What is Pappus Guldinus Theorem?
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).
Why is Pappus theorem used?
Pappus’s theorem has been generalized to the case in which the region is allowed to move along any sufficiently smooth (no corners), simple (no self intersection), closed curve.
Which country give rise to Theorem of Pappus?
Pappus of Alexandria (/ˈpæpəs/; Greek: Πάππος ὁ Ἀλεξανδρεύς; c. 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 first theorem of Pappus Galdinus?
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.
How do you prove Pappus 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.
Who was Pappus and what contributions did he make to math?
Pappus of Alexandria , (flourished ad 320), 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.
What is second proposition of pappus?
Pappus’s Theorem for Volume The second theorem of Pappus states that the volume of a solid of revolution obtained by rotating a lamina about a non-intersecting axis lying in the same plane is equal to the product of the area of the lamina and the distance traveled by the centroid of. Figure 2.
Which axioms in the geometry of Pappus are also true statement in Euclidean geometry?
Which axioms in the geometry of Pappus are also true statements in Euclidean geometry? Ans: Axioms 1, 3, 4, and 6 (with no exceptions).
What have you learned about projective geometry?
Projective geometry can be thought of as the collection of all lines through the origin in three-dimensional space. That is, each point of projective geometry is actually a line through the origin in three-dimensional space. The distance between two points can be thought of as the angle between the corresponding lines.