Search results
Results from the WOW.Com Content Network
A two-column proof published in 1913. A particular way of organising a proof using two parallel columns is often used as a mathematical exercise in elementary geometry classes in the United States. [29] The proof is written as a series of lines in two columns.
The American high-school geometry curriculum was eventually codified in 1912 and developed a distinctive American style of geometric demonstration for such courses, known as "two-column" proofs. [49] This remains largely true today, with Geometry as a proof-based high-school math class.
For example, in the line geometry case, we can identify H as a 12-dimensional subgroup of the 16-dimensional general linear group, GL(4), defined by conditions on the matrix entries h 13 = h 14 = h 23 = h 24 = 0, by looking for the stabilizer of the subspace spanned by the first two standard basis vectors. That shows that X has dimension 4.
This is a list of unusually long mathematical proofs.Such proofs often use computational proof methods and may be considered non-surveyable.. As of 2011, the longest mathematical proof, measured by number of published journal pages, is the classification of finite simple groups with well over 10000 pages.
One of many examples from algebraic geometry in the first half of the 20th century: Severi (1946) claimed that a degree-n surface in 3-dimensional projective space has at most (n+2 3 )−4 nodes, B. Segre pointed out that this was wrong; for example, for degree 6 the maximum number of nodes is 65, achieved by the Barth sextic , which is more ...
In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.
Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should ...
In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem [1] [2] [3] after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the Euler–Poincaré characteristic (a topological invariant defined as the alternating sum of the Betti numbers of a topological space) of a closed even-dimensional Riemannian manifold is equal to the integral of a certain ...