Aryabhata-GREAT INDIAN MATHMATICIAN,ASTROLOGER

Aryabhata is also known as Aryabhata I to distinguish him from the later mathematician of the same name who lived about 400 years later. Al-Biruni has not helped in understanding Aryabhata's life, for he seemed t...o believe that there were two different mathematicians called Aryabhata living at the same time. He therefore created a confusion of two different Aryabhatas which was not clarified until 1926 when B Datta showed that al-Biruni's two Aryabhatas were one and the same person.

We know the year of Aryabhata's birth since he tells us that he was twenty-three years of age when he wrote Aryabhatiya which he finished in 499. We have given Kusumapura, thought to be close to Pataliputra (which was refounded as Patna in Bihar in 1541), as the place of Aryabhata's birth but this is far from certain, as is even the location of Kusumapura itself. As Parameswaran writes in [26]:-

... no final verdict can be given regarding the locations of Asmakajanapada and Kusumapura.

We do know that Aryabhata wrote Aryabhatiya in Kusumapura at the time when Pataliputra was the capital of the Gupta empire and a major centre of learning, but there have been numerous other places proposed by historians as his birthplace. Some conjecture that he was born in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that he was born in the north-east of India, perhaps in Bengal. In [8] it is claimed that Aryabhata was born in the Asmaka region of the Vakataka dynasty in South India although the author accepted that he lived most of his life in Kusumapura in the Gupta empire of the north. However, giving Asmaka as Aryabhata's birthplace rests on a comment made by Nilakantha Somayaji in the late 15th century. It is now thought by most historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on the Aryabhatiya.
 Aryabhata

Madhava--GREAT INDIAN MATHMATICIAN

Madhava of Sangamagramma was born near Cochin on the coast in the Kerala state in southwestern India. It is only due to research into Keralese mathematics over the last twenty-five years that the remarkable cont...ributions of Madhava have come to light. In Rajagopal and Rangachari put his achievement into context when they write:-

[Madhava] took the decisive step onwards from the finite procedures of ancient mathematics to treat their limit-passage to infinity, which is the kernel of modern classical analysis.

All the mathematical writings of Madhava have been lost, although some of his texts on astronomy have survived. However his brilliant work in mathematics has been largely discovered by the reports of other Keralese mathematicians such as Nilakantha who lived about 100 years later.

Madhava discovered the series equivalent to the Maclaurin expansions of sin x, cos x, and arctan x around 1400, which is over two hundred years before they were rediscovered in Europe. Details appear in a number of works written by his followers such as Mahajyanayana prakara which means Method of computing the great sines. In fact this work had been claimed by some historians such as Sarma (see for example [2]) to be by Madhava himself but this seems highly unlikely and it is now accepted by most historians to be a 16th century work by a follower of Madhava. This is discussed in detail in [4].

Jyesthadeva wrote Yukti-Bhasa in Malayalam, the regional language of Kerala, around 1550. In [9] Gupta gives a translation of the text and this is also given in [2] and a number of other sources. Jyesthadeva describes Madhava's series as follows:-

The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude.

This is a remarkable passage describing Madhava's series, but remember that even this passage by Jyesthadeva was written more than 100 years before James Gregory rediscovered this series expansion. Perhaps we should write down in modern symbols exactly what the series is that Madhava has found. The first thing to note is that the Indian meaning for sine of θ would be written in our notation as r sin θ and the Indian cosine of would be r cos θ in our notation, where r is the radius. Thus the series is

r θ = r(r sin θ)/1(r cos θ) - r(r sin θ)3/3r(r cos θ)3 + r(r sin θ)5/5r(r cos θ)5- r(r sin θ)7/7r(r cos θ)7 + ...

putting tan = sin/cos and cancelling r gives

θ = tan θ - (tan3θ)/3 + (tan5θ)/5 - ...

which is equivalent to Gregory's series

tan-1θ = θ - θ3/3 + θ5/5 - ...

Now Madhava put q = π/4 into his series to obtain

π/4 = 1 - 1/3 + 1/5 - ...

and he also put θ = π/6 into his series to obtain

π = √12(1 - 1/(3×3) + 1/(5×32) - 1/(7×33) + ...

We know that Madhava obtained an approximation for π correct to 11 decimal places when he gave

π = 3.14159265359

which can be obtained from the last of Madhava's series above by taking 21 terms. In [5] Gupta gives a translation of the Sanskrit text giving Madhava's approximation of π correct to 11 places.

Perhaps even more impressive is the fact that Madhava gave a remainder term for his series which improved the approximation. He improved the approximation of the series for π/4 by adding a correction term Rn to obtain

π/4 = 1 - 1/3 + 1/5 - ... 1/(2n-1) ± Rn

Madhava gave three forms of Rn which improved the approximation, namely

Rn = 1/(4n) or
Rn = n/(4n2 + 1) or
Rn = (n2 + 1)/(4n3 + 5n).

There has been a lot of work done in trying to reconstruct how Madhava might have found his correction terms. The most convincing is that they come as the first three convergents of a continued fraction which can itself be derived from the standard Indian approximation to π namely 62832/20000.

Madhava also gave a table of almost accurate values of half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle. It is thought that the way that he found these highly accurate tables was to use the equivalent of the series expansions

sin θ = θ - θ3/3! + θ5/5! - ...

cos θ = 1 - θ2/2! + θ4/4! - ...

Jyesthadeva in Yukti-Bhasa gave an explanation of how Madhava found his series expansions around 1400 which are equivalent to these modern versions rediscovered by Newton around 1676. Historians have claimed that the method used by Madhava amounts to term by term integration.

Rajagopal's claim that Madhava took the decisive step towards modern classical analysis seems very fair given his remarkable achievements. In the same vein Joseph writes in :-

We may consider Madhava to have been the founder of mathematical analysis. Some of his discoveries in this field show him to have possessed extraordinary intuition, making him almost the equal of the more recent intuitive genius Srinivasa Ramanujan, who spent his childhood and youth at Kumbakonam, not far from Madhava's birthplace.

PANINI- GREAT INDIANS/BHARTIYA

Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in the 4th, 5th, 6th and 7th century BC and there is... also no agreement among historians about the extent of the work which he undertook. What is in little doubt is that, given the period in which he worked, he is one of the most innovative people in the whole development of knowledge. We will say a little more below about how historians have gone about trying to pinpoint the date when Panini lived.

Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of the Indian Hindus and Panini is considered the founder of the language and literature. It is interesting to note that the word "Sanskrit" means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.

A treatise called Astadhyayi (or Astaka ) is Panini's major work. It consists of eight chapters, each subdivided into quarter chapters. In this work Panini distinguishes between the language of sacred texts and the usual language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 basic elements like nouns, verbs, vowels, consonants he put them into classes. The construction of sentences, compound nouns etc. is explained as ordered rules operating on underlying structures in a manner similar to modern theory. In many ways Panini's constructions are similar to the way that a mathematical function is defined today. Joseph writes in [2]:-

[Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. ... On the basis of just under 4000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. ... An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was ... partly an outcome of linguistic developments in India.

Joseph goes on to make a convincing argument for the algebraic nature of Indian mathematics arising as a consequence of the structure of the Sanskrit language. In particular he suggests that algebraic reasoning, the Indian way of representing numbers by words, and ultimately the development of modern number systems in India, are linked through the structure of language.

Panini should be thought of as the forerunner of the modern formal language theory used to specify computer languages. The Backus Normal Form was discovered independently by John Backus in 1959, but Panini's notation is equivalent in its power to that of Backus and has many similar properties. It is remarkable to think that concepts which are fundamental to today's theoretical computer science should have their origin with an Indian genius around 2500 years ago.

At the beginning of this article we mentioned that certain concepts had been attributed to Panini by certain historians which others dispute. One such theory was put forward by B Indraji in 1876. He claimed that the Brahmi numerals developed out of using letters or syllables as numerals. Then he put the finishing touches to the theory by suggesting that Panini in the eighth century BC (earlier than most historians place Panini) was the first to come up with the idea of using letters of the alphabet to represent numbers.

There are a number of pieces of evidence to support Indraji's theory that the Brahmi numerals developed from letters or syllables. However it is not totally convincing since, to quote one example, the symbols for 1, 2 and 3 clearly do not come from letters but from one, two and three lines respectively. Even if one accepts the link between the numerals and the letters, making Panini the originator of this idea would seem to have no more behind it than knowing that Panini was one of the most innovative geniuses that world has known so it is not unreasonable to believe that he might have made this step too.

