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| [[File:Kushyar ibn Labban division.GIF|thumb|right|200px|division algorithm as described in ''Principles of Hindu Reckoning''<br><math>\tfrac{5625}{243}=23\tfrac{36}{243}</math>]]
| | Making sure you have the correct size is very important; a poor fitting helmet can be uncomfortable and unsafe. For more serious cyclists, next to bicycles themselves, proper shoes are the most important piece of equipment. If you go on a regular mountain biking, you will develop a healthier body and disposition. There should not be a strain and similarly you shouldn't find yourself catching your breath. Just like coasting, you'll also spend a great deal of time pedaling while standing. <br><br>If you reverse breathe it means that you are trying to fill up something that is deflating. In fact, Downhill Mountain biking is the most popular form of competition biking. Is it best to purchase a MTB from your local mountain bike shop or go online. From personal experience they can be not easy to maintain by yourself so a mechanical system may be better for you. A smart shopper knows his or her rights, and you should also know this before finalizing any purchase or transaction online. <br><br>The steeper the angles, the more beneficial it would be for stability and high speed pedaling. If you do it as soon as you get home, then its done and you can concentrate on eating and relaxing. There are great coaches, who will train you to tweet like a bird in spring or Link in, befriend and get a fan page. Mounting biking is a fun sport for professionals and beginners alike. The bike shop personnel should be able to advise you on how to choose the right frame size. <br><br>June 2011 saw the successful launch of my very first book, WELCOME TO YOUR LIFE – simple insights for your inspiration & empowerment (. If you have any issues with regards to wherever and how to use [http://fungonline.com/profile/124586/jumaestas Info size bike mountain bike sizing.], you can make contact with us at the web site. Bikes are a great way to get around - they're fun, they're cheap to fuel (they burn only calories) and they're a great way to get fit. The apparel worn by rider is very much for their safety or protection. The back chain ring is a cog set featuring seven, eight or nine cogs, depending on how many "speeds" you have (21, 24 or 27). One of the problems is that they just haven't caught on and become commercially available enough to make them an everyday sight. <br><br>If you can afford it, a full suspension mountain bike is always worth the purchase. Listed below are some of the common terms which you will come across. Something that sounds to me, to be nothing more than hard work. The price range of lightweight bicycles prices vary from $200. The kids will have a blast exploring any one of the six river parks, and more specifically, walking the suspension bridge across to Fishtrap Park. |
| '''''Principles of Hindu Reckoning''''' (''Kitab fi usul hisab al-hind'') is a mathematics book written by 10th–11th-century Persian mathematician [[Kushyar ibn Labban]]. It is the second-oldest book extant in Arabic about Hindu arithmetic using [[Hindu numerals]]( ० ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹), preceded by ''Kibab al-Fusul fi al-Hisub al-Hindi'' by [[Abu'l-Hasan al-Uqlidisi|Abul al-Hassan Ahmad ibn Ibrahim al-Uglidis]], written in 952. Although [[Al-Khwarzimi]] also wrote a book about Hindu arithmetics in 825, he did not use Hindu numerals, and the Arabic original was lost, only a 12th-century translation is extant. Kushyar ibn Labban did not mention the Indian sources for ''Hindu Reckoning'', and there is no earlier Indian book extant which covers the same topics as discussed in this book. ''Principles of Hindu Reckoning'' becomes one of the foreign sources for Hindu Reckoning in the 10th–11th century in India.
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| ==Indian dust board==
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| Hindu arithmetic was conducted on a dust board similar to the Chinese counting board. A dust board is a flat surface with a layer of sand and lined with grids. Very much like the Chinese count rod numerals, a blank on a sand board grid stood for zero, and zero sign was not necessary.<ref>George Ifrah, The Universal History of Numbers, p554</ref> Shifting of digits involves erasing and rewriting, unlike counting board.
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| ==Content==
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| There is only one Arabic copy extant, now kept in the Aya Sophya Library in Istanbul. There is also a Hebrew translation with commentary, kept in the [[Bodleian Library]] of [[Oxford University]]. In 1965 University of Wisconsin Press published an English edition of this book translated by Martin Levey and Marvin Petruck, based on both the Arabic and Hebrew editions. This English translation included 31 plates of facsimile of original Arabic text.<ref>Martin Levey and Marvin Petruck tr, Kushyar Ibn Labban, ''Principles of Hindu Reckoning'', The University of Wisconsin Press, 1965. Library of Congress Catalog 65-11206</ref>
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| ''Principles of Hindu Reckoning'' consists of two parts dealing with arithmetics in two numerals system in India at his time.
