What is the square root of 1/4?
"the arc of length to both sides. Like and , the square root of 5 appears extensively in the formulae for exact trigonometric constants, including in the sines and cosines of every angle whose measure in degrees is divisible by 3 but not by 15. The simplest of these are As such the computation of its value is important for generating trigonometric tables. Since is geometrically linked to half-square rectangles and to pentagons, it also appears frequently in formulae for the geometric properties of figures derived from them, such as in the formula for the volume of a dodecahedron. Hurwitz's"
"Square root In mathematics, a square root of a number ""a"" is a number ""y"" such that ; in other words, a number ""y"" whose ""square"" (the result of multiplying the number by itself, or ) is ""a"". For example, 4 and −4 are square roots of 16 because . Every nonnegative real number ""a"" has a unique nonnegative square root, called the ""principal square root"", which is denoted by , where √ is called the ""radical sign"" or ""radix"". For example, the principal square root of 9 is 3, which is denoted by = 3, because and 3 is"
"1/4 are ""een half"" (""a half"") and ""een kwart"" (""a quarter"") respectively, although the regular ""een tweede"" and ""een vierde"" are also possible, but rarer. In 3/4, the space is often left out: ""driekwart"". When combined with a full cardinal, the full cardinal comes first and they are separated by ""en"" and spaces. The word ""en"" can be left out if the numerator is not 1. The combination 1 1/2 is usually expressed irregularly as ""anderhalf"", which literally means ""other half"" (""ander"" was originally a synonym of ""tweede"", and this combination meant ""second, minus a half""). These express repetition, like"
"Square root of 2 The square root of 2, or the (1/2)th power of 2, written in mathematics as or , is the positive algebraic number that, when multiplied by itself, gives the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property. Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. As a good rational approximation for"
"square root of a positive number is usually defined as the side length of a square with the area equal to the given number. But the square shape is not necessary for it: if one of two similar planar Euclidean objects has the area ""a"" times greater than another, then the ratio of their linear sizes is . A square root can be constructed with a compass and straightedge. In his Elements, Euclid (fl. 300 BC) gave the construction of the geometric mean of two quantities in two different places: Proposition II.14 and Proposition VI.13. Since the geometric mean of"
"Quarter (United States coin) The quarter, short for quarter dollar, is a United States coin worth 25 cents, one-fourth of a dollar. It has a diameter of .955 inches (24.26 mm) and a thickness of .069 inches (1.75 mm). The coin sports the profile of George Washington on its obverse, and its reverse design has changed frequently. It has been produced on and off since 1796 and consistently since 1831. The choice of as a denomination—as opposed to the more common elsewhere—originated with the practice of dividing Spanish milled dollars into eight wedge-shaped segments. ""Two bits"" (that is, two ""pieces"
"three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, formula_3. A geometric mean is often used when comparing different items—finding a single ""figure of merit"" for these items—when each item has multiple properties that have different numeric ranges. For example, the geometric mean can give a meaningful value to compare two companies which are each rated at 0 to 5 for their environmental sustainability, and are rated at 0 to 100 for their financial viability. If an arithmetic mean were used instead of a geometric mean, the financial viability would"
"square tiling, {4,4}. {3,6} are related to the triangular tiling, {3,6}, and {6,3} related to the hexagonal tiling, {6,3}. ""b"" and ""c"" are whole numbers. There are 2 special cases {""b"",0) and (""b"",""b"") with reflective symmetry, while the general cases exist in chiral pairs (""b"",""c"") and (""c"",""b""). Regular maps of the form {4,4} can be represented as the finite regular skew polyhedron {4,4 | ""m""}, seen as the square faces of a ""m""×""m"" duoprism in 4-dimensions. Here's an example {4,4} mapped from a plane as a chessboard to a cylinder section to a torus. The projection from a cylinder to"
"Following : consider the algebra of quaternion-valued continuous functions on the compact space , again with the topology of uniform convergence. If a quaternion ""q"" is written in the form ""q"" = ""a"" + ""ib"";+ ""jc"" + ""kd"" then the scalar part a is the real number (""q"" − ""iqi"" − ""jqj"" − ""kqk"")/4. Likewise being the scalar part of −""qi"", −""qj"" and −""qk"" : b,c and d are respectively the real numbers (−""qi"" − ""iq"" + ""jqk"" − ""kqj"")/4, (−""qj"" − ""iqk"" − ""jq"" + ""kqi"")/4 and (−""qk"" + ""iqj"" − ""jqk"" − ""kq"")/4. Then we may state :"
"of precision is equivalent to that of multiplying two ""n""-digit numbers. Another useful method for calculating the square root is the shifting nth root algorithm, applied for . The name of the square root function varies from programming language to programming language, with codice_1 (often pronounced ""squirt"" ) being common, used in C, C++, and derived languages like JavaScript, PHP, and Python. The square of any positive or negative number is positive, and the square of 0 is 0. Therefore, no negative number can have a real square root. However, it is possible to work with a more inclusive set"
