Born in 476 CE in Kusumpur ( Bihar ), Aryabhatt's intellectual brilliance remapped the boundaries of mathematics and astronomy. In 499 CE, at the age of 23, he wrote a text on astronomy and an unparallel treatise on mathematics called "Aryabhatiyam." He formulated the process of calculating the motion of planets and the time of eclipses. Aryabhatt was the first to proclaim that the earth is round, it rotates on its axis, orbits the sun and is suspended in space  1000 years before Copernicus published his heliocentric theory. He is also acknowledged for calculating p (Pi) to four decimal places: 3.1416 and the sine table in trigonometry. Centuries later, in 825 CE, the Arab mathematician, Mohammed Ibna Musa credited the value of Pi to the Indians, "This value has been given by the Hindus." And above all, his most spectacular contribution was the concept of zero without which modern computer technology would have been nonexistent. Aryabhatt was a colossus in the field of mathematics.
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Showing posts with label Aryabhata. Show all posts
Showing posts with label Aryabhata. Show all posts
Wednesday, April 8, 2015
ARYABHATT  MASTER ASTRONOMER AND MATHEMATICIAN
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Sunday, April 5, 2015
Aryabhata about Earth and Eclipse
Aryabhatta is the first famous mathematician and astronomer of Ancient India. In his book Aryabhatteeyam, Aryabhatta clearly provides his birth data. In the 10th stanza, he says that when 60 x 6 = 360 years elapsed in this Kali Yuga, he was 23 years old. The stanza of the sloka starts with “Shastyabdanam Shadbhiryada vyateetastra yascha yuga padah.” “Shastyabdanam Shadbhi” means 60 x 6 = 360. While printing the manuscript, the word “Shadbhi” was altered to “Shasti”, which implies 60 x 60 = 3600 years after Kali Era. As a result of this intentional arbitrary change, Aryabhatta’s birth time was fixed as 476 A.D Since in every genuine manuscript, we find the word “Shadbhi” and not the altered “Shasti”, it is clear that Aryabhatta was 23 years old in 360 Kali Era or 2742 B.C. This implies that Aryabhatta was born in 337 Kali Era or 2765 B.C. and therefore could not have lived around 500 A.D., as manufactured by the Indologists to fit their invented framework.
Bhaskara I is the earliest known commentator of Aryabhatta’s works. His exact time is not known except that he was in between Aryabhatta (2765 B.C.) and Varahamihira (123 B.C.)." The implications are profound , if indeed this is the case.The zero is by then in widespread use and if he uses Classical Sanskrit then he ante dates Panini. Bhaskara mentions the names of Latadeva, Nisanku and Panduranga Svami as disciples of Aryabhatta.
Time to tell the world we dont believe in their theories !!!
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World's first "ZERO" found
Search for the world's first zero leads to the home of Angkor Wat
The first recorded zero has been rediscovered on a stone tablet deep in the Cambodian jungle  a single dot chiseled into stone, hidden decades ago from the grasp of the Khmer Rouge. This is one of the only photos in existence of the priceless find.
The first recorded zero has been rediscovered on a stone tablet deep in the Cambodian jungle  a single dot chiseled into stone, hidden decades ago from the grasp of the Khmer Rouge. This is one of the only photos in existence of the priceless find.
zero inscribed in chaturbhuj temple Gwalior India 
USbased mathematician, Amir Aczel, made it his life’s work to find the world’s first zero. Having already discovered the first magic square inscribed on the doorway of a 10thcentury Indian temple, this ‘mathematical archaeologist’ had come to know of K127  a stone stele first documented in 1931 that clearly held the inscription “605”. Dated to AD 683, it’s the oldest known representation of zero  a numeral that Aczel describes as the most significant of them all.
He writes at The Huffington Post:
"Zero is not only a concept of nothingness, which allows us to do arithmetic well and to algebraically define negative numbers, but it is also an important placeholding device. In that role, zero enables our base10 number system to work, so that the same 10 numerals can be used over and over again, at different positions in a number. This is exactly what makes our number system so efficient and powerful. Without that little zero we would be stuck in the Middle Ages!"
Until fairly recently, anthropologists believed that the Western number system took hold as late as the 13th century, when Italian mathematician Leonardo of Pisa (or Fibonacci) had taken what he’s learned from Arab traders and introduced it to the Europeans. Before then, the zeroless Roman system had been the standard. "With the exception of the Mayan system, whose zero glyph never left the Americas, ours is the only one known to have a numeral for zero,” Aczel writes for the Smithsonian Magazine. "Babylonians had a mark for nothingness, say some accounts, but treated it primarily as punctuation. Romans and Egyptians had no such numeral either.”
It was thought that the Arabic nations had themselves borrowed that number system from ancient civilisations on the Indian subcontinent, because of the discovery of a 9thcentury zero inscribed in the Chaturbujha temple in the city of Gwalior in India.
