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Hoffman's Packing Puzzle
Hoffman's packing puzzle is an assembly puzzle named after Dean G. Hoffman, who described it in 1978. The puzzle consists of 27 identical rectangular cuboids, each of whose edges have three different lengths. Its goal is to assemble them all to fit within a cube whose edge length is the sum of the three lengths. writes that the first person to solve the puzzle was David A. Klarner, and that typical solution times can range from 20 minutes to multiple hours. Construction The puzzle itself consists only of 27 identical rectangular cuboid-shaped blocks, although physical realizations of the puzzle also typically supply a cubical box to fit the blocks into. If the three lengths of the block edges are , , and , then the cube should have edge length . Although the puzzle can be constructed with any three different edge lengths, it is most difficult when the three edge lengths of the blocks are close enough together that , as this prevents alternative solutions in which four blocks o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoffman Packing Puzzle
Hoffman is a surname of Germany, German and Jews, Jewish origin. The original meaning in medieval times was "steward", i.e. one who manages the property of another. In English language, English and other European languages, including Yiddish and Dutch language, Dutch, the name can also be spelled Hoffmann, Hofmann (surname), Hofmann, Hofman, Huffman (other), Huffman, Hofmans. People with the surname A * Aaron Hoffman (1880–1944), American writer, director and comedian * Abbie Hoffman (1936–1989), American social activist of prominence in the 1960s and 1970s * Abraham Hoffman (1938–2015), Israeli basketball player * Al Hoffman (1902–1960), Russian-born American songwriter * Cloudant, Alan Hoffman (born 1982), American entrepreneur * Albert Hofmann (1906–2008), Swiss chemist and discoverer of LSD * Alex Hoffman-Ellis (born 1989), American football player * Alice Hoffman (born 1952), American author * Anthony Hoffman (1739–1790), New York politician * Arthur Su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC, one of the most well-known mechanical puzzles of modern day is the Rubik's Cube, invented by the Hungarian architect Ernő Rubik in 1974. The puzzles are typically designed for a single player, where the goal is for the player to see through the principle of the object, rather than accidentally coming up with the right solution through trial and error. With this in mind, they are often used as an intelligence test or in problem solving training. History The oldest known mechanical puzzle comes from Greece and appeared in the 3rd century BC. The game consists of a square divided into 14 parts, and the aim was to create different shapes from these pieces. This is not easy to do. (see Ostomachion loculus Archimedius) In Iran "puzzle-lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dean G
Dean may refer to: People * Dean (given name) * Dean (surname), a surname of Anglo-Saxon English origin * Dean (South Korean singer), a stage name for singer Kwon Hyuk * Dean Delannoit, a Belgian singer most known by the mononym Dean Titles * Dean (Christianity), persons in certain positions of authority within a religious hierarchy * Dean (education), persons in certain positions of authority in some educational establishments * Dean of the Diplomatic Corps, most senior ambassador in a country's diplomatic corps * Dean of the House, the most senior member of a country's legislature Places * Dean, Victoria, Australia * Dean, Nova Scotia, Canada * De'an County, Jiujiang, Jiangxi, China United Kingdom * Lower Dean, Bedfordshire, England * Upper Dean, Bedfordshire, England * Dean, Cumbria, England * Dean, Oxfordshire, England * Dean, a hamlet in Cranmore, Somerset, England * Dean Village, Midlothian, Scotland * Forest of Dean, Gloucestershire, England * Dene (valley) common topon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron, whose polyhedral graph is the same as that of a cube. Special cases are a cube, with 6 squares as faces, a rectangular prism, rectangular cuboid or rectangular box, with 6 rectangles as faces, for both, cube and rectangular prism, adjacent faces meet in a right angle. General cuboids By Euler's formula the numbers of faces ''F'', of vertices ''V'', and of edges ''E'' of any convex polyhedron are related by the formula ''F'' + ''V'' = ''E'' + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges. Along with the rectangular cuboids, any parallelepiped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David A
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Progression
An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence (a_n) is given by: :a_n = a + (n - 1)d, If there are ''m'' terms in the AP, then a_m represents the last term which is given by: :a_m = a + (m - 1)d. A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series. Sum Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the th root of the product of numbers, i.e., for a set of numbers , the geometric mean is defined as :\left(\prod_^n a_i\right)^\frac = \sqrt /math> or, equivalently, as the arithmetic mean in logscale: :\exp For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, \sqrt = 4. As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, \sqrt = 1/2. The geometric mean applies only to positive numbers. The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures: values of the human population or inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inequality Of Arithmetic And Geometric Means
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which case they are both that number). The simplest non-trivial case – i.e., with more than one variable – for two non-negative numbers and , is the statement that :\frac2 \ge \sqrt with equality if and only if . This case can be seen from the fact that the square of a real number is always non-negative (greater than or equal to zero) and from the elementary case of the binomial formula: :\begin 0 & \le (x-y)^2 \\ & = x^2-2xy+y^2 \\ & = x^2+2xy+y^2 - 4xy \\ & = (x+y)^2 - 4xy. \end Hence , with equality precisely when , i.e. . The AM–GM inequality then follows from taking the positive square root of both sides and then dividing both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AM-GM Inequality
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which case they are both that number). The simplest non-trivial case – i.e., with more than one variable – for two non-negative numbers and , is the statement that :\frac2 \ge \sqrt with equality if and only if . This case can be seen from the fact that the square of a real number is always non-negative (greater than or equal to zero) and from the elementary case of the binomial formula: :\begin 0 & \le (x-y)^2 \\ & = x^2-2xy+y^2 \\ & = x^2+2xy+y^2 - 4xy \\ & = (x+y)^2 - 4xy. \end Hence , with equality precisely when , i.e. . The AM–GM inequality then follows from taking the positive square root of both sides and then dividing bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square () and a cube (). It is a closed, compact, convex figure whose 1- skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in ''n'' dimensions is equal to \sqrt. An ''n''-dimensional hypercube is more commonly referred to as an ''n''-cube or sometimes as an ''n''-dimensional cube. The term measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The hypercube is the special case of a hyperrectangle (also called an ''n-orthotope''). A ''unit hypercube'' is a hypercube whose side has length one unit. Often, the hypercube whose corners (or ''vertices'') are the 2''n'' points in R''n'' with each coordinate equal to 0 or 1 is called ''the'' unit hypercube. Construction A hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