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| * Part I mainly dealt with decimal algorithm of subtraction, multiplication, division, extraction of square root and cubic root in place value [[Hindu–Arabic numeral system|Hindu-numeral]] system. However, a section on "halving", was treated differently, i.e., with a hybrid of decimal and sexagesimal numeral.
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| The similarity between decimal Hindu algorithm with Chinese algorithm in [[Mathematical Classic of Sun Zi]] are striking,<ref>Lam Lay Yong, Ang Tian Se, Fleeting Footsteps, p52</ref> except the operation halving, as there was no hybrid decimal/sexagesimal calculation in China.
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| * Part II dealt with operation of subtraction, multiplication, division, extraction of square root and cubic root in [[sexagesimal]] number system. There was only positional decimal arithmetic in China, never any sexagesimal arithmetic.
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| * Unlike [[Abu'l-Hasan al-Uqlidisi]]'s ''Kitab al-Fusul fi al-Hisab al-Hindi'' (''The Arithmetics of Al-Uqlidisi'') where the basic mathematical operation of addition, subtraction, multiplication and division were described in words, ibn Labban's book provided actual calculation procedures expressed in Hindu-Arabic numerals.
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| ==Decimal arithmetics==
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| ===Addition===
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| [[File:Rod calculus addition.GIF|thumb|left|150px|Rod calculus addition]]
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| [[File:LABBANADD.GIF|thumb|right|150px|Hindu addition ala ibn Labban]]
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| Kushyar ibn Labban described in detail the addition of two numbers.
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| The Hindu addition is identical to rod numeral addition in [[Mathematical Classic of Sun Zi]]<ref>Lam Lay Yong, Ang Tian Se, Fleeting Footstep, p 47 World Scientific</ref>
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| {| border="0" width="500" align="center" style="border: 1px solid #999; background-color:#FFFFFF"
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| |-align="center" bgcolor="#EFEFEF"
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| ! operation
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| ! Rod calculus
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| ! Hindu rekoning
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| |-align="center" bgcolor="#EFEFEF"
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| | Layout
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| | Arrange two numbers in two rows
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| | Arrange two numbers in two rows
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| |-align="center" bgcolor="#EFEFEF"
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| | order of calculation
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| | from left to right
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| | from left to right
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| |-align="center" bgcolor="#EFEFEF"
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| | result
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| | placed on top row
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| | Placed on top row
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| |-align="center" bgcolor="#EFEFEF"
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| |remove lower row
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| |remove digit by digit from left to right
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| |digit not removed
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| |}
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| There was a minor difference in the treatment of second row, in Hindu reckoning, the second row digits drawn on sand board remained in place from beginning to end, while in rod calculus, rods from lower rows were physically removed and add to upper row, digit by digit.
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| ===Subtraction===
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| [[File:SUNZISUB.GIF|thumb|left|150px|400AD Sun Zi subtraction algorithm]] | |
| [[File:LABBANSUB.GIF|thumb|right|150px|11th-century Hindu subtraction 5625–839]]
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| In the 3rd section of his book, Kushyar ibn Labban provided step by step algorithm for subtraction of 839 from 5625. Second row digits remained in place at all time. In rod calculus, digit from second row was removed digit by digit in calculation, leaving only the result
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| in one row.
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| ===Multiplcation===
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| [[File:Multiplication algorithm.GIF|thumb|left|150px|Sun Zi multiplcation]]
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| [[File:Labban multiplication.GIF|thumb|right|150px|ibn Labban multiplication]]
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| Kushyar ibn Labban multiplication is a variation of Sun Zi mulitiplication.