But then in 1931, French archaeologist Georges Cœdès insisted that zero actually came from the east  quite possibly Cambodia  having discovered an even older representation of the numeral on artefact K127, found in the ruins of a 7thcentury temple in the Mekong region.
At The Huffington Post, Aczel states that Cœdès, an expert in the Old Khmer language, translated the first use of zero  "Chaka parigraha 605 pankami roc…” to mean “The Chaka era has reached 605 on the fifth day of the waning moon…”. The '6' here appears as an inverted '9', which is how six was written in Old Khmer.
During the 1960s and 70s, when Pol Pot’s violent Khmer Rouge army tore through Cambodia, destroying thousands of priceless and ancient artefacts along the way, K127 disappeared from the Cambodian National Museum in Phnom Penh. After years of research in an effort to track it down, Aczel rediscovered it among thousands of artefacts in a large shed in Siem Reap  the location of Angkor Wat  that had been maintained by the Angkor Conservation group.
Having written about his discovery in the earliest zero in his forthcoming book, Finding Zero, Aczel reports that he’s now working with the Cambodian government to move K127 to a museum in Phnom Penh, where the public will be able to see this significant piece of numeric history for themselves.
Sources: The Huffington Post, Smithsonian Magazine
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Sunday, March 29, 2015
Aryabhata contributes ‘ZERO, Pi’ etc to Mathematics and calculates Eclipses in Astronomy
Aryabhata, born in 476 CE, was the first in the line of great mathematicianastronomers from the classical age of Indian mathematics and Indian astronomy.
There is a general tendency to misspell his name as “Aryabhatta” by analogy with other names having the “bhatta” suffix, but all his astronomical text spells his name as Aryabhata.
He mentions in his work Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476
There is a general tendency to misspell his name as “Aryabhatta” by analogy with other names having the “bhatta” suffix, but all his astronomical text spells his name as Aryabhata.
He mentions in his work Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476
Though his birthplace is uncertain, he went to Kusumapura (Pataliputra or modern day Patna) for advanced studies and lived there for sometime as the head of an institution (kulapati).
Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.
Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.
He wrote many books on mathematics, astronomy etc but most of them are lost today.
His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sumsofpower series, and a table of sines.
And Arabic translation of Aryabhata’s work is Al ntf or Alnanf and it claims that it is a translation by Aryabhata, but the original Sanskrit name of this work is not known.
His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sumsofpower series, and a table of sines.
And Arabic translation of Aryabhata’s work is Al ntf or Alnanf and it claims that it is a translation by Aryabhata, but the original Sanskrit name of this work is not known.
Place Value System and ZERO
The placevalue system, first seen in the 3rdcentury Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah explains that knowledge of zero was implicit in Aryabhata’s placevalue system as a place holder for the powers of ten with null coefficients.
However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.
However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.
Approximation of π
Aryabhata worked on the approximation for pi (π), and may have come to the conclusion that is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes :
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
Translation : “Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached.”
This calculates to 3.1416 close to the actual value Pi (3.14159).
Aryabhata used the word āsanna (approaching / approximating), to mean that not only is this an approximation but that the value is incommensurable (or irrational).
This is quite a sophisticated insight, because the irrationality of pi(π) was proved only in 1761 by Johann Heinrich Lambert.
After Aryabhatiya was translated into Arabic (during 820 CE) this approximation was mentioned in AlKhwarizmi‘s book on algebra.
Aryabhata used the word āsanna (approaching / approximating), to mean that not only is this an approximation but that the value is incommensurable (or irrational).
This is quite a sophisticated insight, because the irrationality of pi(π) was proved only in 1761 by Johann Heinrich Lambert.
After Aryabhatiya was translated into Arabic (during 820 CE) this approximation was mentioned in AlKhwarizmi‘s book on algebra.
Contributions in Trigonometry
In Ganitapada 6, Aryabhata gives the area of a triangle as :
tribhujasya phalashariram samadalakoti bhujardhasamvargah
Translation : “for a triangle, the result of a perpendicular with the halfside is the area.”
Aryabhata discussed the concept of sine in his work by the name of ardhajya, which literally means “halfchord (halfwave)“. For simplicity, people started calling it jya.
When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba.
However, in Arabic writings, vowels are omitted, and it was abbreviated as jb.
Later writers substituted it with jaib, meaning “pocket” or “fold (in a garment)“.
Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means “cove” or “bay“; thence comes the English SINE.
Alphabetic code has been used by him to define a set of increments. If we use Aryabhata’s table and calculate the value of sin(30) (corresponding to hasjha) which is 1719/3438 = 0.5; the value is correct. His alphabetic code is commonly known as the Aryabhata cipher.
When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba.
