The views and opinions expressed in this page are strictly those of the page author. Pappus article about pappus by the free dictionary. Introduction to the finite geometry of pappus youtube. They have appeared also recently in commutative algebra in connection with the containment problem for symbolic and. Relationship with pappus ringel 7 showed that any stretched version of the projective pseudoline arrangement rin9 shown in a would contradict pappus theorem. Index of the propositions used in book 7 of pappus collection. Theorems of pappus on surfaces of revolution wolfram. Pappuss theorem 1 3 2 4 5 6 9 8 7 the collinearity of 123, 456, 159, 168, 249, 267, 348, 357 imples the collineartity of 7,8,9. The following suggestions are leading to a relationship in plane geometry attributed to pappus. Index of the propositions used in book 7 of pappus collection ken saito this article was originally printed in jinbun kenkyu. Ad 200350 greek mathematician, astronomer, and geographer whose chief importance lies in his commentaries on the mathematical work of his predecessors. The first theorem of pappus states that the surface area s of a surface of revolution generated by the.
Partially supported by the projects mtm201021740c0202, e15 grupo. The theorem, which can also be thought of as a generalization of the pythagorean theorem, is named after the greek mathematician pappus of alexandria 4th century ad, who discovered it. Let ct be a curve in a space form mn of sectional curvature. Prove pappuss centroid theorems without calculus physics. If the vertices of a triangle are projected onto a given line, the perpendiculars from the projections to the corresponding sidelines of the triangle intersect at one point, the orthopole of the line with respect to the triangle. In mathematics, pappuss centroid theorem is either of two related theorems dealing with the. Finding surface area and volume of a sphere using only pappus. A bridge between algebra and geometry article pdf available in the american mathematical monthly 1096 june 2002 with 2,548 reads how we measure reads. Pappus theorem on volumes department of mathematics. Pappus was a master of the elegant theorem, as evidenced by the countless theorems of pappus found in the mathematical literature, and it comes as no surprise that he was successful in finding an ingenious way of proving the truth of what he called an ancient theorem. Greek mathematician of the second half of the third century. Areas of surfaces of revolution, pappuss theorems iitk.
The first two books were devoted to arithmetic, and the third through fifth books deal primarily with geometry. Top 10 tips for getting started with prezi video in your online classroom. Pdf a synthetic proof of pappus theorem in tarskis. It gives how sequence of instructions or data will be executed. Nov 14, 2016 in the present work we study parameter spaces of two line point configurations introduced by boroczky. How are these theorems proved without using calculus. Michael j flynn classified computers on the basis of multiplicity of instruction stream and data streams in a computer system. In mathematics, pappus s centroid theorem also known as the guldinus theorem, pappus guldinus theorem or pappus s theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. Although pappus of alexandria is known mainly for his very informed commentaries on the work of earlier greek geometers, he also proved some original. In ancient analysis, the geometer assumes what is to be done, and then uses. Pappus centroid theorem pdf pappus centroid theorem pdf pappus centroid theorem pdf download. In partial fulfillment of the requirements for the degree of.
A synthetic proof of pappus theorem in tarskis geometry halinria. Let s be the surface generated by revolving this curve about the xaxis. A generalization of pythagorass theorem and application to explanations of variance contributions in linear models james e. A simple proof for the theorems of pascal and pappus. In this paper, we report on the formalization of a synthetic proof of pappus theorem. The hutchinson dictionary of scientific biography helicon publishing, 2004 pappus of alexandria lived c. The euclidean pseudoline arrangement b is derived from a by taking line 0 as the line at in. Areas of surfaces of revolution, pappuss theorems let f.
The role of frenet motion in pappus type theorems m. Finding surface area and volume of a sphere using only pappus centroid theorem. Atul dixit and darij grinberg, orthopoles and the pappus theorem, forum geometricorum, 4 2004 5359. The first theorem of pappus states that the surface area a of a surface of revolution obtained by rotating a plane curve c about a nonintersecting axis which lies in. Pappus of alexandria, mathematical collection iv 2125, pp. Suppose we have three points on one line represented by vectors a, b, and c and three points on a nonparallel line represented by vectors d, e, and f. Consider the curve c given by the graph of the function f. A synthetic proof of pappus theorem in tarskis geometry. Systems engineering project overview lessontitle presentaonid project1 targetcourse 645.
A synthetic proof of pappus theorem in tarskis geometry gabriel braun julien narboux the date of receipt and acceptance should be inserted later abstract in this paper, we report on the formalization of a synthetic proof of pappus theorem. Jul 18, 2015 use the theorem of pappus to determine the surface area of this region as well. So i ask if there are pappus like theorems which one could apply for three dimensional bodies. What links here related changes upload file special pages permanent link page. Descartestreatmentofthepappuslocus theorem an example of ancient analysis denitions. Pappuss centroid theorem volume by george kotzabassis on prezi. Fast and provable algorithms for learning twolayer. Pappus centroid theorem pdf the surface of revolution generated by a smooth curve. The theorems are attributed to pappus of alexandria and paul guldin. Jul 07, 2016 pappus s centroid theorems were discovered 17 centuries ago, when calculus wasnt invented yet.
Pappus s first theorem states that the area of a surface generated by rotating a figure about an external axis a distance from its centroid equals the product of the arc length of the generating figure and the distance traversed by. Pappus was the author of mathematical collections in eight books, only the last six of which are extant. Sep 12, 2015 for the love of physics walter lewin may 16, 2011 duration. Century ad proposed two theorems for determining the area and volume of surfaces of revolution. Let r be the triangular region bounded by the line y x, the xaxis, and the vertical line x r. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1. Long before the invention of calculus, pappus of alexandria ca.651 285 859 700 325 719 102 743 1413 649 175 674 1454 541 729 326 1345 607 281 566 1458 1498 1368 1026 362 191 56 913 1467 460 933 35 862 1002 116 809 367 134 1194