Theorem of pappus tells us that volume is equal to area of the plane region, times the distance traveled by the centroid of the same plane region, if the plane region is revolved around the xaxis. Other than that he was born at alexandria in egypt and that his. Pappus was a greek geometer during the third century ad his theorems about from eng 111 at rutgers university. Proof of pappus theorem using affine geometry mathematics. 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. A look at some of the top funny educational videos while the internet is pretty well stocked with educational videos of all kinds, ones that make you chuckle while learning about various math or science concepts are pretty rare. The euclidean pseudoline arrangement b is derived from a by taking line 0 as the line at in. After the simulation, the position of the joints of the moving platform was noted with respect to simulation time and these points were given as input to the matlab for getting the work envelope. Then surface area of the cone as per pappus theorem is ab multiplied by distance traveled by the c. This theorem, this expression is the expression of the first theorem of pappus guldinus. Pappus s hexagon theorem states that every two triples of collinear points abc and abc none of which lie on the intersection of the two lines can be completed to form a pappus configuration, by adding the six lines ab, ab, ac, ac, bc, and bc, and their three intersection points x abab, y acac, and z bcbc. Click the red button on the figure to start the animation.
We prove a generalization of both pascals theorem and its converse, the braikenridge maclaurin theorem. Very little is known about his life, but the written records suggest he was probably a teacher. Pappus of alexandria 290 350, was a hellenized egyptian born in alexandria. Centroid theorem of pappus guldinus volume and surface area shear moment diagram, the equation method shear moment diagram. An application of pappus involution theorem in euclidean and noneuclidean geometry.
Center of mass, pappus theorem pappus theorem let b be a blob in the xy plane, floating entirely above the x axis. 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. In this video i will explain the first theorem of pappus guldinius of finding the area of. Use the theorem of pappus to determine the surface area of this region as well. Top 10 tips for getting started with prezi video in your online classroom. Lesson 45 centroid theorem of pappus guldinus volume and surface area. James gregory and the pappusguldin theorem selections from the gpu 1 james gregory and the pappusguldin theorem selections from. Then three pairwise intersections 1 bc bc, 2 ac ac, and 3 ab ab are incident to a third straight line. Dutch progressive rock band pythagoras started out back in the late 1970s, and released two studio albums before calling it quits in 1984.
Use theorems of pappus and guldinus to calculate area created by revolving curve about an axis, or calculate the volume created by revolving. Apolloniuss theorem is an elementary geometry theorem relating the length of a median of a triangle to the lengths of its sides. Aug 01, 2017 use theorems of pappus and guldinus to calculate area created by revolving curve about an axis, or calculate the volume created by revolving area about an axis. Theorems of pappus and guldinus mechanical engineering video edurev is made by best teachers of mechanical engineering. Pappus centroid theorem pdf pappus centroid theorem pdf pappus centroid theorem pdf download. Pappuss hexagon theorem states that every two triples of collinear points abc and abc none of which lie on the intersection of the two lines can be completed to form a pappus configuration, by adding the six lines ab, ab, ac, ac, bc, and bc, and their three intersection points x abab, y acac, and z bcbc. The theorems are attributed to pappus of alexandria and paul guldin. Wikimedia commons has media related to pappusguldinus theorem. The seventh book of pappus s collection, his commentary on the domain or treasury of analysis, figures prominently in the history of both ancient and modern mathematics. For instance, if b is a circle the result is a torus. The corolla, formed of the petals, may be 1 tubular, with five petal lobes, sometimes split open, 2 ligulate, or tonguelike, with a very short basal tube, or 3 bilabiate, with. Pappus related things you might have been looking for when you found this page.
If an internal link led you here, you may wish to change the link to point directly to. Let r be the triangular region bounded by the line y x, the xaxis, and the vertical line x r. Now the second pappusguldin theorem gives the volume when this region is rotated through. If two sets of k lines meet in k2 distinct points, and if. Let three points a, b, c be incident to a single straight line and another three points a,b,c incident to another straight line. Teachingtree is an open platform that lets anybody organize educational content. Our goal is for students to quickly access the exact clips they need in order to learn individual concepts. This theorem is also known as the pappus guldinus theorem and pappus s centroid theorem, attributed to pappus of alexandria. Pappuss theorem, in mathematics, theorem named for the 4thcentury greek geometer pappus of alexandria that describes the volume of a solid, obtained by revolving a plane region d about a line l not intersecting d, as the product of the area of d and the length of the circular path traversed by. Pappuss centroid theorem volume by george kotzabassis on prezi. A video lecture that will explain both the theorems of pappus and guldinus with examples. James gregory and the pappusguldin theorem conclusion.
Then autocad is used for determining the work volume. A simplified proof of the pappus leisenring theorem. A similar calculation may be made using the y coordinate of the. His main contribution to mathematics was primarily as an encyclopedist. The first theorem of pappus guldinus says that the area of the sphere is given by a 2 rcl because we already know a 4 r2, we can solve this equation for rc in terms of r and l. Pappus centroid theorem pdf the surface of revolution generated by a smooth curve. Pappus of alexandria greek mathematician britannica. For more information on how to enroll for credit go to. Nothing is known of his life, except from his own writings that he had a son named hermodorus, and was a teacher in alexandria.