However, in Arabic writings, vowels are omitted, and it was abbreviated as jb.
Later writers substituted it with jaib, meaning “pocket” or “fold (in a garment)“.
Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means “cove” or “bay“; thence comes the English SINE.
Alphabetic code has been used by him to define a set of increments. If we use Aryabhata’s table and calculate the value of sin(30) (corresponding to hasjha) which is 1719/3438 = 0.5; the value is correct. His alphabetic code is commonly known as the Aryabhata cipher.
Indeterminate or Diophantine Equations
An example from Bhāskara’s commentary on Aryabhatiya :
Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85.
They were discussed extensively in ancient Vedic text Baudhayana Sulba Sutras, which date to 800 BCE.
Aryabhata’s method of solving such problems is called the kuṭṭaka (कुट्टक) method.
Kuttaka means “pulverizing” or “breaking into small pieces“, and the method involves a recursive algorithm for writing the original factors in smaller numbers. Today this algorithm, elaborated by Bhaskara in 621 CE, is the standard method for solving firstorder diophantine equations and is often referred to as the Aryabhata algorithm.
The diophantine equations are of interest in cryptology, and the RSA Conference, 2006, focused on the kuttaka method and earlier work in the Sulbasutras.
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85.
They were discussed extensively in ancient Vedic text Baudhayana Sulba Sutras, which date to 800 BCE.
Aryabhata’s method of solving such problems is called the kuṭṭaka (कुट्टक) method.
Kuttaka means “pulverizing” or “breaking into small pieces“, and the method involves a recursive algorithm for writing the original factors in smaller numbers. Today this algorithm, elaborated by Bhaskara in 621 CE, is the standard method for solving firstorder diophantine equations and is often referred to as the Aryabhata algorithm.
The diophantine equations are of interest in cryptology, and the RSA Conference, 2006, focused on the kuttaka method and earlier work in the Sulbasutras.
In his contribution towards Algebra, Aryabhata provided elegant results for the summation of series of squares and cubes in his book Aryabhatiya.
Aryabhata’s contributions in Astronomy
Aryabhata’s system of astronomy was called the audAyaka system, in which days are reckoned from sunrise, dawn at lanka or “equator“.
Some of his later writings on astronomy, which apparently proposed a second model (or ardharAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta’s khanDakhAdyaka.
In some texts, he seems to ascribe the apparent motions of the heavens to the Earth’s rotation and he may have believed that the planet’s orbits as elliptical rather than circular.
Some of his later writings on astronomy, which apparently proposed a second model (or ardharAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta’s khanDakhAdyaka.
In some texts, he seems to ascribe the apparent motions of the heavens to the Earth’s rotation and he may have believed that the planet’s orbits as elliptical rather than circular.
Motions of the Solar System
In the first chapter of his book Aryabhatia, he insisted that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, contrary to the thenprevailing view in other parts of the world, that the sky rotated.
Here, he gives the number of rotations of the earth in a yuga, and made more explicit in his gola chapter.
Here, he gives the number of rotations of the earth in a yuga, and made more explicit in his gola chapter.
Eclipses
Lunar and Solar eclipses were scientifically explained by Aryabhata by stating that the Moon and planets shine by reflected sunlight.
Instead of the prevailing cosmogony in which eclipses were caused by pseudoplanetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth’s shadow and solar eclipse occurs when Moon intersects Sunrays from falling on Earth.
He discussed the size and extent of the Earth’s shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata’s methods provided the core.
His computational paradigm was so accurate that 18thcentury scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.
Instead of the prevailing cosmogony in which eclipses were caused by pseudoplanetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on Earth. Thus, the lunar eclipse occurs when the moon enters into the Earth’s shadow and solar eclipse occurs when Moon intersects Sunrays from falling on Earth.
He discussed the size and extent of the Earth’s shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata’s methods provided the core.
His computational paradigm was so accurate that 18thcentury scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.
Sidereal Periods
Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; whereas the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days) is an error of 3 minutes and 20 seconds over the length of a year (365.25636 days).
Heliocentrism
Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the mean speed of the sun.
Aryabhata’s calculations were based on an underlying heliocentric model, in which the planets orbit the Sun, though this has been rebutted.
Aryabhata’s calculations were based on an underlying heliocentric model, in which the planets orbit the Sun, though this has been rebutted.
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Thursday, December 11, 2014
WESTERN NEWTON,ETC STOLE INDIAN CALCULUS FROM ANCIENT SCRIPTURES
Now,people are blinded by falsehood of Newton as father of calculus.Infact he stole it from Indian,who practiced calculus in a school of Astronomy in Malabar,Kerla 2000 years before Jesus came. It is same port where Vasco De Gama landed in 1498 for christian conversion of Hindus. Stupid King at that time let Vasco de Gama come but did not realize that it will be like East India Company which came to dupe Indians and Hindus like what Germans did ,stole Swastika and turned this pious sign to wrong end. Now with internet, people are understanding and started researching.