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| {| border="0" width="500" align="center" style="border: 1px solid #999; background-color:#FFFFFF"
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| |-align="center" bgcolor="#EFEFEF"
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| ! operation
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| ! Sun Zi
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| ! Hindu
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| |-align="center" bgcolor="#EFEFEF"
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| | multiplicant
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| | placed at upper row,
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| | placed at upper row,
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| |-align="center" bgcolor="#EFEFEF"
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| | multiplier
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| | third row
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| | 2nd row below multiplicant
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| |-align="center" bgcolor="#EFEFEF"
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| | alignment
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| | last digit of multiplier with first digit of multiplcant
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| | last digit of multiplier with first digit of multiplcant
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| |-align="center" bgcolor="#EFEFEF"
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| |multiplyier padding
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| |rod numeral blanks
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| |rod numeral style blanks, not Hindu numeral 0
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| |-align="center" bgcolor="#EFEFEF"
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| | order of calculation
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| | from left to right
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| | from left to right
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| |-align="center" bgcolor="#EFEFEF"
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| |product
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| |placed at center row
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| |merged with multiplicant
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| |-align="center" bgcolor="#EFEFEF"
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| | shifiting of multiplier
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| |one position to the right
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| |one position to the right
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| |-align="center" bgcolor="#EFEFEF"
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| |}
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| ===Division===
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| Professor [[Lam Lay Yong]] discovered that the Hindu division method describe by Kushyar ibn Labban is totally identical to rod calculus division in 5th century[[Mathematical Classic of Sun Zi]]<ref>Lam Lay Yong, Ang Tian Se, Fleeting Footstep, p43, World Scientific</ref>
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| [[File:Sunzi division.GIF|thumb|left|150px|Sunzi division algorithm for <math>\tfrac{6561}{9}</math>]]
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| [[File:Kushyar ibn Labban division.GIF|thumb|right|150px|Hindu decimal division <math>\tfrac{5625}{243}</math>ala ibn Labban]]
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| {| border="0" width="500" align="center" style="border: 1px solid #999; background-color:#FFFFFF"
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| |-align="center" bgcolor="#EFEFEF"
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| ! operation
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| ! Sun Zi division
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| ! Hindu division
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| |-align="center" bgcolor="#EFEFEF"
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| | dividend
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| | on middle row,
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| | on middle row,
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| |-align="center" bgcolor="#EFEFEF"
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| | divisor
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| | divisor at bottom row
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| | divisor at bottom row
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| |-align="center" bgcolor="#EFEFEF"
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| |Quotient
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| |placed at top row
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| |placed at top row
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| |-align="center" bgcolor="#EFEFEF"
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| |divisor padding
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| |rod numeral blanks
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| |rod numeral style blanks, not Hindu numeral 0
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| |-align="center" bgcolor="#EFEFEF"
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| | order of calculation
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| | from left to right
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| | from left to right
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| |-align="center" bgcolor="#EFEFEF"
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| |Shifting divisor
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| |one position to the right
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| |one position to the right
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| |-align="center" bgcolor="#EFEFEF"
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| | Remainder
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| | numerator on middle row,denominator at bottom
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| | numerator on middle row,denominator at bottom
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| |-align="center" bgcolor="#EFEFEF"
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| |}
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| Besides the totally identical format, procedure and remainder fraction, one tell tell sign which discloses the origin of this division algorithm is in the missing 0 after 243, which in true Hindu numeral should be written as 2430, not 243blank; blank space is a feature of rod numerals (and abacus).
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| ===Divide by 2===
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| Divide by 2 or "halving" in Hindu reckoning was treated with a hybrid of decimal and sexagesimal numerals:
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| It was calculated not from left to right as decimal arithmetics, but from right to left:
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| After halving the first digit 5 to get 2{{frac|1|2}}, replace the 5 with 2, and ''write 30 under it'':
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| :::::::: 5622
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| :::::::: 30
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| Final result:
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| ::::::::: 2812
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| ::::::::: 30
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| ===Extraction of square root===
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| [[File:Sunzi sqrt.GIF|thumb|left|250px|Sun Zi algorithm for sqrt of 234567=383<math>\tfrac{311}{968}</math>]]
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| [[File:Labbansqrt.GIF|thumb|right|250px|ibn Labban square root of 63342]]
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| Kushyar ibn Labban described the algorithm for extraction of square root with example of
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| <math>\sqrt(63342)=255\frac{371}{511}</math>
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| Kushyar ibn Labban square root extraction algorithm is basically the same as Sun Zi algorithm
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| {| border="0" width="500" align="center" style="border: 1px solid #999; background-color:#FFFFFF"
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| |-align="center" bgcolor="#EFEFEF"
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| ! operation
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| ! Sun Zi square root
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| ! ibn Labban sqrt
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| |-align="center" bgcolor="#EFEFEF"
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| | dividend
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| | on middle row,
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| | on middle row,
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| |-align="center" bgcolor="#EFEFEF"
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| | divisor
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| | divisor at bottom row
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| | divisor at bottom row
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| |-align="center" bgcolor="#EFEFEF"
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| |Quotient
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| |placed at top row
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| |placed at top row
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| |-align="center" bgcolor="#EFEFEF"
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| |divisor padding
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| |rod numeral blanks
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| |rod numeral style blanks, not Hindu numeral 0
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| |-align="center" bgcolor="#EFEFEF"
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| | order of calculation
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| | from left to right
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| | from left to right
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| |-align="center" bgcolor="#EFEFEF"
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| |divisor doubling
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| |multiplied by 2
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| |multiplied by 2
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| |-align="center" bgcolor="#EFEFEF"
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| |Shifting divisor
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| |one position to the right
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| |one position to the right
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| |-align="center" bgcolor="#EFEFEF"
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| |Shifting quotient
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| |Positioned at beginning, no subsequent shift
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| |one position to the right
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| |-align="center" bgcolor="#EFEFEF"
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| | Remainder
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| | numerator on middle row,denominator at bottom
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| | numerator on middle row,denominator at bottom
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| |-align="center" bgcolor="#EFEFEF"
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| | final denominator
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| | no change
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| | add 1
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| |-align="center" bgcolor="#EFEFEF"
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| |}
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| The approximation of non perfect square root using Sun Zi algorithm yields result slightly higher than the true value in decimal part, the square root approximation of Labban gave slightly lower value, the integer part are the same.
