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Cyclic algorithm to solve indeterminate quadratic equations
The chakravala method (Sanskrit: चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly
Chakravala_method
Indian mathematician and astronomer (1114–1185)
William Brouncker in 1657, though his method was more difficult than the chakravala method. The first general method for finding the solutions of the problem
Bhāskara_II
Indian inventions
Apollonius, two of the greatest minds produced by antiquity." Chakravala method – The Chakravala method, a cyclic algorithm to solve indeterminate quadratic equations
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
Type of Diophantine equation
equations. Bhaskara II is generally credited with developing the chakravala method, building on the work of Jayadeva and Brahmagupta. Solutions to specific
Pell's_equation
Branch of pure mathematics
square root is not rational.) For that matter, the eleventh-century chakravala method amounts—in modern terms—to an algorithm for finding the units of a
Number_theory
Polynomial equation whose integer solutions are sought
equation in positive integers is x = 226153980, y = 1766319049 (see Chakravala method). In 1900, David Hilbert proposed the solvability of all Diophantine
Diophantine_equation
Mathematical lemma
Bhaskara's Lemma is an identity used as a lemma during the chakravala method. It states that: N x 2 + k = y 2 ⟹ N ( m x + y k ) 2 + m 2 − N k = ( m y
Bhaskara's_lemma
to have been made during classical antiquity in Europe. Chakravala method: The Chakravala method, a cyclic algorithm to solve indeterminate quadratic equations
Timeline_of_Indian_innovation
Pell equations, which he treated using cyclic procedures such as the chakravāla method. In the 14th century, Narayana Pandita completed his Ganita Kaumudi
History_of_mathematics
Development of mathematics in South Asia
of Pell's equation using the chakravala method. The general indeterminate quadratic equation using the chakravala method. Indeterminate cubic equations
Indian_mathematics
solution (including zero and negative solutions) to quadratic equations. Chakravala method, sign convention, madhava series, and the sine and cosine in trigonometric
Indian_people
11th-century Indian mathematician
was an Indian mathematician, who further developed the cyclic method (Chakravala method) that was called by Hermann Hankel "the finest thing achieved
Jayadeva_(mathematician)
Efficient way of calculating GCD. Booth's multiplication algorithm Chakravala method: a cyclic algorithm to solve indeterminate quadratic equations, including
List_of_algorithms
Indian mathematician and astronomer (598–668)
identity Brahmagupta's formula Brahmagupta theorem Brahmagupta triangle Chakravala method List of Indian mathematicians History of science and technology on
Brahmagupta
apsidal precession of the Sun. 12th century: Bhāskara II develops the Chakravala method, solving Pell's equation. 12th century: Al-Tusi develops a numerical
Timeline of scientific discoveries
Timeline_of_scientific_discoveries
List of notable people who belong to the Brahmin caste
Indian mathematician who wrote an article on the difference between Chakravala method and Continued Fractions. Ashutosh Mukherjee, Indian mathematician
List_of_Brahmins
Eratosthenes 263 AD – Gaussian elimination described by Liu Hui 628 – Chakravala method described by Brahmagupta c. 820 – Al-Khawarizmi described algorithms
Timeline_of_algorithms
Quadratic homogeneous polynomial in two variables
were extended to a complete solution of Pell's equation known as the chakravala method, attributed to either of the Indian mathematicians Jayadeva or Bhāskara
Binary_quadratic_form
positive number has two square roots. Furthermore, it also gives the Chakravala method which was the first generalized solution of so-called Pell's equation
Timeline_of_mathematics
Indian mathematician (1892–1953)
publications, including an article on the Chakravala method where he showed how the method differed from the method of continued fractions. He pointed out
A._A._Krishnaswami_Ayyangar
Treatise on algebra by Bhāskara II
quadratic equations, including Pell's equation which is known as chakravala method or cyclic method. Bijaganita is the first text to recognize that a positive
Bijaganita
1356 mathematical treatise by Narayana Pandita
examples. Quadratic. 17 rules and 10 examples. Includes a variant of the Chakravala method. Ganita Kaumudi contains many results from continued fractions. In
Ganita_Kaumudi
Products of numbers of the form a^2 + nb^2 are also of that form
obtained. The general method for solving the Pell equation given by Bhaskara II in 1150, namely the chakravala (cyclic) method, was also based on this
Brahmagupta's_identity
Decomposition of a number into a product
small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division: checking if the number is divisible by prime numbers
Integer_factorization
Expression of a product of sums of squares as a sum of squares
obtained. The general method for solving the Pell equation given by Bhaskara II in 1150, namely the chakravala (cyclic) method, was also based on this
Brahmagupta–Fibonacci identity
Brahmagupta–Fibonacci_identity
Hypothetical world power structure
to establish it as a world religion. Also, the first references to a Chakravala Chakravartin (an emperor who rules over all four of the continents) appears
World_domination
CHAKRAVALA METHOD
CHAKRAVALA METHOD
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Indian, Sanskrit
With a Discus; Emperor
Boy/Male
Tamil
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
Surname or Lastname
English
English : topographic name from Middle English lang, long ‘long’ + strete ‘road’.Translation of Dutch Langestraet, cognate with 1.The confederate general James Longstreet (1821–1904), was born in SC, came from an old Dutch family in New Netherland with the name Langestraet; he was the nephew of Augustus B. Longstreet, a Methodist clergyman born in Augusta, GA, in 1790.