Astronomy school of Kerla and also Ujjain in Madhya Pradesh produced a student,namedAryabhatta who calculated value of Pi of 3.1416 and the solar year of 365.358 days . He is the one who produced heliocentric universe 4200 years before Copernicus, with elliptically orbiting planets and a spherical earth spinning on its axis explaining the motion of the heavens. Aryabhatta is father of Trigonometry and Algebra,when Europe was in the dark ages.. Westerners, both Germans and British stole his theory and propogated as their, but truth get revealed slowly but sure. Germans are destroyed ,so west heading that way because of stolen sanctity of pios ancient Indian scriptures and misusing it in wrong way.
Before thete, it was a GreeckPythagoras" who copied Bhaskara's theorem from the great Sanskrit mathematics text Baudhayana Sulba Sutra, published thousands of years earlier.
Newtons laws of motion were lifted from the Sanskrit texts of 4000 BC and Aryabhatta’s written work in 2700 BC in Sanskrit.
“When Vedic ideas are proved correct, it is just dreaming , come right. When Western work ( lifted from ancient Vedanta ) is proved right, it is scientific knowledge ”  Nikola Tesla .
Aryabhatta’s (2700 BC), formula giving the tatkalikagati (instantaneous motion) is given by the following 
u' v' = v'  v ± e (sin w'  sin w) (i)
where u, v, w are the true longitude, mean longitude, mean anomaly respectively at any particular time and u', v', w' the values of the respective quantities at a subsequent instant; and e is the eccentricity or the sine of the greatest equation of the orbit.
Astronomy school of Kerla and also Ujjain in Madhya Pradesh produced a student,namedAryabhatta who calculated value of Pi of 3.1416 and the solar year of 365.358 days . He is the one who produced heliocentric universe 4200 years before Copernicus, with elliptically orbiting planets and a spherical earth spinning on its axis explaining the motion of the heavens. Aryabhatta is father of Trigonometry and Algebra,when Europe was in the dark ages.. Westerners, both Germans and British stole his theory and propogated as their, but truth get revealed slowly but sure. Germans are destroyed ,so west heading that way because of stolen sanctity of pios ancient Indian scriptures and misusing it in wrong way.
Aryabhatta was the first to determine the circumference of the earth, with an error of 64 miles 4000 yrs ago. .Aryabhatta gave square, cube, triangle, trapezium, circle and sphere in geometry.
He was called Arjehir by the Arabs.
Remember that Galileo was killed by church when he told world what he learned from Indian Scriptures that ,that it is earth that circles the sun .(Aryabhatta explained this 4 millenuims years before)
Calculus was developed and many books were written ,some of them are here
Parameshwara's book of Calculus , including Drigganita was available even to the Arabs. The East India company was based in Calicut. Several Europeans like Fillippo Sasetti who came to Kerala to study Sanskrit in the end of the 15th century. It was this Italian who revealed the vicious and secret Portuguese Inquisition ordered by St Francis Xavier , in Goa, to the Western world. Finally it was the British who stopped this dutch Francis Xavior to stop but they took over from Dutch and ended of controlling India for 300 years. Time is ripe to pay it back now.
In 1580 Matteo Ricci borrowed Calculus Malayalam texts from Calicut kings in 1580, never to return it.
They took Calculus to Europe , from where the likes of Gottfried Wilhelm Von Liebniz , Isaac Newton and Robert Hooke raced with each other to translate , reinvent and market it in their own names, in a acrimonious manner.
Newton copied laws of gravity from "Surya Sidhanta" the great Sanskrit astronomical work written in the Vedic age . Reproduced in another written text by Bhaskara , 1200 years before Newton it clearly explains gravity without an apple. However Vedic gravity was a push ( after observing the solar eclipse ) and NOT a pull.
Before thete, it was a GreeckPythagoras" who copied Bhaskara's theorem from the great Sanskrit mathematics text Baudhayana Sulba Sutra, published thousands of years earlier.
Thanks to John Wallis , while he was the keeper of Oxford Univeristy archives who first started pondering over translated Mathematics stolen from India.
John Wallis patented Vedic Math infinity and infinitesimal ( Vishnu reclining in horizontal 8 position ) in his own name. Rest he could NOT understand and passed it to Newton.
You all know late Shakuntala Devi ,who has beaten all supercomputers in mathmatical calculation.
Also India produced great mathmaticianRamanujan,but during British regime, he was not terated properly and was not given Noble Prize.
Newtons gravity laws of explaining gravity as pull or attraction is all wrong.In fact It is explained in GURUTVAKARSHAN that gravity is a property of matter and akasha warp. If Magnet is reason for gravity, how come SUN HAS IMMENSE GRAVITY WITHOUT MAGNET ,IRON PER SE AND MOON WITH MASS .
