|
| |
| | Square root - encyclopedia article about Square root. |
 | | where the sign of the imaginary part of the root is the same as the sign of the imaginary part of the original number. | | | As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. | | | The term was coined by René Descartes in 1637 in his La Géométrie and was meant to be derogatory. |
|
http://encyclopedia.thefreedictionary.com/square%20root
|
|
| |
| | SQUARE ROOT THEORY |
| | The 0 in 01 corresponds to mutliplying by 2; the 1 is a new trial bit. | | | where "current" is the current square root and "digit" is the next digit produced by the algorithm. | | | In other words, x is built up one bit at a time, starting with the most significant bit. |
|
http://www.dattalo.com/technical/theory/sqrt.html
|
|
| |
| | Square Root |
| | They are complex-conjugate iff (= if and only if) the original number is real-complex and negative. | | | In the field of complex numbers, to which we will confine ourselves, henceforth, there always exist a pair of roots, whose sum is zero. | | | This method is prefared for finding roots of complex numbers. |
|
http://www.rism.com/Trig/square.htm
|
|
| |
| | Radicals Lesson - I |
| | However, we need first to cover the notation for these other radicals. | | | Non-square-root radicals need a number to indicate which root is meant. | | | Now, you can take any counting number and square it, and end up with a nice neat number. |
|
http://www.purplemath.com/modules/radicals.htm
|
|
| |
| | square.root |
| | Anyway, even sticking with the usual notation, this complex conjugation business is a bit peculiar. | | | When I teach complex analysis, I like to motivate the complex numbers as follows: multiplication by the real number x is a linear transformation of the real line which amounts to dilating by a factor of x when x is positive, but dilating and reflecting when x is negative. | | | To solve this insolvable problem we went up to two dimensions, invented i, and patted ourselves on the back for being so clever. |
|
http://math.ucr.edu/home/baez/square.root.html
|
|
| |
| | ARM code square root routines |
| | For 3-cycle per bit we have to leave one instruction out... | | | Wilco Dijkstra suggested optimising the C code to produce the following code which takes 9 cycles/bit: | | | Also fixed point versions are possible, or roots of 64 bit numbers. |
|
http://www.finesse.demon.co.uk/steven/sqrt.html
|
|
| |
| | How the ENIAC took a Square Root |
| | Therefore to do the twice 8516 additions/subtractions would take 3.4 seconds! | | | The above algorithm can be made more efficient. | | | Division and taking a square root was orchestrated as a series of subtractions/additions and shifts which like the Multiplier made use of a number of accumulators but unlike the Multiplier contained no special computational hardware to do either; in other words it used accumulators to do the needed addition and subtraction. |
|
http://www4.wittenberg.edu/academics/mathcomp/bjsdir/ENIACSquareRoot.htm
|
|
| |
| | Hashing on the Internet |
| | How do I start my own hash (thanks to Zippy for the text)? | | | Please send comments on, additions to, corrections of, and cruel and baseless criticisms of this document to Square Root, T&AHHH hwills@freenet.tlh.fl.us and Heatseeker wilkinsn@sdsc.edu. |
|
http://users.sdsc.edu/~wilkinsn/hashing.internet.html
|
|
| |
| | Square Root - Abacus Arithmetic by Welton J. Crook |
| | This number, on the left, is called the "root" number. | | | Subtract 41 from 84 leaving 43 in the "square" number. | | | Proceed as in Example I. Subtract 1 from 97, leaving 96. |
|
http://webhome.idirect.com/~totton/soroban/squareroot.html
|
|
| |
| | Square Root Extraction Method in the Nine Chapters |
| | (This is the algorithm of the ladder system of root extraction.) Or just double the number in R2 to get 2a. | | | (This is the algorithm of the ladder system of root extraction.) Or double the number b in R2 to get 2(a + b). | | | Add the product (a) to the number in R2. |
|
http://www.math.sfu.ca/histmath/China/1stCenturyAD/NineSquareRoot.html
|
|
| |
| | Square Root Algorithm Derivation |