"Four fours Four fours is a mathematical puzzle. The goal of four fours is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four (no other digit is allowed). Most versions of four fours require that each expression have exactly four fours, but some variations require that each expression have the minimum number of fours. The first printed occurrence of this activity is in ""Mathematical Recreations and Essays"" by W. W. Rouse Ball 6th edition published in 1914. In this book it is described as a"
"Quarter (unit) The quarter ( ""one-fourth"") is used as the name of several distinct English units based on ¼ sizes of some base unit. The ""quarter of London"" mentioned by the Magna Carta as the national standard measure for wine, ale, and grain was ¼ ton or tun. It continued to be used, e.g., to regulate the prices of bread. This quarter was a unit of 8 bushels of 8 gallons each, understood at the time as a measure of both weight and volume: the grain gallon or half-peck was composed of 76,800 (Tower) grains weight; the ale gallon was"
"Quart The quart (abbreviation qt.) is an English unit of volume equal to a quarter gallon. It is divided into two pints or four cups. Historically, the exact size of the quart has varied with the different values of gallons over time and in reference to different commodities. Presently, three kinds of quarts remain in use: the and of the US customary system and the of the British imperial system. All are roughly equal to one metric litre. The term comes from the Latin ""quartus"" (meaning one-quarter) via the French ""quart"". However, although the French word """" has the same"
"be written in exponent notation, as ""a"". Square roots of negative numbers can be discussed within the framework of complex numbers. More generally, square roots can be considered in any context in which a notion of ""squaring"" of some mathematical objects is defined (including algebras of matrices, endomorphism rings, etc.) The Yale Babylonian Collection YBC 7289 clay tablet was created between 1800 BC and 1600 BC, showing and /2 = 1/ as 1;24,51,10 and 0;42,25,35 base 60 numbers on a square crossed by two diagonals. (1;24,51,10) base 60 corresponds to 1.41421296 which is a correct value to 5 decimal points"
"on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ or the Coptic letter Ϥ. The magnetic ink character recognition ""CMC-7"" font also uses this variety of ""4"". 4 4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5. Four is the smallest composite number, its proper divisors being and . 4 is the smallest squared prime (""p"") and the only even number in this form. 4 is also the only square one more than a prime number. A number is a multiple of 4 if"
"the generators, though pointed out that the formula has a widely copied misprint in it. A generic quaternary cubic can be written as a sum of 5 cubes of linear forms, unique up to multiplication by cube roots of unity. This was conjectured by Sylvester in 1851, and proven 10 years later by Clebsch. The union of the 5 planes where these 5 linear forms vanish is called the Sylvester pentahedron. Quaternary cubic In mathematics, a quaternary cubic form is a degree 3 homogeneous polynomial in four variables. The zeros form a cubic surface in 3-dimensional projective space. and studied"
"= f = (1/4) [ f + f + f + f ]. After substitution with corresponding inbreeding coefficients, gathering of terms and simplifying, this becomes f = (1/4) [ 3 f + (1/4) [2 f + f + 1 ]] , which is a version for iteration—useful for observing the general pattern, and for computer programming. A ""final"" version is f = (1/16) [ 12 f + 2 f + f + 1 ] . The ""Second Cousins (SC)"" pedigree is on the left. Parents in the pedigree not related to the ""common Ancestor"" are indicated by numerals instead"
"square root of 2 (which is roughly 1.41421) is a well-posed problem. Many algorithms solve this problem by starting with an initial approximation ""x"" to formula_2, for instance ""x"" = 1.4, and then computing improved guesses ""x"", ""x"", etc. One such method is the famous Babylonian method, which is given by ""x"" = ""x""/2 + 1/""x"". Another method, which we will call Method X, is given by ""x"" = (""x"" − 2) + ""x"". We have calculated a few iterations of each scheme in table form below, with initial guesses ""x"" = 1.4 and ""x"" = 1.42. Observe that the"
"Integer square root In number theory, the integer square root (isqrt) of a positive integer ""n"" is the positive integer ""m"" which is the greatest integer less than or equal to the square root of ""n"", For example, formula_2 because formula_3 and formula_4. One way of calculating formula_5 and formula_6 is to use Newton's method to find a solution for the equation formula_7, giving the iterative formula The sequence formula_9 converges quadratically to formula_5 as formula_11. It can be proven that if formula_12 is chosen as the initial guess, one can stop as soon as to ensure that formula_14 For"
"Quaternary cubic In mathematics, a quaternary cubic form is a degree 3 homogeneous polynomial in four variables. The zeros form a cubic surface in 3-dimensional projective space. and studied the ring of invariants of a quaternary cubic, which is a ring generated by invariants of degrees 8, 16, 24, 32, 40, 100. The generators of degrees 8, 16, 24, 32, 40 generate a polynomial ring. The generator of degree 100 is a skew invariant, whose square is a polynomial in the other generators given explicitly by Salmon. Salmon also gave an explicit formula for the discriminant as a polynomial in"
"Square root of 5 The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as: It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are: which can be rounded down to 2.236 to within 99.99% accuracy. The approximation (≈ 2.23611) for the square root"