Newton's third lawabout every action has an equal and opposite reaction is infact law of KARMA of Gita, explained that you get what you do.
Calculus was written in Malayalam atleast 200 years before Newton was born, by the Kerala school of Calculus. Calculus in Sanskrit was written 4800 years ago.
Pythogorus stole his theorem from Vedic texts 2500 years ago . Pythagoras was a student of Mathematics in India .
The 6000 year old Vedic texts taken to Palestine by King David's mistress the attractive dusky long haired Bathsheba ( Solomon's mother ) from Calicut in 3000 years ago. A lot of these ancient palm leaf texts were recovered from the Solomon's temple at Jerusalem by the Templar Knights .
P. Johnstone: “Gravitation was known to the Hindus (Indians) before the birth of Newton. The system of blood circulation was discovered by them centuries before Harvey was heard of.”
Aryabhatta’s (2700 BC), formula giving the tatkalikagati (instantaneous motion) is given by the following 
u' v' = v'  v ± e (sin w'  sin w) (i)
where u, v, w are the true longitude, mean longitude, mean anomaly respectively at any particular time and u', v', w' the values of the respective quantities at a subsequent instant; and e is the eccentricity or the sine of the greatest equation of the orbit.
"True motion in minutes is equal to the cosine (of the mean anomaly) multiplied by the difference (of the mean anomalies) and divided by the cheda, added or subtracted contrarily (to the mean motion)."
δu = δv ± e cos θ δ θ.
δu = δv ± e cos θ δ θ.
Proof of the Differential Formula
Let a point P (See Fig. 1) move on a circle. Let its position at two successive intervals be denoted by P and Q. Now, if P and Q are taken very near each other, the direction of motion in the interval PQ is the same as that of the tangent at P.
Let PT be measured along the tangent at P equal to the arc PQ. Then PT would be the motion of the point P if its velocity at P had not changed direction.
"The difference between the longitudes of a planet found at any time on a certain day and at the same time on the following day is called its (sphuta) gati (true rate of motion) for that interval of time."
the differential of an inverse sine function. This result
if T_{n} denotes the nth jya (or Rsine), C_{n} the circumference of the corresponding circle, A_{n} the area of the nth annulus and S the area of the surface of the sphere, then we shall have
the summation being taken so as to include all the Rsines in a quadrant of the circle. Since there are ordinarily 24 Rsines in a Hindu trigonometrical table, we have
Hence approximately
S = 21600 x 2 x 3437
Area of the surface = circumference x diameter.
Hence the area of a lune is numerically equal to the diameter of the sphere. As the number of limes is equal to the number of parts of the circumference of the sphere, we get
William passed over the stolen ( translated to English by Kashmiri Pandits ) papers to his son, Sir John Frederick Hershel, ( 17921871 ) an English citizen. He made full use of the Chemical and Botanical Vedic papers too. He also dabbled with Kerala Calculus. This man is buried next to Isaac Newton and Charles Darwin, in Westminister Abbey next to the English Kingsprobably to ironically reveal, that these men were NOT scientists , but thieving politicians.
John send his son Sir William James Herschel ( 1833 1917 ) to steal more, which he did and how! He patented the ancient Indian finger printing method . The Indian Panchatantra stories, which were written 5000 years ago, have episodes of written contracts , signed by a indelible Indian ink thumb print. James was Rothschilds represenative in India, overseeing the change over after the First war of Independence ( Sepoy's mutiny ) in 1857merrily taking finger prints all all and sundrythis man really got a kick out of all this.
Let a point P (See Fig. 1) move on a circle. Let its position at two successive intervals be denoted by P and Q. Now, if P and Q are taken very near each other, the direction of motion in the interval PQ is the same as that of the tangent at P.
Let PT be measured along the tangent at P equal to the arc PQ. Then PT would be the motion of the point P if its velocity at P had not changed direction.
"The difference between the longitudes of a planet found at any time on a certain day and at the same time on the following day is called its (sphuta) gati (true rate of motion) for that interval of time."
The tatkalikagati (instantaneous motion) of a planet is the motion which it would have, had its velocity during any given interval of time remained uniform."
In the figure given above, let the arc PQ = A. Then
R (sin BOQ  sin BOP) = QN  PM = Qn
which is the Bhogya Khanda
R (sin
which is the Bhogya Khanda
Now from the similar triangles PTr and PMO
R : PT : : R cos w : Tr ................ (iii)
Tr = PT cos w.
But Tr = R(sin w'  sin w) and PT = R(w'  w)
(sin w'  sin w) = (w'  w) cos w.
Thus the Tatkalika Bhogya Khanda (the instantaneous sine difference) in modern notation is
δ (sin θ) = cos θ δ θ.