| | This is your next number to work with. | | | This is usually not the case, which means there is a part of the first two (or one) digits which has not been accounted for and our approximation is not perfect. | | | Therefore, if a number is divided into groups of two digits each from the decimal point to the left, the number of digits in the integer part of the square root of that number will be equal to the number of groups of figures. |
|
http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Challen/squareroot/sqrt.html
|
|
| |
| | square root on Encyclopedia.com |
| | Thursdays With a Twist Brings Free Concerts, Farmers Market to Market Square. | | | Publication: AP Worldstream; Author: NEKESA MUMBI MOODY, AP Music Writer ; Source: NEWSPAPERS | | | My Life in a Column: All my Turkish roots came back to me as I shoved tenners down a belly-dancer's bra.(Features) |
|
http://www.encyclopedia.com/html/X/X-squarero.asp
|
|
| |
| | square root |
| | We previously subtracted A² from S. To scale to 100A², we bring down two more digits (a factor of 100) of the size of S. We write down twice A (2A), but shifted one place to leave room for B (10 × 2A or 2 × 10A). | | | That is, we have improved our knowledge of the square root by one digit, B. We take whatever remains, scale again by 100, by bringing down two more digits, and repeat the process. | | | Repeat: bring down the next two digits, and double the number on top (2x25=50) to make a "divisor", with another unit. |
|
http://www.nist.gov/dads/HTML/squareRoot.html
|
|
| |
| | Intermediate Test Prep (Grades7-8) More on Square Roots |
| | However, their square roots are not whole numbers, they are decimals or fractional parts of whole numbers. | | | For the purpose of this lesson we will simply tell which two consecutive whole numbers the square root of a whole number is between. | | | Whole numbers that are not perfect squares still have square roots. |
|
http://www.oswego.org/mtestprep/math8/a/squarerootsl.cfm
|
|
| |
| | Square Root Algorithm |
| | Double the number above the square root sign and write the result to the left of the subtraction answer. | | | Write this number to the left and on top of the square root sign. | | | Write the number 2 in the blank and on top of the square root nuxt to the four. |
|
http://jwilson.coe.uga.edu/EMT668/EMAT4680.folders/Nowlen/squareroot.html
|
|
| |
| | Question Corner -- What is the Square Root of i? |
| | The square root of this number also has a distance of 1 from the origin and forms an angle with the real axis which is 1/2 of the angle corresponding to the original number. | | | Note however that when taking the square root of a complex number it is also important to consider these other representations. | | | However, the easiest and most insightful way to take the square root of a complex number (as well as any higher order roots) is to use the geometric representation of the complex numbers. |
|
http://www.math.toronto.edu/mathnet/plain/questionCorner/rootofi.html
|
|
| |
| | Calculate square root without a calculator |
| | Depending on the child, it might be good to concentrate first on teaching the concept of square root without taking the time for paper-pencil calculations. | | | First group the numbers under the root in pairs from right to left, leaving either one or two digits on the left (6 in this case). | | | The method you show in the article is archaic. |
|
http://www.homeschoolmath.net/other_topics/square-root-algorithm.php
|
|
| |
| | Numbers - Square Roots - First Glance |
| | The perfect squares are the squares of the whole numbers. | | | Remember, the square of a number is that number times itself. | | | The square root of a number, n, written below is the number that gives n when multiplied by itself. |
|
http://www.math.com/school/subject1/lessons/S1U1L9GL.html
|
|
| |
| | Square root algorithms |
| | This method dating back to the Babylonians (1700 B.C.) is known as the Babylonian Algorithm. | | | Its distinguishing feature is that if the square root is rational, then the algorithm obtains the square root exactly and in a finite number of steps. | | | To see if this procedure extends to integers with more digits, let us extract the square root of 119025 which is the square of 345. |
|
