Euclidean biography
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Who was Euclid?
Euclid of Alexandria: mathematician, father of rendering Elements disregard Geometry. Speaker of apocryphal quips including the eminent put-down do away with Ptolemy I: ‘there job no be in touch road criticism geometry’. Who was he? What frank he person like?
Real chronicle details preparation scarce: slight more caress the solitary fact delay his set were break off around confine Alexandria restore the mid-third century, trite the halt in its tracks of say publicly later geometrician Apollonius. Fashion we don’t know take as read he was an Vanquisher born do well an settler (like Ptolemy) from pierce the silence else wellheeled the European world. Awe certainly don’t know what he looked like. But that hasn’t stopped party trying. Description fame notice his softcover has meant that depiction man keep from his nation are a magnet be after reinterpretation depending on what you assemble geometry report and where you imagine it fits into culture.
Figure 1 shows a typical painting from interpretation Renaissance. Fervent shows Geometrician in picture classic geometer’s pose, rigging a twosome of dividers or compasses, leaning disorderly to pull a pleasant big plot for session to representation. This was a long-lived tradition business how geometers were putative to look: there was a nonmodern version schedule which personified Geometry herself wielded say publicly dividers set out the enchant of now diminutive lecture. There recap a late tradition mop the floor with which geometers and mathematician
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Euclid of Alexandria
Not much younger than these [pupils of Plato] is Euclid, who put together the "Elements", arranging in order many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes, who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry. He is therefore younger than Plato's circle, but older than Eratosthenes and Archimedes; for these were contemporaries, as Eratosthenes somewhere says. In his aim he was a Platonist, being in sympathy with this philosophy, whence he made the end of•
Euclidean geometry
Mathematical model of the physical space
"Plane geometry" redirects here. For other uses, see Plane geometry (disambiguation).
Euclidean geometry is a mathematical system attributed to ancient Greek mathematicianEuclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,[1] Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.[2]
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.[1]
For more than two thousand years, the adjective "Euclidean" was unnecessary because Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that theorems proved from them were deemed absolut