This formula has been used by Bhaskara to calculate the ayanavalana ("angle of position").
Tr = PT cos w.
But Tr = R(sin w'  sin w) and PT = R(w'  w)
(sin w'  sin w) = (w'  w) cos w.
Thus the Tatkalika Bhogya Khanda (the instantaneous sine difference) in modern notation is
δ (sin θ) = cos θ δ θ.
This formula has been used by Bhaskara to calculate the ayanavalana ("angle of position").
the epithet Tatkalika (instantaneous) gati (motion) to denote these differentials.
Theory of proportion (similar triangles) –
(1) The sinedifference sin (θ + δ θ)  sin θ varies as the cosine and decreases as θ increases.
(2) The cosinedifference cos (θ + δ θ)  cos θ varies as the sine negatively and numerically increases as θ increases.
(2) The cosinedifference cos (θ + δ θ)  cos θ varies as the sine negatively and numerically increases as θ increases.
(1) The difference of the sinedifference varys as the sine negatively and increases (numerically) with the angle.
(2) The difference of the cosinedifference varys as the cosine negatively and decreases (numerically) with the angle.
For Δ_{2} (sin θ),
(2) The difference of the cosinedifference varys as the cosine negatively and decreases (numerically) with the angle.
For Δ_{2} (sin θ),
the differential of an inverse sine function. This result
if T_{n} denotes the nth jya (or Rsine), C_{n} the circumference of the corresponding circle, A_{n} the area of the nth annulus and S the area of the surface of the sphere, then we shall have
the summation being taken so as to include all the Rsines in a quadrant of the circle. Since there are ordinarily 24 Rsines in a Hindu trigonometrical table, we have
Hence approximately
S = 21600 x 2 x 3437
Area of the surface = circumference x diameter.
If l_{n} denotes the length of the nth transverse arc, we have
Therefore,
the summation being taken so as to include all the Rsines.
Hence the area of a lune is numerically equal to the diameter of the sphere. As the number of limes is equal to the number of parts of the circumference of the sphere, we get
Area of the surface = circumference x diameter.
It pays to remember that 4600 years back, half this planet was doing grunt grunt for language and wearing animal skins!
Rothschild , who owned British East India company gave a lot of stolen Vedic Maths and Astronomy papers in Sanskrit to their bloodline represented by German Jew Sir Frederick William Herschel ( 17381822 ) from Hanover. But this man was NOT smart enough. So Rothschild made a observatory for him, so that he could atleast patent the vedic Astronomical data in his name. The British made a big hue and cry when William "discovered " Uranus on March 13th 1781 hi hi the stupid Indians never knew all this. . They were jubilant as Indian Vedic astrology does NOT use Uranus ( Shweta ) Neptune ( Shyama ) Pluto ( Teevra ), just because they are too far away to affect your DNA and they stay in one single rashi for too long. Vedic rishi astrologists did NOT need a telescope, they read off from Aakashik records.
Rothschild , who owned British East India company gave a lot of stolen Vedic Maths and Astronomy papers in Sanskrit to their bloodline represented by German Jew Sir Frederick William Herschel ( 17381822 ) from Hanover. But this man was NOT smart enough. So Rothschild made a observatory for him, so that he could atleast patent the vedic Astronomical data in his name. The British made a big hue and cry when William "discovered " Uranus on March 13th 1781 hi hi the stupid Indians never knew all this. . They were jubilant as Indian Vedic astrology does NOT use Uranus ( Shweta ) Neptune ( Shyama ) Pluto ( Teevra ), just because they are too far away to affect your DNA and they stay in one single rashi for too long. Vedic rishi astrologists did NOT need a telescope, they read off from Aakashik records.
Ptolemy came to India in 155 AD, and he stole from the astronomical data from Surya Siddhanta (12.8590) , the most significant being the diameters of Mercury, Venus, Mars, Jupiter and Saturn . You must understand that these diameters were calculated accurately more than 6 millenniums ago when even the atmospheric refraction of earth was different.
Much before in 500 BC Pythagoras came to India and stole his theorem.
Much before in 500 BC Pythagoras came to India and stole his theorem.
William passed over the stolen ( translated to English by Kashmiri Pandits ) papers to his son, Sir John Frederick Hershel, ( 17921871 ) an English citizen. He made full use of the Chemical and Botanical Vedic papers too. He also dabbled with Kerala Calculus. This man is buried next to Isaac Newton and Charles Darwin, in Westminister Abbey next to the English Kingsprobably to ironically reveal, that these men were NOT scientists , but thieving politicians.
John send his son Sir William James Herschel ( 1833 1917 ) to steal more, which he did and how! He patented the ancient Indian finger printing method . The Indian Panchatantra stories, which were written 5000 years ago, have episodes of written contracts , signed by a indelible Indian ink thumb print. James was Rothschilds represenative in India, overseeing the change over after the First war of Independence ( Sepoy's mutiny ) in 1857merrily taking finger prints all all and sundrythis man really got a kick out of all this.