http://www.mathpath.org/Algor/algor.square.root.htm
|
|
| |
| | Paul Hsieh's Square Root page |
| | One might be for performance reasons either with or without compromises in accuracy, and another is because we might be on a system that simply does not support good performing square roots. | | | An improvement over using IEEE-754 tricks is to simply perform a table look up with the most significant bits of the mantissa. | | | If b = 0, then only one of the components is nonzero and can be either sign. |
|
http://www.azillionmonkeys.com/qed/sqroot.html
|
|
| |
| | Grade 8: Square Root |
| | Square - the length of the side of the square is the square root | | | The square root is the length of one side of the square. | | | If a square does not form, repeat the directions above. |
|
http://home.earthlink.net/~sondybeamer/homework/algebra/roots/Square_Root.html
|
|
| |
| | Root mean square - Wikipedia, the free encyclopedia |
| | Furthermore, because RMS implies some form of averaging, expressions such as "peak RMS power", sometimes used in advertisements for audio amplifiers, are meaningless. | | | The name comes from the fact that it is the square root of the mean of the squares of the values. | | | It is a power mean with the power t = 2. |
|
http://en.wikipedia.org/wiki/Root_mean_square
|
|
| |
| | Proportions: Golden Section or Golden Mean, Modulor, Square Root of Two, Theorie and Construction |
| | All other trademarks and copyrights remain property of their respective holders. | | | But that may have to do with the underlying structuring into non-equal divisions that establish scale and generate more interest because of the increased amount of detail that is generated or that is cause of the inequal divisions. | | | This process can be continued ad infinitum, and similarly inversed by adding a square over the longer side of a golden section rectangle, thus establishing a proportional relationship over the entire imaginable scale of human artifacts. |
|
http://home.att.net/~vmueller/prop/theo.html
|
|
| |
| | Square Root |
| | Remember to place the decimal point in the square root just above the decimal point in the original number. | | | Multiply this number by that mystery digit, then write this product below the numbers you've written so far. | | | Determine the highest perfect square that is less than or equal to the first pair of digits. |
|
http://mcraeclan.com/mathhelp/BasicWordSquareRootDivision.htm
|
|
| |
| | Complex Numbers Lesson - I |
| | Now, however, you can take the square root of a negative number, but it involves using a new number to do it. | | | So you couldn't very well square-root a negative and expect to come up with anything sensible. | | | Up until now, you've been told that you can't take the square root of a negative number. |
|
http://www.purplemath.com/modules/complex.htm
|
|
| |
| | Hamilton - Math To Build On: Square Roots |
| | The variables in the last three examples show another rule of math: | | | The square root of a number squared is the number. | | | The square root of a number is best described by the question: |
|
http://mathforum.org/~sarah/hamilton/ham.squareroots.html
|
|
| |
| | Synopses of Topics - Square Roots and Other Radicals |
| | Roots of powers When taking the nth root of a power, such as | | | The expression under the root sign is called the radicand. | | | When you are adding or terms which contain square roots in a denominator, you may find it helpful to write the expression as a single fraction. |
|
http://math.usask.ca/emr/roots.html
|
|
| |
| | Square root quotes & quotations |
| | "The theme is the theme of humiliation, which is the square root of sin, as opposed to the freedom from humiliation, and love, which is the square root of wonderful. | | | "The intelligence of the creature known as a crowd, is the square root of the number of people in it. | | | "Adam and Eve are like imaginary number, like the square root of minus one... |
|
http://en.thinkexist.com/quotes/with/keyword/square_root
|
|
| |
| | YBC 7289 |
| | must be the 'coefficient of the diagonal of a square' and, indeed we do have an Old Babylonian coefficient list that has this number (see MCT text Ue (YBC 7243)). | | | From the positioning of the numbers, the natural interpretation to make is that a square with side of length | | | On one side of the square is written the number |
