Why is Pappus theorem used?

Theorem of Pappus lets us find volume using the centroid and an integral. where V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.

Who invented Pappus Theorem?

Paul Guldin
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. The theorems are attributed to Pappus of Alexandria and Paul Guldin.

What did Pappus of Alexandria discover?

290 – c. 350 AD) was one of the last great Greek mathematicians of antiquity, known for his Synagoge (Συναγωγή) or Collection ( c. 340), and for Pappus’s hexagon theorem in projective geometry.

What is the first theorem of Pappus?

Pappus’s theorem, in mathematics, theorem named for the 4th-century 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 …

What is Pappus theorem mechanics?

The Pappus–Guldin Theorems Suppose that a plane curve is rotated about an axis external to the curve. Then 1. the resulting surface area of revolution is equal to the product of the length of the curve and the displacement of its centroid; 2.

What does the second theorem of Pappus indicate?

The volume of the solid of revolution can be determined using the 2nd theorem of Pappus: V=Ad. d=2πm. A=πab.

What is Guldinus rule?

It states that the volume of each solid of revolution is equal to the area of its base multiplied by the circumference of the circle in which the center of gravity of that figure is revolved. This is the Theorem of Pappus (or the Pappus-Guldin Theorem).

What is the Pappus problem?

Unlike the geometrical problems that occupied Descartes’ early researches, the Pappus problem is a locus problem, i.e., a problem whose solution requires constructing a curve—the “Pappus curve” according to Bos’s terminology—that includes all the points that satisfy the relationship stated in the problem.

Which country give rise to Theorem of Pappus?

of Alexandria
Pappus’s theorem, in mathematics, theorem named for the 4th-century 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 …

What math did Descartes create?

analytical geometry
René Descartes invented analytical geometry and introduced skepticism as an essential part of the scientific method. He is regarded as one of the greatest philosophers in history. His analytical geometry was a tremendous conceptual breakthrough, linking the previously separate fields of geometry and algebra.

What is meant by centroid?

centroid. / (ˈsɛntrɔɪd) / noun. the centre of mass of an object of uniform density, esp of a geometric figure. (of a finite set) the point whose coordinates are the mean values of the coordinates of the points of the set.

How is Pappus’s theorem related to Guldinus theorem?

Pappus’s theorem (also known as Pappus’s centroid theorem, Pappus-Guldinus theorem or the Guldinus theorem) deals with the areas of surfaces of revolution and with the volumes of solids of revolution. The Pappus’s theorem is actually two theorems that allow us to find surface areas and volumes without using integration.

When do you use pappus’s centroid theorem?

Pappus’s centroid theorem. The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas.

What is the GAGA theorem in algebraic geometry?

18.726: Algebraic Geometry (K.S. Kedlaya, MIT, Spring 2009) GAGA (updated 30 Apr 2009) We now discuss a classic theorem of algebraic geometry, Serre’s GAGA, which exposes a tight relationship between algebraic geometry over the complex numbers and complex analytic geometry.

Which is the proof of Pappus’s hexagon theorem?

Theorem 1.1 (Pappus’s hexagon Theorem). Let A,B,C be three points on a straight line and let X,Y,Z be three points on another line. If the lines AY , BZ, CX intersect the lines BX, CY, AZ, respectively then the three points of intersection are collinear. Here intersecting means that two lines have exactly one point in common.