There are other works which are closely associated with the Astadhyayi which some historians attribute to Panini, others attribute to authors before Panini, others attribute to authors after Panini. This is an area where there are many theories but few, if any, hard facts.

We also promised to return to a discussion of Panini's dates. There has been no lack of work on this topic so the fact that there are theories which span several hundreds of years is not the result of lack of effort, rather an indication of the difficulty of the topic. The usual way to date such texts would be to examine which authors are referred to and which authors refer to the work. One can use this technique and see who Panini mentions.

There are ten scholars mentioned by Panini and we must assume from the context that these ten have all contributed to the study of Sanskrit grammar. This in itself, of course, indicates that Panini was not a solitary genius but, like Newton, had "stood on the shoulders of giants". Panini must have lived later than these ten but this is absolutely no help in providing dates since we have absolutely no knowledge of when any of these ten lived.

What other internal evidence is there to use? Well of course Panini uses many phrases to illustrate his grammar any these have been examined meticulously to see if anything is contained there to indicate a date. To give an example of what we mean: if we were to pick up a text which contained as an example "I take the train to work every day" we would know that it had to have been written after railways became common. Let us illustrate with two actual examples from the Astadhyayi which have been the subject of much study. The first is an attempt to see whether there is evidence of Greek influence. Would it be possible to find evidence which would mean that the text had to have been written after the conquests of Alexander the Great? There is a little evidence of Greek influence, but there was Greek influence on this north east part of the Indian subcontinent before the time of Alexander. Nothing conclusive has been identified.

Another angle is to examine a reference Panini makes to nuns. Some argue that these must be Buddhist nuns and therefore the work must have been written after Buddha. A nice argument but there is a counter argument which says that there were Jaina nuns before the time of Buddha and Panini's reference could equally well be to them. Again the evidence is inconclusive.

There are references by others to Panini. However it would appear that the Panini to whom most refer is a poet and although some argue that these are the same person, most historians agree that the linguist and the poet are two different people. Again this is inconclusive evidence.

Let us end with an evaluation of Panini's contribution by Cardona in [1]:-

Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.
 

JYESTHADEVA- GREAT INDIAN MATHMATICIAN

Jyesthadeva lived on the southwest coast of India in the district of Kerala. He belonged to the Kerala school of mathematics built on the work of Madhava, Nilakantha Somayaji, Paramesvara and others.

Jyesthadeva... wrote a famous text Yuktibhasa which he wrote in Malayalam, the regional language of Kerala. The work is a survey of Kerala mathematics and, very unusually for an Indian mathematical text, it contains proofs of the theorems and gives derivations of the rules it contains. It is one of the main astronomical and mathematical texts produced by the Kerala school. The work was based mainly on the Tantrasamgraha of Nilakantha.

The Yuktibhasa is a major treatise, half on astronomy and half on mathematics, written in 1501. The Tantrasamgraha on which it is based consists of 432 Sanskrit verses divided into 8 chapters, and it covers various aspects of Indian astronomy. It is based on the epicyclic and eccentric models of planetary motion. The first two chapters deal with the motions and longitudes of the planets. The third chapter Treatise on shadow deals with various problems related with the sun's position on the celestial sphere, including the relationships of its expressions in the three systems of coordinates, namely ecliptic, equatorial and horizontal coordinates.

The fourth and fifth chapters are Treatise on the lunar eclipse and On the solar eclipse and these two chapters treat various aspects of the eclipses of the sun and the moon. The sixth chapter is On vyatipata and deals with the complete deviation of the longitudes of the sun and the moon. The seventh chapter On visibility computation discusses the rising and setting of the moon and planets. The final chapter On elevation of the lunar cusps examines the size of the part of the moon which is illuminated by the sun and gives a graphical representation of it.

The Yuktibhasa is very important in terms of the mathematics Jyesthadeva presents. In particular he presents results discovered by Madhava and the treatise is an important source of the remarkable mathematical theorems which Madhava discovered. Written in about 1550, Jyesthadeva's commentary contained proofs of the earlier results by Madhava and Nilakantha which these earlier authors did not give. In [4] Gupta gives a translation of the text and this is also given in [2] and a number of other sources. Jyesthadeva describes Madhava's series as follows:-

The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude.

This is a remarkable passage describing Madhava's series, but remember that even this passage by Jyesthadeva was written more than 100 years before James Gregory rediscovered this series expansion. To see how this description of the series fits with Gregory's series for arctan(x) see the biography of Madhava. Other mathematical results presented by Jyesthadeva include topics studied by earlier Indian mathematicians such as integer solutions of systems of first degree equation solved by the kuttaka method, and rules of finding the sines and the cosines of the sum and difference of two angles.

Not only does the mathematics anticipate work by European mathematicians a century later, but the planetary theory presented by Jyesthadeva is similar to that adopted by Tycho Brahe.
 

SAGE CHARAK AND CHARAK SAMHITA

Acharya Charak was one of the principal contributors to the ancient art and science of Ayurveda, a system of medicine and lifestyle developed in Ancient India. Acharya Charak has been crowned as the Father of Medicine. His ...renowned work, the “Charak Samhita“, is considered as an encyclopedia of Ayurveda. His principles, diagoneses, and cures retain their potency and truth even after a couple of millennia. When the science of anatomy was confused with different theories in Europe, Acharya Charak revealed through his innate genius and enquiries the facts on human anatomy, embryology, pharmacology, blood circulation and diseases like diabetes, tuberculosis, heart disease, etc.

The following statements are attributed to Acharya Charak:

“A physician who fails to enter the body of a patient with the lamp of knowledge and understanding can never treat diseases. He should first study all the factors, including environment, which influence a patient’s disease, and then prescribe treatment. It is more important to prevent the occurrence of disease than to seek a cure.”

These remarks appear obvious today, though they were often not heeded, and were made by Charak, in his famous Ayurvedic treatise Charak Samhita. The treatise contains many such remarks which are held in reverence even today. Some of them are in the fields of physiology, etiology and embryology.

In the “Charak Samhita” he has described the medicinal qualities and functions of 100,000 herbal plants. He has emphasized the influence of diet and activity on mind and body. He has proved the correlation of spirituality and physical health contributed greatly to diagnostic and curative sciences. He has also prescribed and ethical charter for medical practitioners two centuries prior to the Hippocratic oath. Through his genius and intuition, Acharya Charak made landmark contributions to Ayurvedal. He forever remains etched in the annals of history as one of the greatest and noblest of rishi-scientists.

Under the guidance of the ancient physician Atreya, Agnivesa had written an encyclopedic treatise in the eighth century B.C. However, it was only when Charaka revised this treatise that it gained popularity and came to be known as Charakasamhita. For two millennia it remained a standard work on the subject and was translated into many foreign languages, including Arabic and Latin.
 SAGE CHARAK

Bhaskaracharya- The mathmatician , astrologer.

Bhaskaracharya – The Crown Jewel of Mathematics and Astronomy


A Glance at the Astronomical Achievements of Bhaskaracharya...

1. The Earth is not flat, has no support and has a power of attraction.

2. The north and south poles of the Earth experience six months of day and six months of night.

3. One day of Moon is equivalent to 15 earth-days and one night is also equivalent to 15 earth-days.

4. Bhaskaracharya had accurately calculated apparent orbital periods of the Sun and orbital periods of Mercury, Venus, and Mars. There is slight difference between the orbital periods he calculated for Jupiter and Saturn and the corresponding modern values.

5. Earth’s atmosphere extends to 96 kilometers and has seven parts.

6. There is a vacuum beyond the Earth’s atmosphere.

There have been several unscrupulous attempts to argue that there are traces of Diophantine influence in Bhaskara's work, but this once again seems like an attempt by European scholars to claim European influence on (all) the great works of mathematics. These claims should be ignored. Particularly in the field of algebra, Diophantus only looked at specific cases and did not achieve the general methods of the Indians.
 The period between 500 and 1200 AD was the golden age of Indian Astronomy. In this long span of time Indian Astronomy flourished mainly due to emi...nent astronomers like Aryabhat, Lallacharya, Varahamihir, Brahmagupta, Bhaskaracharya and others. Bhaskaracharya’s Siddhanta Shiromani is considered as the pinnacle of all the astronomical works of those 700 hundred years. It can be aptly called the “essence” of ancient Indian Astronomy and mathematics. In the ninth century Brahmagupta’s Brahmasphutasiddhanta was translated in Arabic. The title of the translation was ‘Sind Hind’. This translation proved to be a watershed event in the history of numbers. The Arabs quickly grasped the importance of the Indian decimal system of numbers. They played a key role in transmitting this system of numbers to Europeans. For a long time Europeans were using Roman Numerals, which were very tedious to handle. After accepting the decimal system of numbers, European mathematicians made a remarkable progress in mathematics, but that was about 500 years after Bhaskaracharya.
From 750 AD Onwards India was engulfed in waves of foreign attacks. In 1205 AD Bakhtiyar Khilji destroyed the magnificent Nalanda University, which was a renowned center of knowledge for about 800 years. India was in utter chaotic state till the country was colonized by British. All universities and learning centers in India were destroyed, knowledge was lost and hardly any progress was made in mathematics and astronomy. A few scholars like Keshav Daivadnya, Ganesh Daivadnya Madhav, Sawai Jai Singh and others tried to keep the flame of knowledge burning in that dark period.


