|
Pi A)
The number (; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining , to avoid relying on the definition of the length of a curve. The number is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as \tfrac are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of appear to be randomly distributed, but no proof of thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constant
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an Letter (alphabet), alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as and pi, occurring in such diverse contexts as geometry, number theory, statistics, and calculus. Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (). Other constants are notable more for historical reasons than for their mathematical properties. The more popular constants have been studied throughout the ages and computed to many decimal places. All named mathematical constants are Definable real number, definable numbers, and usually are also computable numbers (Chaitin's constant being a significant exception). Basic mathematical constants These a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supercomputer
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2022, supercomputers have existed which can perform over 1018 FLOPS, so called Exascale computing, exascale supercomputers. For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013). Since November 2017, all of the TOP500, world's fastest 500 supercomputers run on Linux-based operating systems. Additional research is being conducted in the United States, the European Union, Taiwan, Japan, and China to build faster, more powerful and technologically superior exascale supercomputers. Supercomputers play an important role in the field of computational science, and are used for a wide range of computationally intensive tasks in various fields, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
