What is the Pappus problem?
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.
What was the Pappus locus problem to three and four lines?
The bulk of the remainder of this book is occupied by Descartes’s solution to “the locus problems of Pappus.” According to Pappus, given three or four lines in a plane, the problem is to find the locus of a point that moves so that the product of the distances from two of the fixed lines (along specified directions) is …
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 is Pappus of Alexandria known for?
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.
Who invented geometry?
Euclid lived 2300 years ago in Alexandria, in northern Egypt. His was a brilliant mind. He devised a method of learning Geometry starting from the simplest idea – an Axiom – something we can all agree is self-evident.
What is the meaning I think therefore I am?
“I think; therefore I am” was the end of the search Descartes conducted for a statement that could not be doubted. He found that he could not doubt that he himself existed, as he was the one doing the doubting in the first place. In Latin (the language in which Descartes wrote), the phrase is “Cogito, ergo sum.”
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 does Pappus mean?
: an appendage or tuft of appendages that crowns the ovary or fruit in various seed plants and functions in dispersal of the fruit.
What is a pappus on a plant?
plant reproduction each flower, known as a pappus, is bristlelike, scaly, or feathery and borne at the top of the ovary. The corolla, formed of the petals, may be (1) tubular, with five petal lobes, sometimes split open, (2) ligulate, or tonguelike, with a very short basal tube, or (3) bilabiate, with…
Which is the theorem of the geometry of Pappus?
Theorem 1.10 Each point in the geometry of Pappus lies on exactly three lines. Pf. Let X be any point. By corrected axiom 3, there is a line not containing X. This line contains points A,B,C [Axiom 2]. X lies on lines meeting two of these points, say B and C [Axiom 5]. There is exactly one line through X parallel to BC [Axiom 4].
What did pappus say about explanatory lemmas?
Pappus wrote of them by explanatory lemmas” [ 1, p. 49]. These lemmas, according to C. Taylor, are statements” [ 13, p. li]. himself, and some for which he falsely assumes credit. A theorem he discovered, con- cerning the incidence of points and lines, is the subject of this article.
Where does the theorem of P appus come from?
THE THEOREM OF P APPUS. Two propositions of Book VII (translated from at the point κ, it can be concluded that all go through ηµκ. stated again that the straight lines go through ηµκ [ 6 ]. as the ﬁrst great theorem of what was to become projective geometry.
How are properties of incidence unchanged after Pappus?
Properties of incidence, which remain unchanged under stretching, translation, or rotation of the plane, are projectively inv ariant. Thus, for invariants, b ut distance, angle magnitude, linear order, and parallelism are not. variant concepts) would not appear until centuries after Pappus.