Birth and Education of Bhaskaracharya :

Ganesh Daivadnya has bestowed a very apt title on Bhaskaracharya. He has called him ‘Ganakchakrachudamani’, which means, ‘a gem among all the calculators of astronomical phenomena.’ Bhaskaracharya himself has written about his birth, his place of residence, his teacher and his education, in Siddhantashiromani as follows,
‘ A place called ‘Vijjadveed’, which is surrounded by Sahyadri ranges, where there are scholars of three Vedas, where all branches of knowledge are studied, and where all kinds of noble people reside, a brahmin called Maheshwar was staying, who was born in Shandilya Gotra (in Hindu religion, Gotra is similar to lineage from a particular person, in this case sage Shandilya), well versed in Shroud (originated from ‘Shut’ or ‘Vedas’) and ‘Smart’ (originated from ‘Smut’) Dharma, respected by all and who was authority in all the branches of knowledge. I acquired knowledge at his feet’.
From this verse it is clear that Bhaskaracharya was a resident of Vijjadveed and his father Maheshwar taught him mathematics and astronomy. Unfortunately today we have no idea where Vijjadveed was located. It is necessary to ardently search this place which was surrounded by the hills of Sahyadri and which was the center of learning at the time of Bhaskaracharya. He writes about his year of birth as follows,
‘I was born in Shake 1036 (1114 AD) and I wrote Siddhanta Shiromani when I was 36 years old.’
Bhaskaracharya has also written about his education. Looking at the knowledge, which he acquired in a span of 36 years, it seems impossible for any modern student to achieve that feat in his entire life. See what Bhaskaracharya writes about his education,
‘I have studied eight books of grammar, six texts of medicine, six books on logic, five books of mathematics, four Vedas, five books on Bharat Shastras, and two Mimansas’.
Bhaskaracharya calls himself a poet and most probably he was Vedanti, since he has mentioned ‘Parambrahman’ in that verse.
 
SIDDHANTASHIROMANI
...
Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years old. This is a mammoth work containing about 1450 verses. It is divided into four parts, Lilawati, Beejaganit, Ganitadhyaya and Goladhyaya. In fact each part can be considered as separate book. The numbers of verses in each part are as follows,
Lilawati has 278, Beejaganit has 213, Ganitadhyaya has 451 and Goladhyaya has 501 verses.
One of the most important characteristic of Siddhanta Shiromani is, it consists of simple methods of calculations from Arithmetic to Astronomy. Essential knowledge of ancient Indian Astronomy can be acquired by reading only this book. Siddhanta Shiromani has surpassed all the ancient books on astronomy in India. After Bhaskaracharya nobody could write excellent books on mathematics and astronomy in lucid language in India. In India, Siddhanta works used to give no proofs of any theorem. Bhaskaracharya has also followed the same tradition.
Lilawati is an excellent example of how a difficult subject like mathematics can be written in poetic language. Lilawati has been translated in many languages throughout the world. When British Empire became paramount in India, they established three universities in 1857, at Bombay, Calcutta and Madras. Till then, for about 700 years, mathematics was taught in India from Bhaskaracharya’s Lilawati and Beejaganit. No other textbook has enjoyed such long lifespan.

BHASKAR’S MATHEMATICS

Lilawati and Beejaganit together consist of about 500 verses. A few important highlights of Bhaskar’s mathematics are as follows,
Terms for numbers
In English, cardinal numbers are only in multiples of 1000. They have terms such as thousand, million, billion, trillion, quadrillion etc. Most of these have been named recently. However, Bhaskaracharya has given the terms for numbers in multiples of ten and he says that these terms were coined by ancients for the sake
of positional values.

Bhaskar’s terms for numbers are as follows:
eka(1), dasha(10), shata(100), sahastra(1000), ayuta(10,000), laksha(100,000), prayuta (1,000,000=million), koti(107), arbuda(108), abja(109=billion), kharva (1010), nikharva (1011), mahapadma (1012=trillion), shanku(1013), jaladhi(1014), antya(1015=quadrillion), Madhya (1016) and parardha(1017).

Kuttak

Kuttak is nothing but the modern indeterminate equation of first order. The method of solution of such equations was called as ‘pulverizer’ in the western world. Kuttak means to crush to fine particles or to pulverize. There are many kinds of Kuttaks. Let us consider one example.
In the equation, ax + b = cy, a and b are known positive integers. We want to also find out the values of x and y in integers. A particular example is,
100x +90 = 63y
Bhaskaracharya gives the solution of this example as, x = 18, 81, 144, 207… And y=30, 130, 230, 330…
Indian Astronomers used such kinds of equations to solve astronomical problems. It is not easy to find solutions of these equations but Bhaskara has given a generalized solution to get multiple answers.

Chakrawaal

Chakrawaal is the “indeterminate equation of second order” in western mathematics. This type of equation is also called Pell’s equation. Though the equation is recognized by his name Pell had never solved the equation. Much before Pell, the equation was solved by an ancient and eminent Indian mathematician, Brahmagupta (628 AD). The solution is given in his Brahmasphutasiddhanta. Bhaskara modified the method and gave a general solution of this equation. For example, consider the equation 61x2 + 1 = y2. Bhaskara gives the values of x = 22615398 and y = 1766319049
There is an interesting history behind this very equation. The Famous French mathematician Pierre de Fermat (1601-1664) asked his friend Bessy to solve this very equation. Bessy used to solve the problems in his head like present day Shakuntaladevi. Bessy failed to solve the problem. After about 100 years another famous French mathematician solved this problem. But his method is lengthy and could find a particular solution only, while Bhaskara gave the solution for five cases. In his book ‘History of mathematics’, see what Carl Boyer says about this equation,
‘In connection with the Pell’s equation ax2 + 1 = y2, Bhaskara gave particular solutions for five cases, a = 8, 11, 32, 61, and 67, for 61x2 + 1 = y2, for example he gave the solutions, x = 226153980 and y = 1766319049, this is an impressive feat in calculations and its verifications alone will tax the efforts of the reader’
Henceforth the so-called Pell’s equation should be recognized as ‘Brahmagupta-Bhaskaracharya equation’.

Simple mathematical methods

Bhaskara has given simple methods to find the squares, square roots, cube, and cube roots of big numbers. He has proved the Pythagoras theorem in only two lines. The famous Pascal Triangle was Bhaskara’s ‘Khandameru’. Bhaskara has given problems on that number triangle. Pascal was born 500 years after Bhaskara. Several problems on permutations and combinations are given in Lilawati. Bhaskar. He has called the method ‘ankapaash’. Bhaskara has given an approximate value of PI as 22/7 and more accurate value as 3.1416. He knew the concept of infinity and called it as ‘khahar rashi’, which means ‘anant’. It seems that Bhaskara had not notions about calculus, One of his equations in modern notation can be written as, d(sin (w)) = cos (w) dw.

PATANJALI YOGA

ACHARYA PATANJALI FATHER OF YOGA


 The Science of Yoga is one of several unique contributions of India to the world. It seeks to discover and realize the ultimate Reality through yogic practices. Acharya Patanjali , the founder, hailed from the district of Gonda (Ganara) in Uttar Pradesh . He prescribed the control of prana (life breath) as the means to control the body, mind and soul. This subsequently rewards one with good health and inner happiness. Acharya Patanjali ‘s 84 yogic postures effectively enhance the efficiency of the respiratory, circulatory, nervous, digestive and endocrine systems and many other organs of the body. Yoga has eight limbs where Acharya Patanjali shows the attainment of the ultimate bliss of God in samadhi through the disciplines of: yam, niyam, asan, pranayam, pratyahar, dhyan and dharna. The Science of Yoga has gained popularity because of its scientific approach and benefits. Yoga also holds the honored place as one of six philosophies in the Indian philosophical system. Acharya Patanjali will forever be remembered and revered as a pioneer in the science of self-discipline, happiness and self-realization.
 

