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Crossed Ladders Problem
The crossed ladders problem is a puzzle of unknown origin that has appeared in various publications and regularly reappears in Web pages and Usenet discussions. The problem Two ladders of lengths ''a'' and ''b'' lie oppositely across an alley, as shown in the figure. The ladders cross at a height of ''h'' above the alley floor. What is the width of the alley? Martin Gardner presents and discusses the problem in his book of mathematical puzzles published in 1979 and cites references to it as early as 1895. The crossed ladders problem may appear in various forms, with variations in name, using various lengths and heights, or requesting unusual solutions such as cases where all values are integers. Its charm has been attributed to a seeming simplicity which can quickly devolve into an "algebraic mess" (characterization attributed by Gardner to D. F. Church). Solution The problem description implies that that and , that and that where ''A'' and ''B'' are the heights of the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Puzzle
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to find the solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles. The academic study of puzzles is called enigmatology. Puzzles are often created to be a form of entertainment but they can also arise from serious mathematical or logical problems. In such cases, their solution may be a significant contribution to mathematical research. Etymology The ''Oxford English Dictionary'' dates the word ''puzzle'' (as a verb) to the 16th century. Its earliest use documented in the ''OED'' was in a book titled ''The Voyage of Robert Dudley...to the West Indies, 1594–95, narrated by Capt. Wyatt, by himself, and by Abram Kendall, master'' (published circa 1595). The word later came to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartic Equation
In mathematics, a quartic equation is one which can be expressed as a ''quartic function'' equaling zero. The general form of a quartic equation is :ax^4+bx^3+cx^2+dx+e=0 \, where ''a'' ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case. History Lodovico Ferrari is attributed with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. The solution of the quartic was published together with that of the cubic by Ferrari's mentor Gerolamo Cardano in the book '' Ars Magna'' (1545). The proof that this was the highest order general polynomial for which such solutions could be found was first given in the Abel–Ruffini theorem in 1824, proving that all attempts at solving the higher order polynomials would be futile. The notes left by Évariste Galois before ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an Open source, open-source collection of Interactive computing, interactive programmes called Demonstrations. It is hosted by Wolfram Research. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Parents' Choice Award in 2008. Wolfram Research's staff organizes and edits the Demonstrations, which may be created by any user of Wolfram Mathematica, Mathematica, then freely published and freely downloaded. Technology The Demonstrations run in Wolfram Mathematica, Mathematica 6 or above and in Wolfram Computable Document Format, CDF Player, which is a free modified version of Wolfram Mathematica and available for Microsoft Windows, Windows, Linux, and macOS and can operate as a web Browser extension, browser plugin. Demonstrations can also be embedded into a website. Each Demonstration page includes a snippet of JavaScript code in the Share section of the sidebar. The Demonstrations typically consist of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Trapezoid
In geometry, a trapezoid () in North American English, or trapezium () in British English, is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the ''bases'' of the trapezoid. The other two sides are called the ''legs'' or ''lateral sides''. (If the trapezoid is a parallelogram, then the choice of bases and legs is arbitrary.) A trapezoid is usually considered to be a convex quadrilateral in Euclidean geometry, but there are also crossed cases. If ''ABCD'' is a convex trapezoid, then ''ABDC'' is a crossed trapezoid. The metric formulas in this article apply in convex trapezoids. Definitions ''Trapezoid'' can be defined exclusively or inclusively. Under an exclusive definition a trapezoid is a quadrilateral having pair of parallel sides, with the other pair of opposite sides non-parallel. Parallelograms including rhombi, rectangles, and squares are then not considered to be trapezoids. Under an inclusive definition, a trapezoid is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossed Ladder Problem, Extended To Triangles
Crossed may refer to: * ''Crossed'' (comics), a 2008 comic book series by Garth Ennis * ''Crossed'' (novel), a 2010 young adult novel by Ally Condie * "Crossed" (''The Walking Dead''), an episode of the television series ''The Walking Dead'' See also * * Crossed out (other) * Cross (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Folding Paper Into Thirds
Fold, folding or foldable may refer to: Arts, entertainment, and media * ''Fold'' (album), the debut release by Australian rock band Epicure * Fold (poker), in the game of poker, to discard one's hand and forfeit interest in the current pot *Above the fold and below the fold, the positioning of news items on a newspaper's front page according to perceived importance *Paper folding, or ''origami'', the art of folding paper Science, technology, and mathematics Biology *Protein folding, the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure **Folding@home, a powerful distributed-computing project for simulating protein folding *Fold coverage, quality of a DNA sequence *Skin fold, an area of skin that folds Computing *Fold (higher-order function), a type of programming operation on data structures * fold (Unix), a computer program used to wrap lines to fit in a specified width * Folding (DSP implementation), a transformat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Triple
A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean triple is one in which , and are coprime (that is, they have no common divisor larger than 1). For example, is a primitive Pythagorean triple whereas is not. Every Pythagorean triple can be scaled to a unique primitive Pythagorean triple by dividing by their greatest common divisor. Conversely, every Pythagorean triple can be obtained by multiplying the elements of a primitive Pythagorean triple by a positive integer (the same for the three elements). The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a^2+b^2=c^2; thus, Pythagorean triples describe the three integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-form Expression
In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. Commonly, the basic functions that are allowed in closed forms are ''n''th root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions. The ''closed-form problem'' arises when new ways are introduced for specifying mathematical objects, such as limits, series, and integrals: given an object specified with such tools, a natural problem is to find, if possible, a ''closed-form expression'' of this object; that is, an expression of this object in terms of previous ways of specifying it. Example: roots of polynomials The quadratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Usenet
Usenet (), a portmanteau of User's Network, is a worldwide distributed discussion system available on computers. It was developed from the general-purpose UUCP, Unix-to-Unix Copy (UUCP) dial-up network architecture. Tom Truscott and Jim Ellis (computing), Jim Ellis conceived the idea in 1979, and it was established in 1980.''From Usenet to CoWebs: interacting with social information spaces'', Christopher Lueg, Danyel Fisher, Springer (2003), , Users read and post messages (called ''articles'' or ''posts'', and collectively termed ''news'') to one or more topic categories, known as Usenet newsgroup, newsgroups. Usenet resembles a bulletin board system (BBS) in many respects and is the precursor to the Internet forums that have become widely used. Discussions are Threaded discussion, threaded, as with web forums and BBSes, though posts are stored on the server sequentially. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartic Equation
In mathematics, a quartic equation is one which can be expressed as a ''quartic function'' equaling zero. The general form of a quartic equation is :ax^4+bx^3+cx^2+dx+e=0 \, where ''a'' ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case. History Lodovico Ferrari is attributed with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. The solution of the quartic was published together with that of the cubic by Ferrari's mentor Gerolamo Cardano in the book '' Ars Magna'' (1545). The proof that this was the highest order general polynomial for which such solutions could be found was first given in the Abel–Ruffini theorem in 1824, proving that all attempts at solving the higher order polynomials would be futile. The notes left by Évariste Galois before ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides , and the hypotenuse , sometimes called the Pythagorean equation: :a^2 + b^2 = c^2 . The theorem is named for the Ancient Greece, Greek philosopher Pythagoras, born around 570 BC. The theorem has been Mathematical proof, proved numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both Geometry, geometric proofs and Algebra, algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
