Pappus theorem youtube downloader

Solid of rotation, pappus centroid theorem a solid of rotation is the figure that results from rotating a plane figure about an external axis an axis on the same plane as the figure such that no two points of the figure are on opposite sides of the axis. Generalization of the pythagorean theorem to three dimensions. Share your videos with friends, family, and the world. This mathematics video covers the pythagorean theorem. Yeah, shes got some pretty unusual demands, but he fell in love with the whole person. There are two results of pappus which relate the centroids to surfaces and solids of revolutions. This is a generalization in a different direction from what the question asked for these references generalize in terms of finding volumes, but koundinya vajjha wanted a generalization in terms of finding the centroid. X lies on lines meeting two of these points, say b and c axiom 5. Use the theorem of pappus to find the volume of the given. Full video on benchmark ktu mobile app download app in mathematics, pappuss centroid theorem. A list of lyrics, artists and songs that contain the term pappus from the website. A centroid is easily visualized as the center of gravity or center of mass of a flat. These three points are the points of intersection of the opposite sides of the hexagon. 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.

David hilbert observed that pappuss theorem is equivalent to the claim that the multiplication of lengths is commutative see, e. Im not sure what hartshorne has in mind, but pappus theorem is a simple consequence of similarity of euclidean triangles in guise of the intercept theorem and theres no need of introducing the circle. Lesson 55 centroid theorem of pappus guldinus volume and surface area duration. For instance, pappus handles the problem of inscribing five regular solids in a sphere in a way quite different from euclid. Theorem of pappus and guldinus engineering mechanics youtube.

It only uses congruence and equivalent equality areas. The volume of a solid formed by rotating a planar region about an axis is equal to the product of the area of the planar region and the distance the centroid travels around the axis. Aug 25, 2015 there are two theorems, both saying similar things. The volume equals the product of the area of the region being rotated times the distance traveled by the centroid of the region in one rotation. A segment of a circle of radius r is bounded by an arc equal to the circumference of the circle. It includes examples and helpful lessons to better understand what the theorem can be used for in the real world. There used to exist a top 100 of mathematical theorems on the web, which is a rather arbitrary list and most of the theorems seem rather elementary, but still is nice to look at. Greg kelly math calculus powerpoints and video lectures. Now the second pappusguldin theorem gives the volume when this region is rotated through. By corrected axiom 3, there is a line not containing x.

Note that this is also valid for the chain of tangent circles starting with and tangent to the two interior semicircles of the arbelos. The centroid of a region is essentially the one point on which the region should balance. He knows that wendy wants the tippytop of peters head to be exactly 10 feet away from. Z b a fx 2 dx, the familiar formula for volume of solid of revolution. Lesson 45 centroid theorem of pappus guldinus volume and surface area duration. Learn how to use the theorem of pappus to find the volume of a solid, in this particular case, a right circular cone. It is meant to entertain and motivate students to learn. This configuration is named after pappus of alexandria. Suppose r is revolved about the line l which does not cut. Chapter wise syllabus from basic to advanced level. In this example i show that using the theorem of pappus to calculate. You can follow it step by step by moving the sliders in order. There are several theorems that generally are known by the generic name pappus s theorem. 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.

In mathematics, pappuss centroid theorem is either of two related theorems dealing with the. Profrobbob i introduce the theorem of pappus and then work through 2 examples. Media in category pappus theorem the following 36 files are in this category, out of 36 total. Mar 22, 2014 use the theorem of pappus to find the volume of the given solid the solid obtained by rotating the triangle with vertices 2, 3, 2, 5, and 8, 4 about the xaxis. In the intermediate value theorem, we assume that if were continuous over the closed interval from a to b, and in fact all of these existence theorems assume that our function is continuous over the closed interval from a to b, then we take on every value between f of a, and f of b, or another way to think about it is, pick a value from f. Pappus not only reproduces known solutions to geometric problems, but he frequently gives own solutions, or improvements and extensions to existing solutions and theorem. David hilbert observed that pappus s theorem is equivalent to the claim that the multiplication of lengths is commutative see, e.