1000 साल में पूरे आर्यावर्त का इस्लामीकरण क्यों नहीं हो पाया??

1000 साल में पूरे आर्यावर्त का इस्लामीकरण क्यों नहीं हो पाया
 
एक कुतर्क आखिर हिन्दू 1000 सालों तक हुए इस्लामी हमलों में कैसे सुरक्षित बचा ?
 इस्लाम की आंधी जिसने आधे एशिया को अरबी मजहब का गुलाम बना दिया यहाँ से आगे क्यों नहीं बढ़ पाया 
इन्टरनेट पर मुस्लिम ये बात बहुत कहते हैं जो की कुछ कुतर्की मुस्लिम विद्वानों की सोच का नतीजा है जो वो इस्लामी शासनकाल के खून और लाशों के ढेर को छुपाने , गैर मुस्लिम के ऊपर किये गए अत्याचारों को झूठा साबित करने , मंदिरों की लूट और कत्लेआम को राजनीतिकरण से जोड़ कर , इस्लाम को शान्ति का मजहब साबित करने और खुद को पाक साफ़ साबित करने के लिए करते हैं |

वैसे तो बहुत से देश में इस्लामीकरण और उसके बाद हुए कत्लेआम की निशानियाँ भी शेष नहीं है पर फिर भी बहुत सी सभ्यताएं इतना सब होने के बाद भी सर उठा के खड़ी हुई हैं इनमे तत्कालीन पारस यूरोप का एक बड़ा हिस्सा और भारत प्रमुख हैं |

जहाँ पारस आज बहुत हद तक इस्लामीकरण की चपेट में है पर आज से कुछ साल पहले वहां की संस्कृति भारत की तरह विकसित थी इतिहास में नजर डालने पे पता चलता है की भारत के राजाओं में राजनीतिक एवं पारिवारिक सम्बन्ध थे |

आखिर 1000 साल में पूरे आर्यावर्त का इस्लामीकरण क्यों नहीं हो पाया जबकि मुस्लिम शासक पूरी ताकत से मंदिरों को तोड़ के मस्जिदे बनवा रहे थे लूट रहे थे धार्मिक स्थानों पे कब्रिस्तान बसाए जा रहे थे , हिन्दुओं को मारा जा रहा था और महिलाओं से ज्यादतियां हो रही थी फिर भी मुस्लिम विचारक इस बात से परेशान हो जाते हैं आखिर इतने सब के बाद भी ये हिन्दू बच कैसे गया आज भी मुस्लिम सिर्फ ३० % हो पाए जब बांग्लादेशियों को भी बसा लिया |

  1 – हिन्दूवीरों की तलवारें

तलवारें जो सदा मलेक्षों के खून की प्यासी रहीं जिन्होंने अपने जीते जी मुस्लिम आक्रान्ताओं को अपने राज्यों में घुसने नहीं दिया डेक्कन वीर शिवाजी और मराठा राजाओं ने 1670 से औरंगजेब की सेनाओं को हराते हुए कुछ ही वर्षों में पुरे मुग़ल साम्राज्य को उखाड़ फेका और 1818 तक राज्य किया उन्होंने हिन्दुकुश पर्वत के आखिरी छोर अफगानिस्तान तक भगवा झंडे गाड दिए |
राजस्थान में राजपूतों और महाराणा प्रताप जैसे वीरों ने कभी मलेचों को टिकने ही नहीं दिया |

भरतपुर और मथुरा में जाट वीरों ने दुशमनो को मार मार के भगाया , वीरदुर्गादास राठौर जैसे राजाओं ने , बुंदेलखंड के वीर छत्रसाल, विजयगढ़ के राजा कृष्णदेव ने इस्लामी शासन जड़ो को कभी उत्तर भारत में मजबूत नहीं होने दिया हिन्दू समाज के लिए हमेशा ऐसे राज्य उपलब्ध थे जहाँ वो सुरक्षित थे |

दूसरी तरफ सिख गुरुओं ने बंदा बैरागी हरी सिंह नलवा और महराजा रणजीत सिंह ने भी अपने अपने छेत्रों में मुस्लिम आक्रांताओ की इट से इट बजा दी |
कुल मिलाके जितनी तेजी से मुस्लिम शासक सत्ता में आये उतनी ही तेजी से सम्पूर्ण भारत में शुर वीरों ने उनसे अपनी तलवारें भी तेज की |

2 – हिन्दुओं में मलेक्षों के प्रति नफरत -

हिन्दुओं के कत्लेआम , औरतों ( विधवा , शादीशुदा , या नाबालिग लड़कियों ) के प्रति होने वाले मुस्लिम सेनाओं और राजाओं के व्यभिचारो , बलात धर्मान्तरण , मंदिरों की लूट और तोड़फोड़ , मंदिरों में गाये की हत्या , धार्मिक स्थलों को तोड़ फोड़ के मस्जिद और कब्रिस्तान बनाने की वजह से समस्त हिन्दू समाज में मलेक्षों के प्रति नफरत थी भले ही बलात धर्मान्तरित किसी एक ही परिवार के लोग होते थे पर वे सभी सामजिक रूप से समाज से निष्काषित ही थे जिस कारण समाज में एक भावना काम कर रही थी और लोग अत्याचारों को सहते हुए भी धर्मान्तरित नहीं हुए |

मुख्य आजीविका का साधन कृषि था और पूरे देश की जमीनें खाली जब कही मुस्लिम शासन पहुचता था हिन्दू समाज वो क्षेत्र ही छोड़ देते थे और नए स्थानों पे बस के नारकीय जीवन से बच जाते थे और अपनी और अपने घर वालों की इज्जत आबरू और धर्म की रक्षा कर लेते थे | ऐसा सदियों से हो रहा था तो ये कोई नई बात नहीं थी मुस्लिम शासन काल से पहले भी जब कोइ राजा युद्ध हार जाता था तो या तो वो किसी मित्र राज्य में शरण लेता था मंत्रियों के साथ या बंदी बना लिया जाता था पर जो मुस्लिम सेनाये करती थी वो कोई नहीं क्योंकि मुस्लिम सेनाओ को हिन्दू लड़कियों को अपने हरम में भरने की आदत थी तो यही था जो वो कर सकते थे |

उदाहरण के लिए जब गुजरात में मुस्लिम शासन आया तो सौराष्ट्र के भगेल राजा रावल चले गए |

उत्तर भारत के झांसी चले गए |

जब शिवाजी का शासन आया तो बहुत से ब्राह्मण वहां चले गए |

ये सरल तरीका था की शिकार ही वहां से हट जाए जहाँ शिकारी पहुचे और इस्लामी शासन में अशक्त छोटे राज्यों की प्रजा के द्वारा अपनाया गया | हिन्दुओं ने लगातार प्रवास का नुकसान स्वीकार किया पर इस्लाम में परिवर्तन नहीं किया |

3 – जजिया –

हिन्दुओं ने मुस्लिम शासकों के द्वारा लगाया गया घ्रणित शरिया टैक्स जजिया स्वीकार किया और पर जनेऊ को नहीं छोड़ा | उच्च कुलीन हिन्दुओं और राजाओं को इस्लाम में परिवर्तन के लिए पैसे / पोस्ट / मुस्लिम महिलाओं ( हरम की ) का भी प्रोत्साहन दिया गया पर शहद ही किसी ने इन प्रस्तावों को स्वीकार किया सभी ने घ्रणित इस्लामी टैक्स को भुगतान किया पर हिन्दू धर्म को नहीं छोड़ा | तलवार को छोड़ कर हुए इन धृष्ट विचारों के युद्ध में भी समाज ने न झुकते हुए पूरी क्षमता से खुद को बचाए रक्खा | अकबर के नवरतन आदि इन्ही चालों का हिस्सा थे हिन्दुओं को आकर्षित करने के लिए |

4 – भक्ति आन्दोलन -

हिंदूइस्म को समेट के रखने में संतो का अविश्वसनीय योगदान रहा धर्मान्तरित हिन्दुओं एवं दुखी हिन्दू समाज को अलग अलग संतों ने श्रेष्टतम हिन्दू धर्म का सन्देश देते हुए उन्हें आपस में जोड़े रक्खा ये भक्ति आन्दोलन का ही असर था की कुछ पीढ़ी पूर्व धर्मान्तरित हुए हिन्दू तो क्या जन्मजात अरबी मुस्लिम भी हिंदूइस्म में खिचे चले आये |

