What does the theorem of Pappus say?

What does the theorem of Pappus say?

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 are the theorems of Pappus and Guldinus used for?

This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Theorem of Pappus and Guldinus”. Explanation: The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve.

How do you find the centroid?

To find the centroid, follow these steps: Step 1: Identify the coordinates of each vertex. Step 2: Add all the x values from the three vertices coordinates and divide by 3. Step 3: Add all the y values from the three vertices coordinates and divide by 3.

What is the application of Varignon Theorem?

The theorem initially stated for two concurrent forces, but, it is true for any number of concurrent or coplanar forces. One of the practical applications of the theorem is to find the unknown reactions when a system is known to be in equilibrium under the action of a number of forces.

What is volume Theorem?

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, then the volume of the solid is the product of base and altitude.

Which is an example of pappus’theorem?

The six vertices of the hexagon can be arranged on the two lines in any particular order. With each arrangement of the vertices, we have an instance of Pappus’ theorem. Below is an example: Now, why don’t you try to draw for yourself your own picture of Pappus’ theorem?!

How is menelaus’theorem stated in Math Garden?

The theorem is stated as follows: Menelaus’ theorem: Given a triangle and three points , , lying on the three lines, , , respectively. Then the three points , , are collinear if and only if The proof that we are about to present is very similar to the proof of Pascal’ theorem that we show in the previous post.

How is P appus theorem similar to Pascal’s theorem?

P appus’ theorem looks very similar to Pascal’s hexagon theorem. In Pascal’s theorem, we have a hexagon inscribed in a circle and the intersection points of the three pairs of opposite sides of the hexagon lie on a straight line.

Who was pappus and what did he do?

PAPPUS’ THEOREM §3.1 Pappus’ Theorem Pappus of Alexandria (c. 300 A.D.) was a Greek mathematician who provided a particularly simple proof of the equality of the base angles of an isosceles triangle. His great work A Mathematical Collectionis an important source of information about ancient Greek mathematics.