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Indian, Sanskrit
Has a Round Mouth
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Hindu, Indian
A Bird
Boy/Male
Indian, Sanskrit
Circle; Assemblage; A Leader
Boy/Male
Indian, Sanskrit
Possessor of the Cakra; Worshipper of Vishnu
Girl/Female
Tamil
Method, Wealth, Protection, Conduct, Auspiciousness, Memory, Well being
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Girl/Female
Tamil
Method, Wealth, Protection, Conduct, Auspiciousness, Memory, Well being
Male
Greek
(Μεθόδιος) Greek name derived from methodos, METHODIOS means "method."
Boy/Male
Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Boy/Male
Indian, Sanskrit
Fierce; Forceful; Whirlwind
Boy/Male
Tamil
Vedhanth | வேதாநà¯à®¤
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Vedhanth | வேதாநà¯à®¤
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Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Full Moon of Chaitra Month
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Tamil
The scriptures, Vedic method of self realization, Knower of the Vedas, One who knows all, Hindu philosophy or ultimate wisdom, King of all
Girl/Female
Tamil
Chairavali | சைராவலீ
Full Moon of Chaitra month
CHAKRAVALA METHOD
CHAKRAVALA METHOD
Boy/Male
Gaelic Irish
Charioteer.
Girl/Female
Tamil
Boy/Male
Tamil
Joyful, Happy, Joyous
Girl/Female
Tamil
Rice, Immortal, Unscathed, Perfect, Untouched i.e. divinity
Boy/Male
Arabic
The Intelligent Learner
Male
Egyptian
, a form of the Hieroglyphic name Saho.
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Muslim
Success. Reconciliation.
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English American
Manly. Masculine. From the hero's meadow.
Boy/Male
Arabic
The Biblical Hud is the English Language Equivalent; A Prophet's Name
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Hindu, Indian
King of Gold
CHAKRAVALA METHOD
CHAKRAVALA METHOD
CHAKRAVALA METHOD
CHAKRAVALA METHOD
CHAKRAVALA METHOD
a.
Of or pertaining to the ancient school of physicians called methodists.
n.
The system of doctrines, polity, and worship, of the sect called Methodists.
n.
One who methodizes.
p. pr. & vb. n.
of Methodize
a.
Alt. of Methodistical
n.
The art and principles of method.
n.
One of a sect of Christians, the outgrowth of a small association called the "Holy Club," formed at Oxford University, A.D. 1729, of which the most conspicuous members were John Wesley and his brother Charles; -- originally so called from the methodical strictness of members of the club in all religious duties.
a.
Alt. of Methodical
a.
Of or pertaining to methodology.
v. t.
To reduce to method; to dispose in due order; to arrange in a convenient manner; as, to methodize one's work or thoughts.
imp. & p. p.
of Methodize
n.
One who observes method.
a.
Of or pertaining to methodists, or to the Methodists.
a.
Proceeding with regard to method; systematic.
a.
Arranged with regard to method; disposed in a suitable manner, or in a manner to illustrate a subject, or to facilitate practical observation; as, the methodical arrangement of arguments; a methodical treatise.
n.
The act or process of methodizing, or the state of being methodized.
n.
An orderly procedure or process; regular manner of doing anything; hence, manner; way; mode; as, a method of teaching languages; a method of improving the mind.
n.
The science of method or arrangement; a treatise on method.
a.
Of or pertaining to the sect of Methodists; as, Methodist hymns; a Methodist elder.
n.
Classification; a mode or system of classifying natural objects according to certain common characteristics; as, the method of Theophrastus; the method of Ray; the Linnaean method.