रसखान और औरंगजेब की बेटी जैबुन्निसा बेगम और भतीजी ताज बेगम महान कृष्ण भक्त हुई जिन्होंने हिन्दुइज्म में न आ पाने के बाद भी भक्तिरस से हिन्दू या मुसलमान क्या सम्पूर्ण आर्यावर्त को तृप्त कर दिया |

ये सब संभव हुआ भक्ति आन्दोलन के कारण |

भक्ति आन्दोलन के द्वारा हिन्दू धर्म ने इस्लाम के प्रचार, जोर-जबरजस्ती एवं राजनैतिक हस्तक्षेप का कड़ा मुकाबला किया। इसका बहुत हद तक इस्लामी विचारधाराओं पे असर पड़ा जिसके बचाव के लिए सूफीवाद का जाल फेका गया जिसे हम आज भी पीर फ़कीर कब्र और साईं के रूप में देख रहे हैं |

भक्ति आन्दोलन बहुत कम समय में पूरे दक्षिणी एशिया (भारतीय उपमहाद्वीप) में फैला तथा लम्बे काल तक चला।
इसमें समाज के सभी वर्गों (निम्न जातियाँ, उच्च जातियाँ, स्त्री-पुरुष, सनातनी, सिख, मुसलमान आदि) का प्रतिनिधित्व रहा।

5 – शुद्धि आन्दोलन -

शुद्धि आन्दोलन का उद्देश्य बलात धर्मान्तरित लोगों को वापस हिन्दू धर्म में लाना था दयांनंद द्वारा चलाये गये ‘शुद्धि आन्दोलन’ के अन्तर्गत उन लोगों को पुनः हिन्दू धर्म में आने का मौका मिला जिन्होने किसी कारणवश इस्लाम धर्म स्वीकार कर लिया था। एनी बेसेंट ने कहा था कि स्वामी दयानन्द ऐसे पहले व्यक्ति थे जिन्होने कहा कि
“ ‘भारत भारतीयों के लिए है। “

शुद्धि आन्दोलन ने कुछ ही समय में लाखों बलात धर्मान्तरित मुसलमानों को स्वधर्म में वापसी करवाई |

6 – मुस्लिम शासकों के अरबी शौक –

अधिकतर मुस्लिम शासक अरबी मरदाना बीमारियों से पीड़ित थे | बाबर जहाँ समलैंगिक और नशेडी था वही शाहजहाँ जहाँगीर अकबर आदि अपने हरम भरने में व्यस्त थे | शाहजहाँ शराब में डूबा रहता था |

7 – इस्लाम का नैतिक रूप से आर्य विरुद्ध होना –

इस्लामी आचरण नैतिक रूप से उसकी शिक्षाओ के कारण वेद विरुद्ध था तो किसी भी आर्य के मन में वो कैसे घुसता ? अधिकतर मुसलमान मांसाहारी और कब पूजक हो जाते थे उन्हें नहाने और शरीर की शुद्धता से कोई मतलब नहीं था जबकि हिन्दू सुबह शाम नहाते थे , मॉस , शराब और बहुविवाह आदि प्रथाएं मुस्लिमो में थी तो जो भी मुसलमान था उसका समाज सिर्फ उतना ही था जहाँ वो है अन्य समाज से वो पूर्णतया निष्काषित था इसीलिए उस समय के समाज ने भी मलेक्ष जैसे शब्द का इस्तेमाल मुसलमानों के लिए किया था |

अंत में अरबों को शारीरिक विजय तो अवश्य प्राप्त हुई, परन्तु धार्मिक रूप में हिन्दू धर्म के युक्ति-युक्त सिद्धान्तों के सामने इस्लाम को पराजय प्राप्त हुई। इसी सत्य को मौलाना अल्ताफ हुसैन हालीजी ने इन शब्दों में स्वीकार किया है-

वह दीने हिजाजीका बेबाक बेड़ा।
 

KNOW OHM, GOD WORD.

Ohm is originated in Hindu Philosophy and later it is propagated by Buddhism everywhere. Hindus believe that as creation began, the divine, all-encompassing consciousness took the form of the first and original vibration manifesting as sound "OM". Before creation began it was "Shunyākāsha", the emptiness or the void. Shunyākāsha, meaning literally "no sky", is more than nothingness, because everything then existed in a latent state of potentiality. The vibration of "OM" symbolises the manifestation of God in form ("sāguna brahman"). "OM" is the reflection of the absolute reality, it is said to be "Adi Anadi", without beginning or the end and embracing all that exists.The mantra "OM" is the name of God, the vibration of the Supreme. When taken letter by letter, A-U-M represents the divine energy (Shakti) united in its three elementary aspects: Bhrahma Shakti (creation), Vishnu Shakti (preservation) and Shiva Shakti (liberation, and/or destruction).

RELIGIOUS INTOLERANCE OF TIPU SULTAN "AURANGZEB" OF SOUTH INDIA

Tipu Sultan had, ruled his kingdom only for sixteen-and-a-half years, from December 7, 1782 to May 4, 1799. The territory of Malabar was under his effective control only for a short period of eight years. If he had not secured the assistance of the wily Purnaiyya, there would not have been so many Muhammadans in the states of Kerala and Karnataka. Hindus also would not have become less prosperous, and fewer in number.

When that Brahmin Prime Minister, Purnaiyya, presented to Tipu Sultan 90,000 soldiers, three crore rupees, and invaluable ornaments made of precious stones, he was tempted to rule as the Emperor of the South India. Tipu did not consider the Hindu rulers of Maharashtra, Coorg and Travancore or the Muslim ruler Nizam as impediments. He was afraid of only the British. He had convinced himself that he could easily become the Emperor of South India if he could somehow vanquish the British. Because of his intense and-British attitude, the so-called progressive and secular historians have made a vain attempt to paint Tipu Sultan as a great national hero.

Opposition to foreign powers need not always be due to love for one's country. To achieve his selfish goal and to face the British forces, Tipu Sultan sought the assistance of another foreign power, the French, who were manoeuvring to establish their own domination in the country. How is it possible, therefore, for Tipu Sultan to be an enemy of foreign forces when he himself had sought help from Napoleon who was then a prisoner in St. Helena Island and also the French King, Louis XVI?

Besides, he also wanted to establish Islamic rule in the country; to achieve that he had to first defeat the British. For this purpose, Tipu Sultan solicited the assistance of Muslim countries like Persia, Afghanistan and Turkey. It is true that Tipu did not harm the Raja of Cochin or anyone for that matter who surrendered and pledged loyalty to him. But how does that make him a friend of Hindus?

 M.A. Gopal Rao, stated a few years ago in one of his articles: 'In a deliberately designed taxation scheme, the religious prejudice of Tipu Sultan became quite clear. His co-religionists, Muslims, were exempted from house tax, commodity tax and also the levy on other items of household use. Those who were converted to Muhammadanism, were also given similar tax exemptions. He had even made provisions for the education of their children. Tipu Sultan discontinued the practice of appointing Hindus in different administrative and military jobs as practised by his father, Hyder Ali Khan, in the past. He had deep hatred towards all non-Muslims. During the entire period of sixteen years of his regime, Purnaiyya was the only Hindu who had adorned the post of Dewan or minister under Tipu Sultan. In 1797 (two years before his death) among the 65 senior Government posts, not even a single Hindu was retained. All the Mustadirs were also Muslims. Among the 26 civil and military officers captured by the British in 1792 there were only 6 non-Muslims. In 1789, when the Nizam of Hyderabad and other Muslim rulers decided that only Muslims would be appointed henceforth in all Government posts, Tipu Sultan also adopted the same policy in his Mysore State. Just because they were Muslims, even those who were illiterate and inefficient, were also appointed to important Government posts. Even for getting promotions, one still had to be a Muslim under Tipu Sultan's regime. Considering the interest and convenience of only Muslim officers, all the records relating to tax revenue, were ordered to be written in Persian rather than in Marathi and Kannada as followed earlier. He even tried to make Persian the State language in place of Kannada. In the end all the Government posts were filled by lazy and irresponsible Muslims. As a consequence the people had to suffer a great deal because of those fun-seeking and irresponsible Muslim officers. The Muslim officers, occupying important posts at all levels, were all dishonest and unreliable persons. Even when people complained to him with evidences against those officers, Tipu Sultan did not care to inquire about the complaints lodged."