"4 4 (four) is a number, numeral, and glyph. It is the natural number following 3 and preceding 5. Four is the smallest composite number, its proper divisors being and . 4 is the smallest squared prime (""p"") and the only even number in this form. 4 is also the only square one more than a prime number. A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because . In addition, 2 + 2 = 2 × 2 = 2 = 4. Continuing the"
"Quartic function In algebra, a quartic function is a function of the form where ""a"" is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial. Sometimes the term biquadratic is used instead of ""quartic"", but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form where . The derivative of a quartic function is"
"are real or complex, the roots are The modulus of the roots of a quadratic formula_27 can be no greater than formula_28 where formula_29 is the golden ratio formula_30 The square root of a univariate quadratic function gives rise to one of the four conic sections, almost always either to an ellipse or to a hyperbola. If formula_31 then the equation formula_32 describes a hyperbola, as can be seen by squaring both sides. The directions of the axes of the hyperbola are determined by the ordinate of the minimum point of the corresponding parabola formula_33. If the ordinate is negative,"
"−1, ""i"" and −""i"" (where ""i"" is the imaginary unit). Since we have squared our figure and then taken roots, we cannot always assume that all the roots will be correct. So the correct fourth roots are ""i"" and −""i"", which are the imaginary numbers defined to square to −1. When a number is raised to a complex power, the result is not uniquely defined (see Failure of power and logarithm identities). If this property is not recognized, then errors such as the following can result: The error here is that the rule of multiplying exponents as when going to"
"called a primitive ""n""th root of unity. The negative unit −1 is the only primitive square root of unity. The imaginary unit ""i"" is one of the two primitive 4th roots of unity; the other one is −""i"". The number ""e"" is the primitive ""n""th root of unity with the smallest positive argument. (It is sometimes called the principal ""n""th root of unity, although this terminology is not universal and should not be confused with the principal value of , which is 1.) The other ""n""th roots of unity are given by for . Although there are infinitely many possible"
"Truncated order-4 apeirogonal tiling In geometry, the truncated order-4 apeirogonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{∞,4}. A half symmetry coloring is tr{∞,∞}, has two types of apeirogons, shown red and yellow here. If the apeirogonal curvature is too large, it doesn't converge to a single ideal point, like the right image, red apeirogons below. Coxeter diagram are shown with dotted lines for these divergent, ultraparallel mirrors. From [∞,∞] symmetry, there are 15 small index subgroup by mirror removal and alternation. Mirrors can be removed if its branch orders are all even,"
"12.23. The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular [altitudes]. So, in a ""non-unequal"" cyclic quadrilateral (that is, an isosceles trapezoid), the length of each diagonal is . He continues to give formulas for the lengths and areas of geometric figures, such as the circumradius of an isosceles trapezoid and a scalene quadrilateral, and the lengths of diagonals in a scalene"
"ordered pairs and quaternions as quadruples, then the correspondence is In the complex numbers, C, there are just two numbers, ""i"" and −""i"", whose square is −1 . In H there are infinitely many square roots of minus one: the quaternion solution for the square root of −1 is the unit sphere in R. To see this, let be a quaternion, and assume that its square is −1. In terms of ""a"", ""b"", ""c"", and ""d"", this means To satisfy the last three equations, either or ""b"", ""c"", and ""d"" are all 0. The latter is impossible because ""a"" is"
"the root to 6840.0. There's only one more trick left to describe. If you want to find the square root of a number that isn't an integer, say 54782.917. Everything is the same, except you start out by grouping the digits to the left and right of the decimal point in groups of two. That is, group 54782.917 as and proceed to extract the square root from these groups of digits. During the 19th century, Napier's bones underwent a transformation to make them easier to read. The rods began to be made with an angle of about 65° so that"
"Quartan prime In mathematics, a quartan prime is a prime number of the form ""x"" + ""y"", where ""x"" > 0, ""y"" > 0 (and ""x"" and ""y"" are integers). The odd quartan primes are of the form 16""n"" + 1. For example, 17 is the smallest odd quartan prime: 1 + 2 = 1 + 16 = 17. With the exception of 2 (""x"" = ""y"" = 1), one of ""x"" and ""y"" will be odd, and the other will be even. If both are odd or even, the resulting integer will be even, and 2 is the only"
"Quaternary numeral system Quaternary is the base- numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number. Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number (the other being 36), making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary. However, it fares no better in the localization of prime numbers (the next best being the primorial base six, senary). Quaternary shares with all"
"3-4 duoprism In geometry of 4 dimensions, a 3-4 duoprism, the second smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of a triangle and a square. The ""3-4 duoprism"" exists in some of the uniform 5-polytopes in the B5 family. The quasiregular complex polytope {}×{}, , in formula_1 has a real representation as a 3-4 duoprism in 4-dimensional space. It has 12 vertices, and 4 3-edges and 3 4-edges. Its symmetry is [2], order 12. The birectified 5-cube, has a uniform 3-4 duoprism vertex figure: The dual of a ""3-4 duoprism"" is called a 3-4 duopyramid. It"