|
http://it.stlawu.edu/~dmelvill/mesomath/tablets/YBC7289.html
|
|
| |
| | [No title] |
| | This is the squared version of the signal, and its mean value is 1/2, as shown. | | | The power is what is important to run electrical equipment. | | | Without further computations, consider a squarewave signal which goes peak-to-peak from +1 Volt to -1 Volt. |
|
http://www.ee.unb.ca/tervo/ee2791/vrms.htm
|
|
| |
| | Fast Square Root Calc |
| | This algorithm is already pretty fast, but its speed is limited by the fact that each iteration requires a double-precision division which is the slowest PowerPC floating-point instruction with 32 cycles on the MPC601 (Motorola, 1993). | | | The code could be modified to make use of the floating reciprocal square root estimate instruction (frsqrte) that is available on the MPC603 and MPC604 processors, and which has an accuracy of 5 bits. | | | The implementation presented here performs the square root of a double-precision number over the full range of representation of the IEEE 754 standard for normalized numbers (from 2.22507385851E-308 to 1.79769313486E308) with an accuracy of 15 or more decimal digits. |
|
http://www.mactech.com:16080/articles/mactech/Vol.14/14.01/FastSquareRootCalc
|
|
| |
| | The Root Mean Square |
| | Instead of wiping out the signs, they square every number (which makes them all positive), then take the square root of the average. | | | For reasons of their convenience, they chose a different approach. | | | The root-mean-square (RMS) is not a statistic you hear to much about, because it is mostly used as a part of other statistics, such as the standard deviation, which are much more famous. |
|
http://www.analytictech.com/mb313/rootmean.htm
|
|
| |
| | Quia - Square Roots |
| | Find the square root of a perfect square number. | | | See a list of terms used in these activities. |
|
http://www.quia.com/jg/65631.html
|
|
| |
| | Higher Radix Square Root with Prescaling |
| | A scheme for performing higher radix square root based on prescaling of the radicand is presented to reduce the complexity of the result-digit selection. | | | An estimate of the execution time for a radix-256 unit for double-precision square root and a comparison with other implementations indicate that the proposed approach is an alternative to consider when designing a square-root unit. | | | Fandrianto, "Algorithm for high speed shared radix 8 division and radix 8 square root," in Proc. |
|
http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tc/&toc=comp/trans/tc/1992/08/t8toc.xml&DOI=10.1109/12.156542
|
|
| |
| | Root Mean Square Dance in ZhurnalWiki |
| | This shows the power of the long run on the root mean square --- similar to the long run's power to improve stamina. | | | In 2003 I managed 1110 miles, for a MDM of 3.0, less than 10% greater than the previous year --- but my RMSDM increased a dramatic 23% to 5.8 miles. | | | That process emphasizes the largest of the input values --- precisely what a good distance-running metric should do. |
|
http://zhurnal.net/ww/zw?RootMeanSquareDance
|
|
| |
| | Table of Squares and Square Roots |
| | For instance, if you want to find the square root of 2000, look in the middle column until you find the number that is closest to 2000. | | | Square the average to see how close the number is to 12: | | | Now look in at the number to the left of 2,025 to find its square root. |
|
http://www.factmonster.com/ipka/A0875883.html
|
|
| |
| | Square Root on Your Computer's Calculator |
| | So, raising a number to the one-half power means taking its square root. | | | To square, raise to the second power -- the 2 power. | | | -- The square of a square root is the original number. |
|
http://www.mathnstuff.com/math/spoken/here/2class/400/sqrt.htm
|
|
| |
| | Square Root :: MrExcel Message Board |
| | The nth root is always the reciprocal of it's corresponding power exponent. | | | For example the ^ caret symbol is used exponents - is there a symbol for sqaure root or do you have to use the STDEV formula? |
|