EVEN THE PLACE-NAMES WERE CHANGED

Gopal Rao had written all these on the basis of the writings of Tipu's own son, Ghulam Muhammad, and Muslim historians like Kirmani. Even the Hindu names of places, the Sultan could not tolerate. Therefore, Mangalapuri (Mangalore) was changed to Jalalabad, Cannanore (Kanwapuram) to Kusanabad, Bepur (Vaippura) to Sultanpatanam or Faruqui, Mysore to Nazarabad, Dharwar to Quarshed-Sawad, Gooty to Faiz-Hissar, Ratnagiri to Mustafabad, Dindigul to Khaliqabad, and Calicut (Kozhikode) to Islamabad. It was after the death of Tipu Sultan that the local people reverted to old names.

ISLAMIC ATROCITIES IN COORG, BEDNUR, AND MANGALORE

The cruelties which Tipu Sultan committed in Coorg, has no parallel in history. On one occasion, he forcibly converted over ten thousand Hindus to Muhammadanism. On another occasion, he captured and converted to Islam more than one thousand Hindu Coorgis before imprisoning them in the Sreerangapatanam fortress. In the period of confusion and anarchy prevailing in Sreerangapatanam during the last war of Tipu Sultan against the British, all the Coorgi prisoners escaped from the prison and became Hindus again after reaching their native kingdom. Against the solemn oath given to the Raja of Coorg, Tipu Sultan forcibly abducted a young princess from the Coorg royal family and made her his wife against her will.

The atrocities committed by Tipu Sultan in Bidnur in North Karnataka during and after its capture by him, were most barbarous and beyond description. Ayaz Khan who was Kammaran Nambiar from Chirackal Kingdom before his forcible conversion to Islam by Hyder Ali Khan, had been appointed as Governor of Bidnur. Tipu Sultan was jealous of and opposed to Ayaz Khan from the very beginning because Hyder Ali Khan had considered the latter more intelligent and smart. When Ayaz Khan learnt that Tipu Sultan was scheming to kill him secretly, he escaped to Bombay with plenty of gold. Tipu Sultan came to Bednur and forcibly converted its entire population to Islam. The people accepted Islam for the sake of their lives.

After the capture of Mangalore, thousands of Christians were also forcibly sent to Sreerangapatanam where all of them were circumcised and converted to Islam. Tipu Sultan's justification was that during the Portuguese domination, prior to the arrival of the British, many Muslims had been converted to Christianity by their Missionaries. He proudly proclaimed his action as a sort of punishment for the conversion of many Muslims by the Portuguese.

Then he marched upto Kumbla on the northern borders of Kerala, forcibly converting to Islam every Hindu on the way. This time, his argument (repeated by the Muslim and secularist historians of today) was that if all belonged to one religion - Muhammadanism - there would be unity and consequently it would be easy to defeat the British!

INSIDE MALABAR

In Malabar, the main target of Tipu Sultan's atrocities were Hindus and Hindu temples. According to Lewis B. Boury, the atrocities committed by Tipu Sultan against Hindus in Malabar were worse and more barbarous than those committed against the Hindus in Hindustan by the notorious Mahmud of Ghazni, Alauddin Khalji, and Nadir Shah. He disputes in his book Mukherjee's version that Tipu Sultan had converted only his opponents. Normally even a cruel person kills or tortures only his enemies. But that argument does not justify the cruelties committed by him against innocent women and children.

DANCE OF THE ISLAMIC SATAN

According to the Malabar Manual of William Logan who was the District Collector for some time, Thrichambaram and Thalipparampu temples in Chirackal Taluqa, Thiruvangatu Temple (Brass Pagoda) in Tellicherry, and Ponmeri Temple near Badakara were all destroyed by Tipu Sultan. TheMalabar Manual mention that the Maniyoor mosque was once a Hindu temple. The local belief is that it was converted to a mosque during the days of Tipu Sultan.

Vatakkankoor Raja Raja Varma in his famous literary work, History of Sanskrit Literature in Kerala, has written the following about the loss and destruction faced by the Hindu temples in Kerala during the military regime (Padayottam) of Tipu Sultan: "There was no limit as to the loss the Hindu temples suffered due to the military operations of Tipu Sultan. Burning down the temples, destruction of the idols installed therein and also cutting the heads of cattle over the temple deities were the cruel entertainments of Tipu Sultan and his equally cruel army. It was heartrending even to imagine the destruction caused by Tipu Sultan in the famous ancient temples of Thalipparampu and Thrichambaram. The devastation caused by this new Ravana's barbarous activities have not yet been fully rectified."

KOZHIKODE MADE A GRAVEYARD

As per the provisions of the Treaty of Mangalore of 1784, the British had allowed Tipu Sultan to have his suzerainty over Malabar. 'In consequence, the Hindus of Malabar had to suffer the most severe enormities the world had ever known in history,' observes K.V. Krishna Iyer, in his famous book, Zamorins of Calicut, based on historical records available from the royal house of Zamorins in Calicut. "When the second-in-line of Zamorins, Eralppad, refused to cooperate with Tipu Sultan in his military operations against Travancore because of Tipu's crude methods of forcible circumcision and conversion of Hindus to Islam, the enraged Tipu Sultan took a solemn oath to circumcise and convert the Zamorin and his chieftains and Hindu soldiers to Islamic faith," he adds.

L.B. Boury writes: "To show his ardent devotion and steadfast faith in Muhammaddan religion, Tipu Sultan found Kozhikode to be the most suitable place. It was because the Hindus of Malabar refused to reject the matriarchal system, polyandry and half-nakedness of women that the 'great reformer' Tipu Sultan tried to honour the entire population with Islam." To the Malabar people, the Muslim harem, Muslim polygamy and the Islamic ritual of circumcision were equally repulsive and opposed to the ancient culture and tradition in Kerala. Tipu Sultan sought a marriage alliance with the matriarchal Muslim family of Arackal Bibi in Cannanore. Kozhikode was then a centre of Brahmins and had over 7000 Brahmin families living there. Over 2000 Brahmin families perished as a result of Tipu Sultan's Islamic cruelties. He did not spare even women and children. Most of the men escaped to forests and foreign lands.

Elamkulam Kunjan Pillai wrote in the Mathrubhoomi Weekly of December 25, 1955: "Muhammadans greatly increased in number. Hindus were forcibly circumcised in thousands. As a result of Tipu's atrocities, strength of Nairs and Chamars (Scheduled Castes) significantly diminished in number. Namboodiris also substantially decreased in number."

The German missionary Guntest has recorded: 'Accompanied by an army of 60,000, Tipu Sultan came to Kozhikode in 1788 and razed it to the ground. It is not possible even to describe the brutalities committed by that Islamic barbarian from Mysore." C.A. Parkhurst also noted that 'Almost the entire Kozhikode was razed to the ground."

TEMPLES DESTROYED

Thali, Thiruvannur, Varackal, Puthur, Govindapuram, Thalikkunnu and other important temples in the town of Kozhikode as well as those nearby were completely destroyed as a result of Tipu's military operations. Some of them were reconstructed by the Zamorin after he returned following the defeat of Tipu Sultan in Sreerangapatanam and the Treaty of 1792.

The devastation caused by Tipu Sultan to the ancient and holy temples of Keraladheeswaram, Thrikkandiyoor and Thriprangatu in Vettum region was terrible. The Zamorin renovated these temples to some extent. The famous and ancient Thirunavaya Temple, known throughout the country as an ancient teaching-centre of the Vedas, revered by the devotees of Vishnu from Tamil Nadu, and existing before the advent of Christ, was also plundered and destroyed by Tipu's army (Malabar Gazetteer). After dismantling and destroying the idol, Tipu converted the Thrikkavu Temple into an ammunition depot in Ponnani (Malabar Manual). It was the Zamorin who repaired the temple later. Kotikkunnu, Thrithala, Panniyoor and other family temples of the Zamorin were plundered and destroyed. The famous Sukapuram Temple was also desecrated. Damage done to the Perumparampu Temple and Maranelira Temple of Azhvancherry Thamprakkal (titular head of all Namboodiri Brahmins) in Edappadu, can be seen even today. Vengari Temple and Thrikkulam Temple in Eranadu, Azhinjillam Temple in Ramanattukara, Indyannur Temple, Mannur Temple and many other temples were defiled and damaged extensively during the military regime.

Tipu Sultan reached Guruvayoor Temple only after destroying Mammiyoor Temple and Palayur Christian Church. If the destruction caused by Tipu's army is not visible today in the Guruvayoor Temple, it is mainly because of the intervention of Hydrose Kutty who had been converted to Islam by Hyder Ali Khan. He secured the safety of the temple and the continuation of land-tax exemption allowed by Hyder Ali earlier, besides the renovation and repairs done by the devotees later. According to available evidences, fearing the wrath of Tipu Sultan, the sacred idol of the Guruvayoor Temple was removed to the Ambalapuzha Sri Krishna Temple in Travancore State. It was only after the end of Tipu's military regime, that the idol was ceremoniously reinstated in the Guruvayoor Temple itself. Even today, daily pujas are conducted in Ambalapuzha Sri Krishna Temple where the idol of Guruvayoor Temple was temporarily installed and worshipped.