It allows us to easily calculate shapes obtained by evolution and as example, lets consider, for example, the case of a line l, a straight segment l, so length l. All structured data from the file and property namespaces is available under the creative commons cc0 license. To interpret the explanations on or computation meets knowledge you need to know what a centroid is. Get youtube premium get youtube tv best of youtube music. Files are available under licenses specified on their description page. Just click on the button to start downloading clips. This contains most of the guides i have created for the game.
The first theorem of pappus states that the surface area sof a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance d 1 traveled by the curves geometric centroid kern and bland 1948, pp. Tap into teacher guides loaded with lessons and project ideas, as well as tips and tricks for handling helicopter parents and inspiring unruly children. Media in category pappusguldinus theorem the following 6 files are in this category, out of 6 total. The role of frenet motion in pappus type theorems m.
Apply the theorem of pappusguldinus to evaluate the volumes or revolution for the rectangular rim section and the inner cutout section. When we revolve this element, clearly we prescribe again some circle, and if we were going to cut and open up this circular element. I link to it here, because you may have been looking for it when you found this page. There are two theorems, both saying similar things. When r is rotated about the xaxis, it generates a cone of volume use the theorem of pappus to determine the ycoordinate of the centroid of r. While most of the world refers to it as it is, in east asia, the theorem is usually referred to as pappus s theorem or midpoint theorem. A centroid is easily visualized as the center of gravity or center of mass of a flat. Pappus theorem, which is more about points and lines, and is a special case of pascals theorem, in which a hexagon is inscribed in a conic. Proofs of the pythagorean theorem by logan kahle, brewster kahle and eric miranda. Me 2301 is a first semester, sophomore level class in statics. Compute the volume of the shape using cylindrical coordinates. This disambiguation page lists mathematics articles associated with the same title. After installing idm, a download this video button pops up whenever you are watching a video anywhere in cyberspace shown in the picture below. Engineering mechanics tutorial previous lecture link.
If the region does not cross the axis, then the volume of the resulting solid of revolution is v 2. Spin b around the x axis, creating a shape of revolution. Theorems of pappus and goldinus mechanical engineering. Proposition if six points 1,2,3,4,5, and 6, on two lines are joined as shown, then their points of intersection a, b, and c are collinear hint to interact with the figure below. The mcgrawhill companies is not associated with any product or vendor mentioned in this book. Pdf file android app 6 days ago adobe acrobat dc pdf reader latest version. Areas of surfaces of revolution and the theorems of pappus.
Consider the curve c given by the graph of the function f. As well as the proof of the pappus theorem, i also go over a brief math. Centroid theorem of pappus guldinus volume and surface area duration. Lesson 55 centroid theorem of pappus guldinus volume and surface area by jeff hanson. Any stretching of rin9 would provide a euclidean stretching of b, necessarily satisfying the premises of the main theorem. From pascals theorem to d constructible curves will traves abstract.
This video is highly rated by mechanical engineering students and has been viewed 267 times. Use pappus theorem to find the moment of a region limited by a semicircunference. Nov 17, 2001 the center of mass of an object of mass m is the single point that moves in the same way as a point mass of mass m would move when subjected to the same external forces that act on the object. Pappus of alexandria, the most important mathematical author writing in greek during the later roman empire, known for his synagoge collection, a voluminous account of the most important work done in ancient greek mathematics. Area of cone of surface of revolution by theorem of pappus guldinus is. The views and opinions expressed in this page are strictly those of the page author.
James gregory and the pappusguldin theorem acknowledgements and references. Areas of surfaces of revolution, pappuss theorems let f. Nine proofs and three variations x y z a b c a b z y c x b a z x c y fig. This page was last edited on 29 november 2019, at 11. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on youtube. Let ct be a curve in a space form mn of sectional curvature. This course is offered as an online course at big bend community college. Now the second pappus guldin theorem gives the volume when this region is rotated through. In mathematics, pappuss centroid theorem is either of two related theorems dealing with the.
Angiosperms each flower, known as a pappus, is bristlelike, scaly, or feathery and borne at the top of the ovary. The obtained values were compared with analytical approach by using pappus guldinus theorem. Pappus s area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. The theorems of pappusguldinus were formulated by the greek geometer pappus of alexandria during the 4th century a. In this video i will explain the first theorem of pappusguldinius of finding the. 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. In mathematics, pappuss centroid theorem also known as the guldinus theorem, pappusguldinus theorem or pappuss theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. He discovered the guldinus theorem to determine the surface and the volume of a solid of revolution.
Nothing is known of his life, other than what can be found in his own writings. Pappus was a greek geometer during the third century ad. The second theorem pappus guldinus helps us calculate the volume of an object that is obtained by revolving an area about this line x. Let s be the surface generated by revolving this curve about the xaxis.
Theorems of pappus on surfaces of revolution wolfram. James gregory and the pappusguldin theorem gregorys proof revealed. Z b a fx 2 dx, the familiar formula for volume of solid of revolution. Throughout this course you will learn to do an analyses of particles, rigid bodies, trusses, frames, and machines in static equilibrium with applied forces and couples. You have the full projective generality of the theorem, but are still asking for an affine proof.1339 449 697 1425 1529 1459 1442 595 494 1338 998 1071 1001 972 683 753 292 1398 139 500 568 806 636 580 419 244 1381 1256 781 932 250 346 1391 10 851 1201 767