Gravity thief Isaac Newton stole everything from GURUTWAKARSHANA the pioneering work in Sankrit of astronomer Mihira Muni ( sage Varahamihira ) in 2660 BC. Mihira Muni was the disciple of Mathematician Aryabhatta. Mihira Muni's observatory was at Sultan Bathery , Western Ghat mountains , Kerala where today you can see a 3800 year old Jain temple converted by Muslim Invader Tipu Sultan as his fort. He stayed at Kapletta at a lake by the name of Pookode lake.
Without understanding the concept of Akasha , written in Vedic texts  he hastily propounded the " Aether Wave theory" and fell flat on his face when asked to explain refraction of light and diffusion. ( the same way his gravitation theory is bullshit too little knowledge is a dangerous thing !.
Without understanding the concept of Akasha , written in Vedic texts  he hastily propounded the " Aether Wave theory" and fell flat on his face when asked to explain refraction of light and diffusion. ( the same way his gravitation theory is bullshit too little knowledge is a dangerous thing !.
When super genius Indian Mathematician Srinivasan Ramanujan arrived at London, he was greeted by Professor Hardy. Hardy made a innocent remark that the number of the taxi , he came in is 1729 a boring number.
Ramanujan looked at the number plate himself and replied casually in a knee jerk manner "No, actually it is a very interesting number. .It is the smallest natural number representable in two different ways as the sum of two cubes" This is known as equation HARDYRAMANUJAN NUMBER,(Hardy has nothing to do except he was British,white).
Ramanujan looked at the number plate himself and replied casually in a knee jerk manner "No, actually it is a very interesting number. .It is the smallest natural number representable in two different ways as the sum of two cubes" This is known as equation HARDYRAMANUJAN NUMBER,(Hardy has nothing to do except he was British,white).
BBC documentary on Madhavan, Aryabhatta ( they say 600 AD while it is 2700).
The sages who gave this planet the Vedas , Upanishads did not care to leave their names; the truths they set down were eternal, and the identity of those who arranged the words irrelevant.
चतुरधिकम्शतम् Four more than hundred (=104)
अष्टगुणम् multiplied by 8 (104 x 8 = 832)
द्वाषष्टि= 62
तथासहस्राणाम्= of 1000 as such (=62000; totalling 62832)
अयुतद्वय= 10,000 x 2 (=20,000)
विष्कम्भस्य= of the diameter
आसन्न: approximately
वृत्तपरिणाह: to the circumference.
In effect, 62832/20000 = 3.1416 !
It interesting to note the large numbers he has used to arrive at Pi and the remark that pi is only an approximate value.
And we have also coded it in Mantras by the KATAPAYADI SYSTEM
Vararuchi was a Mathematician from Kerala who taught at Bhoj Shala University inside the Saraswati Temple in 2860 BC . Today this ancient Hindu university is a Muslim mosque.
खलजीवितखातावगलहालारसंधरः
Gopibhagya madhuvrata srngisodadhisandhiga
Khalajivitakhatava galahalarasandhara
Kaṭapayādi system dictates that:
* As the first digit is 3, the first consonant must be one of ga, ḍa, ba, la
* As the second digit is 1, the second consonant must be one of ka, ṭa, pa, ya
* For the third digit to be 4, the third consonant must be one of gha, ḍha, bha, va…
So to fit3.141592653589793…, the list of consonants in the verse must satisfy the regex
{g,ḍ,b,l}{k,ṭ,p,y}{gh,ḍh,bh,v}{k,ṭ,p,y}{ṅ,ṇ,m,ś}{jh,dh}{kh,ṭh,ph,r}{c,t,ṣ}{ṅ,ṇ,m,ś}{g,ḍ,b,l}{ṅ,ṇ,m,ś}{j,d,h}{jh,dh}{ch,th,s}{jh,dh}{g,ḍ,b,l}…
pi = 3.1415926535897932384626433832792
ga  3 pii  1 bhaa  4 gya  1 ma  5 dhu  9 ra  2 ta 6 shru  5 ga  3 sho  5 da  8 dhi  9 sa 7 dha  9 ga  3 kha  2 la  3 jii  8 vi  4 ta  6 kha  2 ta  6 va  4 ga 3 la  3 ra  2 sa  7 dha  9 ra – 2
pi = 3.1415926535897932384626433832792
From Vadakail Thanks for great knowledge.