Damages caused to the nearby temples at Parampathali, Panmayanadu and Vengidangu are visible even today. The deplorable state of the architecture of the sanctum sanctorum of Parampathali Temple destroyed during the military operations of Tipu Sultan is really heart-rending. The atrocities committed in Kozhikode during the nightmarish days of the military occupation are vividly described in the works of Fra Bartolomaeo who had travelled through Kerala at that time. How cruelly Tipu Sultan, ably assisted by the French Commander M. Lally, had treated the Hindu and Christian population can be clearly understood from his writings.

TALKING RECORDS OF KERALA HISTORY

Govinda Pillai says in his famous book, History of Literature; "During Malayalam Era 965 corresponding to 1789-90, Tipu Sultan crossed over to Malabar with an army of uncivilised barbarians. With a sort of fanatical love for Islamic faith, he destroyed many Hindu temples and Christian churches which were the custodians of precious wealth and religious traditions. Besides, Tipu Sultan abducted hundreds of people and forcibly circumcised and converted them to Islam - an act which was considered by them as more than death."

A small army of 2000 Nairs of Kadathanadu resisted the invasion of the huge army of Tipu Sultan from a fortress in Kuttipuram for a few weeks. They were reduced to starvation and death. Tipu Sultan entered the fort and offered to spare their lives, provided they accepted conversion to Islam. The unfortunate lot of 2000 Nairs were then forced to eat beef after being converted to Islamic faith, at the end of usual religious ritual of mass circumcision. All the members of one branch of Parappanad Royal Family were forcibly converted to Muhammadan faith except for one or two who escaped from the clutches of Tipu Sultan's army. Similarly, one Thiruppad belonging to Nilamboor Royal Family was also forcibly abducted and converted to Islam. Thereafter, it was reported that further conversions of Hindus were attempted through those converts. In the end, when the Kolathiri Raja surrendered and paid tribute, Tipu Sultan got him treacherously killed without any specific reason, dragged his dead body tied to the feet of an elephant through the streets, and finally hanged him from a tree-top to show his Islamic contempt for Hindu Rajas.

Many Nair and Brahmin landlords fled the country leaving their vast wealth behind. The Mappilas forcibly took possession of their lands and wealth. Tipu Sultan did not object to their actions. Most of the Mappila landlords of today claim that they purchased the ownership of the landed properties from Nairs and Brahmins after paying heavy compensation. These blatant lies are being repeated by them in spite of the fact that practically nothing was paid to the Hindu landlords then or later. (The same Islamic treachery was repeated during the Mappila riots of 1921.)

In any case, Tipu Sultan succeeded in mass killing, converting lakhs of Hindus to Islamic faith, driving thousands out of their traditional homes, and finally making the rest extremely poor. Many Hindus belonging to lower castes accepted conversion to Islam under duress. However, many others, especially the Thiyyas, fled to Tellicherry and Mahe for safety.

When the British established their rule in Malabar and the Hindu landlords made efforts to recover their landed properties, illegally occupied by the local Mappilas, Mullahs started preaching to their fanatic followers that "killing of Hindu landlords was a sacred Islamic act," leading to frequent Mappila outrages in Malabar.1

In Cherunad, Vettathunad, Eranad, Valluvanad, Thamarassery and other interior areas, local Mappilas unleashed a reign of terror on the Hindu population, mainly to retain the illegally occupied land and to establish their domination over Hindus as during Tipu's regime. Fearing the organised robberies and violence, people could not even travel freely in the Malabar hinterland of predominantly Mappila population.

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प्राचीन भारत के विमान(प्राचीन सम्रद्ध भारत की गौरवशाली झलक

प्राचीन विमानों की दो श्रेणिया इस प्रकार थीः-

मानव निर्मित विमान, जो आधुनिक विमानों की तरह पंखों के सहायता से उडान भरते थे।
महर्षि भारद्वाज के शब्दों में पक्षियों की भान्ती उडने के कारण वायुयान को विमान कहते हैं। वेगसाम्याद विमानोण्डजानामिति ।।
विमानों के प्रकार:- शकत्युदगमविमान अर्थात विद्युत से चलने वाला विमान, धूम्रयान(धुँआ,वाष्प आदि से चलने वाला), अशुवाहविमान(सूर्य किरणों से चलने वाला), शिखोदभगविमान(पारे से चलने वाला), तारामुखविमान(चुम्बक शक्ति से चलने वाला), मरूत्सखविमान(गैस इत्यादि से चलने वाला), भूतवाहविमान(जल,अग्नि तथा वायु से चलने वाला)।

आश्चर्य जनक विमान, जो मानव निर्मित नहीं थे किन्तु उन का आकार प्रकार आधुनिक ‘उडन तशतरियों’ के अनुरूप है।

विमान विकास के प्राचीन ग्रन्थ

भारतीय उल्लेख प्राचीन संस्कृत भाषा में सैंकडों की संख्या में उपलब्द्ध हैं, किन्तु खेद का विषय है कि उन्हें अभी तक किसी आधुनिक भाषा में अनुवादित ही नहीं किया गया। प्राचीन भारतीयों ने जिन विमानों का अविष्कार किया था उन्हों
ने विमानों की संचलन प्रणाली तथा उन की देख भाल सम्बन्धी निर्देश भी संकलित किये थे, जो आज भी उपलब्द्ध हैं और उन में से कुछ का अंग्रेजी में अनुवाद भी किया जा चुका है। विमान विज्ञान विषय पर कुछ मुख्य प्राचीन ग्रन्थों का ब्योरा इस प्रकार हैः-

1. ऋगवेद- इस आदि ग्रन्थ में कम से कम 200 बार विमानों के बारे में उल्लेख है। उन में तिमंजिला, त्रिभुज आकार के, तथा तिपहिये विमानों का उल्लेख है जिन्हे अश्विनों (वैज्ञिानिकों) ने बनाया था। उन में साधारणत्या तीन यात्री जा सकते थे। विमानों के निर्माण के लिये स्वर्ण, रजत तथा लोह धातु का प्रयोग किया गया था तथा उन के दोनो ओर पंख होते थे। वेदों में विमानों के कई आकार-प्रकार उल्लेखित किये गये हैं। अहनिहोत्र विमान के दो ईंजन तथा हस्तः विमान (हाथी की शक्ल का विमान) में दो से अधिक ईंजन होते थे। एक अन्य विमान का रुप किंग-फिशर पक्षी के अनुरूप था। इसी प्रकार कई अन्य जीवों के रूप वाले विमान थे। इस में कोई सन्देह नहीं कि बीसवीं सदी की तरह पहले भी मानवों ने उड़ने की प्रेरणा पक्षियों से ही ली होगी। याता-यात के लिये ऋग वेद में जिन विमानों का उल्लेख है वह इस प्रकार है-

जल-यान – यह वायु तथा जल दोनो तलों में चल सकता था। (ऋग वेद 6.58.3)
कारा – यह भी वायु तथा जल दोनो तलों में चल सकता था। (ऋग वेद 9.14.1)
त्रिताला – इस विमान का आकार तिमंजिला था। (ऋग वेद 3.14.1)
त्रिचक्र रथ – यह तिपहिया विमान आकाश में उड सकता था। (ऋग वेद 4.36.1)
वायु रथ – रथ की शकल का यह विमान गैस अथवा वायु की शक्ति से चलता था। (ऋग वेद 5.41.6)
विद्युत रथ – इस प्रकार का रथ विमान विद्युत की शक्ति से चलता था। (ऋग वेद 3.14.1).
2. यजुर्वेद में भी ऐक अन्य विमान का तथा उन की संचलन प्रणाली उल्लेख है जिस का निर्माण जुडवा अशविन कुमारों ने किया था। इस विमान के प्रयोग से उन्हो मे राजा भुज्यु को समुद्र में डूबने से बचाया था।

