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For instance, while all the cross-sections of a ball are disks, [2] the cross-sections of a cube depend on how the cutting plane is related to the cube. If the cutting plane is perpendicular to a line joining the centers of two opposite faces of the cube, the cross-section will be a square, however, if the cutting plane is perpendicular to a ...
The Catholic Bible contains 73 books; the additional seven books are called the Apocrypha and are considered canonical by the Catholic Church, but not by other Christians. When citing the Latin Vulgate , chapter and verse are separated with a comma, for example "Ioannem 3,16"; in English Bibles chapter and verse are separated with a colon, for ...
In algebraic geometry, a lemniscate (/ l ɛ m ˈ n ɪ s k ɪ t / or / ˈ l ɛ m n ɪ s ˌ k eɪ t,-k ɪ t /) [1] is any of several figure-eight or ∞-shaped curves. [ 2 ] [ 3 ] The word comes from the Latin lēmniscātus , meaning "decorated with ribbons", [ 4 ] from the Greek λημνίσκος ( lēmnískos ), meaning "ribbon", [ 3 ] [ 5 ...
In the mathematical field of topology, a section (or cross section) [1] of a fiber bundle is a continuous right inverse of the projection function. In other words, if E {\displaystyle E} is a fiber bundle over a base space , B {\displaystyle B} :
It is common in mathematics publications that define the Borromean rings to do so as a link diagram, a drawing of curves in the plane with crossings marked to indicate which curve or part of a curve passes above or below at each crossing. Such a drawing can be transformed into a system of curves in three-dimensional space by embedding the plane ...
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
This file represents the Cavalieri's Principle in action: if you have the same set of cross sections that only differ by a horizontal translation, you will get the same volume. In geometry , Cavalieri's principle , a modern implementation of the method of indivisibles , named after Bonaventura Cavalieri , is as follows: [ 1 ]
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...