovery of hyperbolic space, another type of non-Euclidean space was discovered: elliptic space. Elliptic space is the space you get if you assume the other violation of the parallel postulate: that no parallel lines exist (i.e., all lines in the plane must intersect).
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.
To understand how difficult a leap it was to contradict Euclid, one has to appreciate how deeply entrenched was his description of space. Already in his own, ancient time, Euclid's Elements was a classic. It was a key work in the intellectual revival of the Middle Ages. It was one of the first books printed after the invention of the printing press in 1454, and from 1533 until the eighteenth century it was the only one of all the Greek works to exist as a printed text in the original language. Until the nineteenth century, every work of architecture, the composition in every drawing and every painting, every theory and every equation employed in science were all inherently Euclidean.
Descartes: A circle is all x and y satisfying x2+y2=r2 for some constant number r.
Descartes translated space into numbers, and, more importantly, used his translation to phrase geometry in terms of algebra.
While mathematics and science in the West had withered, the Islamic world had retained faithful versions of many Greek works, including Euclid and Ptolemy. Though they, too, made little progress in abstract mathematics, they made significant advances in calculational methods. Propelled by the religious needs of time and calendar, they had developed all six trigonometric functions, and perfected the astrolabe, a hand-held instrument allowing accurate observation of the altitude of a star or planet.
Thales also addressed the concept of physical space. He recognized that all matter in the world, despite its vast variety, must be intrinsically the same stuff. In the absence of any evidence, it was an amazing leap of intuition. The next natural question was, of course, what is this fundamental stuff? Here, living in a city of harbors, intuition led Thales to choose water.
Ironically, Thales' student and fellow Milesian, Anaximander, came by a comparable leap of intuition to the idea of evolution, and for the lower animal from which humans evolved, chose the fish.
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.
Thanks to Descartes, geometric concepts such as coordinates and graphs, sines and cosines, vectors and tensors, angles and curvature, appear in every context of physics from solid state electronics to the large-scale structure of space-time.
Geometri, barutun icat edilmesinin bir sonucu olarak da yeni önem kazandı: Artık tahkimatların (fortifications) düz hatta uçan top güllelerine karşı koyacak şekilde inşa edilmesi şarttı. Fransızların trace italienne ve Amerika kolonicilerinin "yıldız kale" adını verdiği tabyalar, 15. yüzyıl sonlarından itibaren sadece Avrupa'da değil, Asya'da ve Yenidünya'da, kısacası topların kullanıldığı her yerde inşa edilmeye başlandı.
Yeni tahkimat bilimi, aralarında Galileo'nun da bulunduğu matematikçiler tarafından öğretildi.
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Geometri ile ünlü olmak
Oldukça sivir uca sahip pergel kullanacaksınız. Üzerinde çalıştığınız kağıdın eski bir telefon defteri veya kalın bir mukavva üzerine olması gerekir. Eğer bunların üzerinde çalışmazsanız, pergelin sivri ucu yemek masanını çizecektir. O zaman ünlü olmak için bir sebebiniz daha olur. Dünyanın en sinirli anne ve babasına sahip olursunuz!
Sayfa 117Kitabı okudu