3. विमानिका शास्त्र –1875 ईसवी में भारत के ऐक मन्दिर में विमानिका शास्त्र ग्रंथ की ऐक प्रति मिली थी। इस ग्रन्थ को ईसा से 400 वर्ष पूर्व का बताया जाता है तथा ऋषि भारदूाज रचित माना जाता है। इस का अनुवाद अंग्रेज़ी भाषा में हो चुका है। इसी ग्रंथ में पूर्व के 97 अन्य विमानाचार्यों का वर्णन है तथा 20 ऐसी कृतियों का वर्णन है जो विमानों के आकार प्रकार के बारे में विस्तरित जानकारी देते हैं। खेद का विषय है कि इन में से कई अमूल्य कृतियाँ अब लुप्त हो चुकी हैं। इन ग्रन्थों के विषय इस प्रकार थेः-

विमान के संचलन के बारे में जानकारी, उडान के समय सुरक्षा सम्बन्धी जानकारी, तुफान तथा बिजली के आघात से विमान की सुरक्षा के उपाय, आवश्यक्ता पडने पर साधारण ईंधन के बदले सौर ऊर्जा पर विमान को चलाना आदि। इस से यह तथ्य भी स्पष्ट होता है कि इस विमान में ‘एन्टी ग्रेविटी’ क्षेत्र की यात्रा की क्षमता भी थी।
विमानिका शास्त्र में सौर ऊर्जा के माध्यम से विमान को उडाने के अतिरिक्त ऊर्जा को संचित रखने का विधान भी बताया गया है। ऐक विशेष प्रकार के शीशे की आठ नलियों में सौर ऊर्जा को एकत्रित किया जाता था जिस के विधान की पूरी जानकारी लिखित है किन्तु इस में से कई भाग अभी ठीक तरह से समझे नहीं गये हैं।
इस ग्रन्थ के आठ भाग हैं जिन में विस्तरित मानचित्रों से विमानों की बनावट के अतिरिक्त विमानों को अग्नि तथा टूटने से बचाव के तरीके भी लिखित हैं।
ग्रन्थ में 31 उपकरणों का वर्तान्त है तथा 16 धातुओं का उल्लेख है जो विमान निर्माण में प्रयोग की जाती हैं जो विमानों के निर्माण के लिये उपयुक्त मानी गयीं हैं क्यों कि वह सभी धातुयें गर्मी सहन करने की क्षमता रखती हैं और भार में हल्की हैं।
4. यन्त्र सर्वस्वः – यह ग्रन्थ भी ऋषि भारदूाजरचित है। इस के 40 भाग हैं जिन में से एक भाग ‘विमानिका प्रकरण’के आठ अध्याय, लगभग 100 विषय और 500 सूत्र हैं जिन में विमान विज्ञान का उल्लेख है। इस ग्रन्थ में ऋषि भारदूाजने विमानों को तीन श्रेऩियों में विभाजित किया हैः-

अन्तरदेशीय – जो ऐक स्थान से दूसरे स्थान पर जाते हैं।
अन्तरराष्ट्रीय – जो ऐक देश से दूसरे देश को जाते
अन्तीर्क्षय – जो ऐक ग्रह से दूसरे ग्रह तक जाते
इन में सें अति-उल्लेखलीय सैनिक विमान थे जिन की विशेषतायें विस्तार पूर्वक लिखी गयी हैं और वह अति-आधुनिक साईंस फिक्शन लेखक को भी आश्चर्य चकित कर सकती हैं। उदाहरणार्थ सैनिक विमानों की विशेषतायें इस प्रकार की थीं-

पूर्णत्या अटूट, अग्नि से पूर्णत्या सुरक्षित, तथा आवश्यक्ता पडने पर पलक झपकने मात्र समय के अन्दर ही ऐक दम से स्थिर हो जाने में सक्ष्म।
शत्रु से अदृष्य हो जाने की क्षमता।
शत्रुओं के विमानों में होने वाले वार्तालाप तथा अन्य ध्वनियों को सुनने में सक्ष्म। शत्रु के विमान के भीतर से आने वाली आवाजों को तथा वहाँ के दृष्यों को रिकार्ड कर लेने की क्षमता।
शत्रु के विमान की दिशा तथा दशा का अनुमान लगाना और उस पर निगरानी रखना।
शत्रु के विमान के चालकों तथा यात्रियों को दीर्घ काल के लिये स्तब्द्ध कर देने की क्षमता।
निजि रुकावटों तथा स्तब्द्धता की दशा से उबरने की क्षमता।
आवश्यक्ता पडने पर स्वयं को नष्ट कर सकने की क्षमता।
चालकों तथा यात्रियों में मौसमानुसार अपने आप को बदल लेने की क्षमता।
स्वचालित तापमान नियन्त्रण करने की क्षमता।
हल्के तथा उष्णता ग्रहण कर सकने वाले धातुओं से निर्मित तथा आपने आकार को छोटा बडा करने, तथा अपने चलने की आवाजों को पूर्णत्या नियन्त्रित कर सकने में सक्ष्म।
विचार करने योग्य तथ्य है कि इस प्रकार का विमान अमेरिका के अति आधुनिक स्टेल्थ फाईटर और उडन तशतरी का मिश्रण ही हो सकता है। ऋषि भारदूाजकोई आधुनिक ‘फिक्शन राईटर’ नहीं थे परन्तुऐसे विमान की परिकल्पना करना ही आधुनिक बुद्धिजीवियों को चकित कर सकता है कि भारत के ऋषियों ने इस प्रकार के वैज्ञिानक माडल का विचार कैसे किया। उन्हों ने अंतरीक्ष जगत और अति-आधुनिक विमानों के बारे में लिखा जब कि विश्व के अन्य देश साधारण खेती बाडी का ज्ञान भी पूर्णत्या हासिल नहीं कर पाये थे।

5. समरांगनः सुत्रधारा – य़ह ग्रन्थ विमानों तथा उन से सम्बन्धित सभी विषयों के बारे में जानकारी देता है।इस के 230 पद्य विमानों के निर्माण, उडान, गति, सामान्य तथा आकस्माक उतरान एवम पक्षियों की दुर्घटनाओं के बारे में भी उल्लेख करते हैं।

लगभग सभी वैदिक ग्रन्थों में विमानों की बनावट त्रिभुज आकार की दिखायी गयी है। किन्तु इन ग्रन्थों में दिया गया आकार प्रकार पूर्णत्या स्पष्ट और सूक्ष्म है। कठिनाई केवल धातुओं को पहचानने में आती है।

समरांगनः सुत्रधारा के आनुसार सर्व प्रथम पाँच प्रकार के विमानों का निर्माण ब्रह्मा, विष्णु, यम, कुबेर तथा इन्द्र के लिये किया गया था। पश्चात अतिरिक्त विमान बनाये गये। चार मुख्य श्रेणियों का ब्योरा इस प्रकार हैः-

रुकमा – रुकमानौकीले आकार के और स्वर्ण रंग के थे।
सुन्दरः –सुन्दर राकेट की शक्ल तथा रजत युक्त थे।
त्रिपुरः –त्रिपुर तीन तल वाले थे।
शकुनः – शकुनः का आकार पक्षी के जैसा था।
दस अध्याय संलगित विषयों पर लिखे गये हैं जैसे कि विमान चालकों का परिशिक्षण, उडान के मार्ग, विमानों के कल-पुरज़े, उपकरण, चालकों एवम यात्रियों के परिधान तथा लम्बी विमान यात्रा के समय भोजन किस प्रकार का होना चाहिये।

ग्रन्थ में धातुओं को साफ करने की विधि, उस के लिये प्रयोग करने वाले द्रव्य, अम्ल जैसे कि नींबु अथवा सेब या कोई अन्य रसायन, विमान में प्रयोग किये जाने वाले तेल तथा तापमान आदि के विषयों पर भी लिखा गया है।

सात प्रकार के ईजनों का वर्णन किया गया है तथा उन का किस विशिष्ट उद्देष्य के लिये प्रयोग करना चाहिये तथा कितनी ऊचाई पर उस का प्रयोग सफल और उत्तम होगा। सारांश यह कि प्रत्येक विषय पर तकनीकी और प्रयोगात्मक जानकारी उपलब्द्ध है। विमान आधुनिक हेलीकोपटरों की तरह सीधे ऊची उडान भरने तथा उतरने के लिये, आगे पीछ तथा तिरछा चलने में भी सक्ष्म बताये गये हैं

6. कथा सरित-सागर – यह ग्रन्थ उच्च कोटि के श्रमिकों का उल्लेख करता है जैसे कि काष्ठ का काम करने वाले जिन्हें राज्यधर और प्राणधर कहा जाता था। यह समुद्र पार करने के लिये भी रथों का निर्माण करते थे तथा एक सहस्त्र यात्रियों को ले कर उडने वालो विमानों को बना सकते थे। यह रथ-विमान मन की गति के समान चलते थे।