Search results
Results from the WOW.Com Content Network
Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular it gives a careful treatment of intersection theory by defining the local intersection multiplicity of two subvarieties .
The term "projective geometry" is used sometimes to indicate the generalised underlying abstract geometry, and sometimes to indicate a particular geometry of wide interest, such as the metric geometry of flat space which we analyse through the use of homogeneous coordinates, and in which Euclidean geometry may be embedded (hence its name ...
This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. [ 21 ] [ 22 ] The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane ( plane geometry ) and the three ...
The diagram above shows the nine significant points of the nine-point circle. Points D, E, F are the midpoints of the three sides of the triangle. Points G, H, I are the feet of the altitudes of the triangle.
The book advocates replacing the usual basic quantities of trigonometry, Euclidean distance and angle measure, by squared distance and the square of the sine of the angle, respectively. This is logically equivalent to the standard development (as the replacement quantities can be expressed in terms of the standard ones and vice versa).
John Wesley Young (17 November 1879, Columbus, Ohio – 17 February 1932, Hanover, New Hampshire) was an American mathematician who, with Oswald Veblen, introduced the axioms of projective geometry, coauthored a 2-volume work on them, and proved the Veblen–Young theorem.
It states that if h is a positive even integer, there are infinitely many primes p such that p + h is either prime or the product of two primes. Ying Chun Cai proved the following in 2002: [ 6 ] There exists a natural number N such that every even integer n larger than N is a sum of a prime less than or equal to n 0.95 and a number with at most ...
The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. With the exception of Autolycus' On the Moving Sphere, the Elements is one of the oldest extant Greek mathematical treatises, [9] and it is the oldest extant axiomatic deductive treatment of mathematics.