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An arrow is a graphical symbol, such as ←, ↑ or →, or a pictogram, used to point or indicate direction. In its simplest form, an arrow is a triangle, chevron, or concave kite, usually affixed to a line segment or rectangle, and in more complex forms a representation of an actual arrow (e.g. ➵ U+27B5). The direction indicated by an arrow is the one along the length of the line or rectangle toward the single pointed end. History An older (medieval) convention is the manicule (pointing hand, ☚). Pedro Reinel in c. 1505 first used the fleur-de-lis as indicating north in a compass rose; the convention of marking the eastern direction with a cross is older (medieval). Use of the arrow symbol does not appear to pre-date the 18th century. An early arrow symbol is found in an illustration of Bernard Forest de Bélidor's treatise ''L'architecture hydraulique'', printed in France in 1737. The arrow is here used to illustrate the direction of the flow of water and of the wate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manicule
The manicule, , is a typography, typographic mark with the appearance of a hand with its index finger extending in a pointing gesture. Originally used for handwritten marginal notes, it later came to be used in printed works to draw the reader's attention to important text. Though once widespread, it is rarely used today, except as an occasional archaic novelty or on informal directional signs. Terminology For most of its history, the mark has been inconsistently referred to by a variety of names. William H. Sherman, in the first dedicated study of the mark, uses the term ''manicule'' (from the Latin root ''manicula'', meaning "little hand"), but also identifies 14 further names which he records as having been used: * hand * pointing hand * hand director * pointer * digit * fist * mutton fist * bishop's fist * index * * indicator * * maniple (vestment), maniple * pilcrow History Handwritten manicules The symbol originates in scribal tradition of the medieval and Renaissa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Short History Of The English People
''A Short History of the English People'' is a book written by English historian John Richard Green. Published in 1874, "it is a history, not of English Kings or English Conquests, but of the English People." Background and reception Green began work on the book in 1869, having been given only six months to live after being hit hard by disease that had plagued him throughout his life. Only having around 800 pages to write on, he had to leave out much of what he wanted to include. Green intentionally left out the battles of England feeling they did not play a big role in the formation of the nation, saying that historians "too often turned history into a mere record of the butchery of men by their fellow men." His new ideas, and omission of information that others felt important, meant Green was criticized by other historians as well as the people close to him. Others thought highly of the book, including Francis Adams, who used quotations from the book in his poem ''The Peasant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Logical equivalences In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these. General logical equivalences Logical equivalences involving conditional statements :#p \rightarrow q \equiv \neg p \vee q :#p \rightarrow q \equiv \neg q \rightarrow \neg p :#p \vee q \equiv \neg p \rightarrow q :#p \wedge q \equiv \neg (p \rightarrow \neg q) :#\neg (p \rightarrow q) \equiv p \wedge \neg q :#(p \righta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a cofounder of proof theory and mathematical logic. Life Early life and education Hilbert, the first of two children and only son of O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Notation
Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations, and any other mathematical objects and assembling them into expression (mathematics), expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and property (philosophy), properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula E=mc^2 is the quantitative representation in mathematical notation of mass–energy equivalence. Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols and typeface The use of many symbols is the basis of mathematical notation. They play a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical NOR
In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (''p'' NOR ''q'') is true precisely when neither ''p'' nor ''q'' is true—i.e. when both ''p'' and ''q'' are ''false''. It is logically equivalent to \neg(p \lor q) and \neg p \land \neg q, where the symbol \neg signifies logical negation, \lor signifies OR, and \land signifies AND. Non-disjunction is usually denoted as \downarrow or \overline or X (prefix) or \operatorname. As with its dual, the NAND operator (also known as the Sheffer stroke—symbolized as either \uparrow, \mid or /), NOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NOR functionally complete). The computer used in the spacecraft that first carried humans to the moon, the Apollo Guidance Computer, was constructed entirely using NOR gates with three inputs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAND Operator
In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, alternative denial (since it says in effect that at least one of its operands is false), or NAND ("not and"). In digital electronics, it corresponds to the NAND gate. It is named after Henry Maurice Sheffer and written as \mid or as \uparrow or as \overline or as Dpq in Polish notation by Łukasiewicz (but not as , , , often used to represent disjunction). Its dual is the NOR operator (also known as the Peirce arrow, Quine dagger or Webb operator). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete). This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design. Definition Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
