How do you prove Pappus Theorem?
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.
What is pappus proposition?
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 did Rene Descartes discover in mathematics?
He is credited as the father of analytic geometry, the bridge between algebra and geometry—used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution.
What is the Aristotle analysis?
And even more than in the case of geometry, analysis in Aristotle’s Analytics involves not just the regression to first principles, but also the entire process of elaborating the structural relations between the various elements of arguments and showing how one argument can be ‘reduced’ to another.
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).
Who discovered Euclidean geometry?
mathematician Euclid
Euclidean geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid (c. 300 bce).
What is the first Theorem of Pappus?
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 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.
What is Descartes best known for?
Descartes has been heralded as the first modern philosopher. He is famous for having made an important connection between geometry and algebra, which allowed for the solving of geometrical problems by way of algebraic equations.
What are some major contribution of Descartes in the field of mathematics?
Apart from his work in philosophy, Descartes was a leading mathematician and scientist. He invented the Cartesian coordinate system, developed analytic geometry and laid the foundation for the development of calculus. He also did groundbreaking work in physics most prominently in the field of optics.
What were Aristotle’s main ideas?
Aristotle’s philosophy stresses biology, instead of mathematics like Plato. He believed the world was made up of individuals (substances) occurring in fixed natural kinds (species). Each individual has built-in patterns of development, which help it grow toward becoming a fully developed individual of its kind.