Mathematics Quiz

number theory, algebra, geometry, and analysis

the discovery of properties of abstract objects and the use of pure reason to prove them

a succession of applications of deductive rules to already established results

<p>It is extensively used for modeling phenomena</p> Signup and view all the answers

<p>statistics and game theory</p> Signup and view all the answers

<p>Pappus's centroid theorem, also known as the Guldinus theorem, deals with the surface areas and volumes of surfaces and solids of revolution. The first theorem relates the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane to the product of the arc length s of C and the distance d traveled by the geometric centroid of C. The second theorem relates the volume V of a solid of revolution generated by rotating a plane figure F about an external axis to the product of the area A of F and the distance d traveled by the geometric centroid of F. Its significance lies in its application to the calculation of surface areas and volumes of complex shapes and solids.</p> Signup and view all the answers

<p>The first theorem of Pappus's centroid theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to the product of the arc length s of C and the distance d traveled by the geometric centroid of C. Mathematically, this can be expressed as: $A = 2\pi s \cdot d$.</p> Signup and view all the answers

<p>The second theorem of Pappus's centroid theorem states that the volume V of a solid of revolution generated by rotating a plane figure F about an external axis is equal to the product of the area A of F and the distance d traveled by the geometric centroid of F. Mathematically, this can be expressed as: $V = \pi A \cdot d$.</p> Signup and view all the answers

<p>The theorems are attributed to Pappus of Alexandria and Paul Guldin.</p> Signup and view all the answers

<p>Pappus's statement of this theorem first appeared in print in 1659, but it was known before, by Kepler in 1615 and by Guldin in 1640.</p> Signup and view all the answers