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| ==Sexagesimal arithmetics==
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| ===Multiplication===
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| The Hindu sexagesimal multiplication format was completely different from Hindu decimal arithmetics. Kushyar ibn Labban's example | |
| of 25 degree 42 minutes multiplied by 18 degrees 36 minutes was written vertically as
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| :::::::::::::: 18| |25
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| :::::::::::::: 36| |42
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| with a blank space in between<ref>Kushyar ibn Labban, ''Principles of Hindu Reckoning'', p80, Wisconsin</ref>
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| ==Influence==
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| Kushyar ibn Labban's ''Principles of Hindu Reckoning'' exerted strong influence on later Arabic algorists. His student [[al-Nasawi]] followed his teacher's method. Thirteen century algorist [[Jordanus de Nemore]]'s work was influenced by al-Nasawi. As late as 16th century, ibn Labban's name was still mentioned<ref>Note by Martin Levey and Marvin Petruck to ''Principles of Hindu Reckoning'' pp 40–42</ref>
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| ==References==
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| {{Reflist}}
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| ==External links==
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| *[http://sciences.aum.edu/~sbrown/Hindu%20Arabic%20and%20Chinese.pdf The Development of Hindu-Arabic and Traditional Chinese Arithematics, Chinese Science 13 1996, 35-54 ]
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| {{DEFAULTSORT:Principles Of Hindu Reckoning}}
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| [[Category:Indian mathematics]]
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| [[Category:Mathematical works of medieval Islam]]
| |
Making sure you have the correct size is very important; a poor fitting helmet can be uncomfortable and unsafe. For more serious cyclists, next to bicycles themselves, proper shoes are the most important piece of equipment. If you go on a regular mountain biking, you will develop a healthier body and disposition. There should not be a strain and similarly you shouldn't find yourself catching your breath. Just like coasting, you'll also spend a great deal of time pedaling while standing.
If you reverse breathe it means that you are trying to fill up something that is deflating. In fact, Downhill Mountain biking is the most popular form of competition biking. Is it best to purchase a MTB from your local mountain bike shop or go online. From personal experience they can be not easy to maintain by yourself so a mechanical system may be better for you. A smart shopper knows his or her rights, and you should also know this before finalizing any purchase or transaction online.
The steeper the angles, the more beneficial it would be for stability and high speed pedaling. If you do it as soon as you get home, then its done and you can concentrate on eating and relaxing. There are great coaches, who will train you to tweet like a bird in spring or Link in, befriend and get a fan page. Mounting biking is a fun sport for professionals and beginners alike. The bike shop personnel should be able to advise you on how to choose the right frame size.
June 2011 saw the successful launch of my very first book, WELCOME TO YOUR LIFE – simple insights for your inspiration & empowerment (. If you have any issues with regards to wherever and how to use Info size bike mountain bike sizing., you can make contact with us at the web site. Bikes are a great way to get around - they're fun, they're cheap to fuel (they burn only calories) and they're a great way to get fit. The apparel worn by rider is very much for their safety or protection. The back chain ring is a cog set featuring seven, eight or nine cogs, depending on how many "speeds" you have (21, 24 or 27). One of the problems is that they just haven't caught on and become commercially available enough to make them an everyday sight.
If you can afford it, a full suspension mountain bike is always worth the purchase. Listed below are some of the common terms which you will come across. Something that sounds to me, to be nothing more than hard work. The price range of lightweight bicycles prices vary from $200. The kids will have a blast exploring any one of the six river parks, and more specifically, walking the suspension bridge across to Fishtrap Park.