Pappus s area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. A fourth century theorem for twentyfirst century calculus. Determine the amount of paint required to paint the inside and outside surfaces of the cone, if one gallon of paint covers 300 ft2. How to calculate surface area and volume of a revolving object s. Prezi s director of product marketing on working from home and finding balance. There is exactly one line through x parallel to bc axiom 4. The theorem of pascal concerning a hexagon inscribed in a conic. And we know that because this side over here, it is the side opposite the right angle. Pappus theorem article about pappus theorem by the free.

Pappuss area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. Summarythe centroid theorems of pappus or the pappusguldin. There are several theorems that generally are known by the generic name pappuss theorem. 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. If the region does not cross the axis, then the volume of the resulting solid of revolution is v 2. Pappuss centroid theorem volume by george kotzabassis on. A fourth century theorem for twentyfirst century calculus taylor.

Feb 08, 20 homework statement use pappus theorem for surface area and the fact that the surface area of a sphere of radius c is 4pic2 to find the centroid of the semicircle x sqrt c2 y2 homework equations s 2 pi p l where ssurface area. Euclidean version of pappuss theorem mathematics stack. I dont think you understand the theorem as it is the centroid of the figure you rotate that relates to the theorem. A method for finding the volume of a solid of revolution. You will need to download the powerpoint lectures in order to view them. With this construction you can get 2 more different variations of this proof. 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 the centroid of d during the revolution. 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. Get youtube tv best of youtube music sports gaming movies tv shows. Pappuss centroid theorem volume by george kotzabassis on prezi. The euclidean pseudoline arrangement b is derived from a by taking line 0 as the line at in. Applying pappuss theorem allows us to easily solve for the volume of.

Create marketing content that resonates with prezi video. To interpret the explanations on or computation meets knowledge you need to know what a centroid is. They include pappus s centroid theorem, the pappus chain, pappus s harmonic theorem, and pappus s hexagon theorem. This is a generalization in a different direction from what the question asked for these references generalize in terms of finding volumes, but koundinya vajjha wanted a. The theorem of pappus states that when a region r is rotated about a line l, the volume of the solid generated is equal to the product of the area of r and the distance the centroid of the region has traveled in one full rotation. Intro to the pythagorean theorem video khan academy. If cdenotes the centroid of sand ais the surface area of srecall the notation from section 2, then the socalled pappus theorem states in its classical form 5, chapter 6 that the volume of this solid is given by vs. Any stretching of rin9 would provide a euclidean stretching of b, necessarily satisfying the premises of the main theorem.

Then three pairwise intersections 1 bc bc, 2 ac ac, and 3 ab ab are incident to a third straight line. 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. This course is offered as an online course at big bend community college. A simple proof for the theorems of pascal and pappus. So now were ready to apply the pythagorean theorem. Prove in pappus geometry that for any point p, there is a line not containing p. Pappuss theorem appears in his text synagogue 17, a collection of classical greek geometry with insightful commentary. Pappus s theorem appears in his text synagogue 17, a collection of classical greek geometry with insightful commentary. And in this circumstance were solving for the hypotenuse. In mathematics, pappus s hexagon theorem attributed to pappus of alexandria states that given one set of collinear points,, and another set of collinear points,, then the intersection points, of line pairs and, and, and are collinear, lying on the pappus line.

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. Here you can see the proof due to pappus of the pythagorean theorem. A similar calculation may be made using the y coordinate of the. A simple proof for the theorems of pascal and pappus marian palej geometry and engineering graphics centre, the silesian technical university of gliwice ul. The pappus consists of one to many dry scales, awns small pointed processes, or capillary hairlike bristles. Expert answer since the set of all lines are non empty which is ensured by axiom 1 suppose for the sake of contradiction there exist a point p for which no such line ex view the full answer. The theorems are attributed to pappus of alexandria and paul guldin. Stay connected to your students with prezi video, now in microsoft teams. For more information on how to enroll for credit go to. They include pappuss centroid theorem, the pappus chain, pappuss harmonic theorem, and pappuss hexagon theorem. This result was known to pappus, who referred to it as an ancient theorem hood 1961, cadwell 1966, gardner 1979, bankoff 1981. 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.