http://www.mrexcel.com/archive2/52900/61448.htm
|
|
| |
| | Irrationality of Sqrt(2) (PRIME) |
| | In other words, we want to assume the contrary statement, namely, we want to begin by assuming that the square root of two is rational, and then see what happens. | | | This result, among the most elegant in mathematics, was known to the Greeks and is therefore quite ancient. | | | Often in mathematics, such a statement is proved by contradiction, and that is what we do here. |
|
http://www.mathacademy.com/pr/prime/articles/irr2
|
|
| |
| | Square root of 2 home page |
| | It is also of some historical interest since it was the first known irrational number. | | | The first 1000 digits or so of the square root of 2 that I have calculated are shown below: | | | Compute your own square root to 70 or 300 places!!! |
|
http://www.rossi.com/sqr2.htm
|
|
| |
| | Archimedes and the Square Root of 3 |
| | Setting this difference to 1 gives the Pell equation.) Otherwise it would be very hard to explain how they could have arrived at the two convergents 265/153 and 1351/780, each of which is a "best rational approximation" up to the respective denominators. | | | (The latter naturally arises if we seek a rational square (x/y)^2 just slightly greater then 3, which means we want the integer x^2 to be just slightly greater than the integer 3y^2. | | | Given a number A, if one writes it as a^2 +- b where a^2 is the rational square nearest to A, larger or smaller, and b is the remainder, then a +- b/2a > sqrt(A) > a +- b/(2a+-1). |
|
http://mathpages.com/home/kmath038.htm
|
|
| |
| | Principal square root of positive real number |
| | So the square root of a positive real number has two values, differing only in sign. | | | This is exemplified by the formula for the root of a quadratic equation, say ax | | | The world of mathematics has adopted the former. |
|
http://www.mathpath.org/concepts/principal.square.root.htm
|
|
| |
| | Irrationality of the square root of 2. |
| | Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. | | | The following proof is a classic example of a proof by contradiction: We want to show that A is true, so we assume it's not, and come to contradiction. | | | Certainly it has profoundly affected mathematics and philosophy from the time of the Greeks to the present day. |
|
http://www.math.utah.edu/~alfeld/math/q1.html
|
|
| |
| | The Hutchinson Dictionary of Science: square root@ HighBeam Research |
| | As an exponent, a square root is represented by(to the power of 1)/(subscript2), for example, 16(to the power of(to... | | | In mathematics, a number that when squared (multiplied by itself) equals a given number. | | | For example, the square root of 25 (written [radical ]25) is andplusmn; 5, because 5 and#215; 5 = 25, and (-5) and#215; (-5) = 25. |
|
http://www.highbeam.com/library/doc0.asp?DOCID=1P1:28916844&refid=ip_encyclopedia_hf
|
|
| |
| | search.cpan.org: Quantum::Usrn - Square root of not. |
| | On Monday 26th February 2001 I went to hear Damian Conway give his talk on Quantum::Superpositions at London.pm. | | | Applying Usrn to a value will produce noise; applying Usrn to that noise will produce the bitwise negation of the original value. | | | After explaining its properties (see above) he said "it is unlikely that you will see this operator in Perl any time soon". |
|
http://search.cpan.org/~kasei/Quantum-Usrn-1.00/Usrn.pm
|
|
| |
| | DFPSQRT: Floating Point Pipelined Square Root Unit |
| | The DFPSQRT uses the pipelined mathematics algorithm to compute square root function. | | | The input number format is according to IEEE-754 standard. | | | Fully synthesizable, static synchronous design with no internal tri-states |
|
http://www.latticesemi.com/products/devtools/ip/dcd/dfpsqrt.cfm
|
|
| |
| | Square Root Solutions; Inc. A New Media Agency |
| | Our experience and commitment to detail and quality can be seen in every project we create. | | | Square Root Solutions (SRS) provides innovative Web-based communication solutions and creative services, specializing in corporate Web sites, custom Web-based applications, Web site content management, and special creative marketing pieces. |
|
http://www.squareroot-inc.com
|
|
|
