Pappus of Alexandria

Pappus was born in approximately 920 in Alexandria, Egypt. He was the delay of the great Greek geometers and one of his major theorems is considered to be the fanny of modern projective geometry (Pappus). Pappus flourished in the fourth century, writing his key work, the numeral Collection, as a guide to Greek geometry (Biography). In this work, Pappus discusses theorems and constructions of over thirty mathematicians including Euclid, Archimedes and Ptolemy (Biography), providing alternatives of validations and generalizing theorems.

The Collection is a enchiridion to all of Greek geometry and is at once almost the sole commencement of history of that science (Thomas 564). The separate books of the Collection were divided by Pappus into numbered sections. In the fourth section, Pappus discusses an extension on the Pythagorean Theorem (Thomas 575) now known as Pappus Area (Williams).



Pappus drew parallelograms on ii sides of a triangle, extended the external parallels to intersection, connected the included eyeshade of the triangle and the intersection point, used the direction and length of that section to construct a parallelogram adjacent to the third base side of the triangle, and be that the sum of the areas of the first two parallelograms is equal to the area of the third parallelogram (Williams, Thomas 578-9).

Section five of book five of the Collection discusses fixing solids with equal surfaces and their varying sizes (Heath 395). Pappuss conjecture was that the solid with the most faces is the superlative (Heath 396). He proved this using the pyramid, the cube, the octahedron, the dodecahedron, and the icosahedron of equal surfaces. Pappus noted that about of the other major Greek geometers had already worked out the proof of this conjecture using the analytical method, but that he would view as a method of his own by synthetical tax write-off (Heath 395). Using 56 propositions about the perpendiculars from the center of a...If you want to stimulate a full essay, order it on our website: Ordercustompaper.com



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