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Monday, July 14, 2014
ARYABHATT IS REAL INVENTOR OF PLANATARY MOTION#ARYABHATT
जर्मन खगोलविद Johannes Kepler ने ग्रहों की गति का नियम दिया। 1609 AD में।
लेकिन भारतीय विद्वान आर्यभट्ट ने इसका वर्णन किया है। केपलर से बहुत बहुत पहले, 5 वीं ईसवी सदी में।
आर्यभटीयम के अध्याय 3 का 17 वां श्लोक देखिए….इसका मतलब निकलता है कि…
सारे ग्रहोंउपग्रहों में गति होती है। धुरी पर घूमने के साथ यह अपनी दीर्घवृत्ताकार कक्षा में भी चक्कर लगाते हैं। दोनों गतियों की दिशा नियत रहती है।
लेकिन भारतीय विद्वान आर्यभट्ट ने इसका वर्णन किया है। केपलर से बहुत बहुत पहले, 5 वीं ईसवी सदी में।
आर्यभटीयम के अध्याय 3 का 17 वां श्लोक देखिए….इसका मतलब निकलता है कि…
सारे ग्रहोंउपग्रहों में गति होती है। धुरी पर घूमने के साथ यह अपनी दीर्घवृत्ताकार कक्षा में भी चक्कर लगाते हैं। दोनों गतियों की दिशा नियत रहती है।
आज चर्चा धरती
की लट्टुई गति पर…। यह अपनी धुरी पर चक्कर लगाती है…। पश्चिम से पूर्व की
ओर 23.5 अंश झुककर…। 23 घंटे 56 मिनट और 4 .091 सेकंड में…। माना जाता है
कि फ्रांसीसी भौतिक विद Jean Bernard Leon Foucault ने ‘Foucault पेंडुलम’
बनाया। 1851 में। इससे धरती की दैनिक गति का पता चला…।
अब जिक्र आर्यभट्ट का करुंगा। 5 वीं सदी में इन्होंने आर्यभटीय लिखा। पुस्तक के अध्याय 4 का 9 वां श्लोक देखिए….।
अनुलोमगतिनौस्थः पश्यत्यचलं विलोमगं यद्वत्।
अचलानि भानि तद्वत् समपश्चिमगानि लड्.कायाम्।।
यानि जैसे ही एक व्यक्ति समुद्र में नाव से
आगे बढ़ता है, उसे किनारे की स्थिर चीजें विपरीत दिशा में चलती दिखती हैं।
इसी तरह स्थिर तारे लंका (भूमध्य रेखा) से पश्चिम की जाते दिखते हैं…।
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Wednesday, February 19, 2014
DECODING HINDUISMAryabhatta (476550 A.D.),INVENTOR OF ZERO.FATHER OF ASTRONOMY.Already discribed earth moves around SUN well before Coupernicus.Stolen India.
Aryabhatta (476550 A.D.), one of the world’s greatest mathematicianastronomer, was born in Patliputra in Magadha, modern Patna in Bihar. Many are of the view that he was born in the south of India especially Kerala and lived in Magadha at the time of the Gupta rulers. However, there exists no documentation to ascertain his exact birthplace. Whatever this origin, it cannot be argued that he lived in Patliputra where he wrote his famous treatise the... "Aryabhattasiddhanta" but more famously the "Aryabhatiya", the only work to have survived.
The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry. It also contains continued fractions, quadratic equations, sums of power series and a table of sines. This work is the first we are aware of which examines integer solutions to equations of the form by = ax + c and by = ax  c, where a, b, c are integers. Aryabhatta was an author of at least three astronomical texts and wrote some free stanzas as well.
He wrote that if 4 is added to 100 and then multiplied by 8 then added to 62,000 then divided by 20,000 the answer will be equal to the circumference of a circle of diameter twenty thousand. This calculates to 3.1416 close to the actual value Pi (3.14159).
But his greatest contribution has to be ZERO, for which he became immortal. He certainly did not use the symbol, but the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's placevalue system as a place holder for the powers of ten with null coefficients. The supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the placevalue system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the placevalue system and zero.
He already knew that the earth spins on its axis, the earth moves round the sun and the moon rotates round the earth. He talks about the position of the planets in relation to its movement around the sun. He refers to the light of the planets and the moon as reflection from the sun. Aryabhatta gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon.
This remarkable man was a genius and continues to baffle many mathematicians of today. His works was then later adopted by the Greeks and then the Arabs.
Bhaskara I who wrote a commentary on the Aryabhatiya about 100 years later wrote of Aryabhatta:
"Aryabhatta is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world."
Approximation of π
Aryabhata worked on the approximation for pi and may have come to the conclusion that is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.
SOURCES
BrahmaSphutaSiddhanta VOL 1(BRAMHGUPTA)
BrahmaSphutaSiddhanta VOL 2(BRAMHGUPTA)
BrahmaSphutaSiddhanta VOL 3(BRAMHGUPTA)
BrahmaSphutaSiddhanta VOL 4(BRAMHGUPTA)

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