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√3 Subdivision Scheme
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3 (number), 3. It is denoted mathematically as \sqrt or 3^. It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property. The square root of 3 is an irrational number. It is also known as Theodorus' constant, after Theodorus of Cyrene, who proved its irrationality. In 2013, its numerical value in decimal notation was computed to ten billion digits. Its decimal expansion, written here to 65 decimal places, is given by : : The fraction \frac (...) can be used as a good approximation. Despite having a denominator of only 56, it differs from the correct value by less than \frac (approximately 9.2\times 10^, with a relative error of 5\times 10^). The rounded value of is correct to within 0.01% of the actual value. The fraction \frac (...) is accurate to 1\times 10^. Archimedes reported a range for its value: (\frac)^>3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties. The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry resembling the molecular known as the trigonal planar molecular geometry. Properties An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered its base. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is defined as a hexagon that is both equilateral and equiangular. In other words, a hexagon is said to be regular if the edges are all equal in length, and each of its internal angle is equal to 120°. The Schläfli symbol denotes this polygon as \ . However, the regular hexagon can also be considered as the cutting off the vertices of an equilateral triangle, which can also be denoted as \mathrm\ . A regular hexagon is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). Measurement The longest diagonals of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled ''CRC Concise Encyclopedia of Mathematics''. The free online version became only partially accessible to the public. In 1999 Weisstein we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Penguin Dictionary Of Curious And Interesting Numbers
''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (). Contents The entries are arranged in increasing order of magnitude, with the exception of the first entry on −1 and ''i''. The book includes some irrational numbers below 10 but concentrates on integers, and has an entry for every integer up to 42. The final entry is for Graham's number. In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short glossary, and a brief bibliography. The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers, Fibonacci numbers, prime numbers, factorials, decimal r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Number
In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are and . The quality of a number being transcendental is called transcendence. Though only a few classes of transcendental numbers are known, partly because it can be extremely difficult to show that a given number is transcendental. Transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers form a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The converse is not true: Not all irrational numbers are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, which represents the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when solving the Helmholtz equation in spherical coordinates. Applications Bessel's equation arises when finding separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry And Trigonometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained unsolved for several centuries. During t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-phase Electric Power
Three-phase electric power (abbreviated 3Ï•) is a common type of alternating current (AC) used in electricity generation, transmission, and distribution. It is a type of polyphase system employing three wires (or four including an optional neutral return wire) and is the most common method used by electrical grids worldwide to transfer power. Three-phase electrical power was developed in the 1880s by several people. In three-phase power, the voltage on each wire is 120 degrees phase shifted relative to each of the other wires. Because it is an AC system, it allows the voltages to be easily stepped up using transformers to high voltage for transmission and back down for distribution, giving high efficiency. A three-wire three-phase circuit is usually more economical than an equivalent two-wire single-phase circuit at the same line-to-ground voltage because it uses less conductor material to transmit a given amount of electrical power. Three-phase power is mainly used dire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Engineering
Power engineering, also called power systems engineering, is a subfield of electrical engineering that deals with the generation, transmission, distribution, and utilization of electric power, and the electrical apparatus connected to such systems. Although much of the field is concerned with the problems of three-phase electric power, three-phase AC power – the standard for large-scale power transmission and distribution across the modern world – a significant fraction of the field is concerned with the conversion between rectifier, AC and DC power and the development of specialized power systems such as those used in aircraft or for electric railway networks. Power engineering draws the majority of its theoretical base from electrical engineering and mechanical engineering. History Pioneering years Electricity became a subject of scientific interest in the late 17th century. Over the next two centuries a number of important discoveries were made including the incandes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vesica Piscis
The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. In Latin, "" literally means "bladder of a fish", reflecting the shape's resemblance to the conjoined dual air bladders (swim bladder) found in most fish. In Italian, the shape's name is ' ("almond"). A similar shape in three dimensions is the lemon. This figure appears in the first proposition of Euclid's ''Elements'', where it forms the first step in constructing an equilateral triangle using a compass and straightedge. The triangle has as its vertices the two disk centers and one of the two sharp corners of the vesica piscis. Mathematical description Mathematically, the vesica piscis is a special case of a lens, the shape formed by the intersection of two disks. The mathematical ratio of the height of the vesica piscis to the width across its center is the squar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with 1, unit s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space Diagonal
In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with '' face diagonals'', which connect vertices on the same face (but not on the same edge) as each other. For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals. Axial diagonal An axial diagonal is a space diagonal that passes through the center of a polyhedron. For example, in a cube with edge length ''a'', all four space diagonals are axial diagonals, of common length a\sqrt . More generally, a cuboid with edge lengths ''a'', ''b'', and ''c'' has all four space diagonals axial, with common length \sqrt. A regular octahedron has 3 axial diagonals, of length a\sqrt , with edge length ''a''. A regular icosahedron has 6 axial diagonals of length a\sqrt , where \varphi is the golden ratio (1+\sqrt 5)/2.. Space diagon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
