WRIGHT brothers-discovered Plane

ORVILLE WRIGHT
Born: August 19, 1871
Dayton, Ohio
Died: January 30, 1948
Dayton, Ohio

WILBUR WRIGHT
Born: April 16, 1867
Millville, Indiana
Died: May 30, 1912
Dayton, Ohio
American aviators

The American aviation pioneers Wilbur and Orville Wright were the first to accomplish manned, powered flight in a heavier-than-air machine.

Their early years
Wilbur and Orville Wright were the sons of Milton Wright, a bishop of the United Brethren in Christ. Wilbur was born on April 16, 1867, in Millville, Indiana. Orville was born on August 19, 1871, in Dayton, Ohio. Until the death of Wilbur in 1912, the two were inseparable. Their personalities were perfectly complementary (each provided what the other lacked). Orville was full of ideas and enthusiasms. Wilbur was more steady in his habits, more mature in his judgments, and more likely to see a project through.

While in high school, Wilbur intended to go to Yale and study to be a clergyman. However, he suffered a facial injury while playing hockey, which prevented him from continuing his education. For the next three years he continued his education informally through reading in his father's large library.

In their early years the two boys helped their father, who edited a journal called the Religious Telescope. Later, they began a paper of their own, West Side News. They went into business together as printers producing everything from religious handouts to commercial fliers. In 1892 they opened the Wright Cycle Shop in Dayton. This was the perfect occupation for the Wright brothers because it involved one of the exciting mechanical devices of the time: the bicycle. When the brothers took up the problems of flight, they had a solid grounding in practical mechanics (knowledge of how to build machines).

The exploits of one of the great glider pilots of the late nineteenth century, Otto Lilienthal, had attracted the attention of the Wright brothers as early as 1891, but it was not until the death of this famous aeronautical (having to do with the study of flying and the design of flying machines) engineer in 1896 that the two became interested in gliding experiments. They then decided to educate themselves in the theory and state of the art of flying.


Wilbur Wright (left) and his brother Orville.
Reproduced by permission of AP/Wide World Photos.
Their beginnings in flight
The Wrights took up the problem of flight at a favorable time, for some of the fundamental, or basic, theories of aerodynamics were already known; a body of experimental data existed; and, most importantly, the recent development of the internal combustion engine made available a sufficient source of power for manned flight.

The Wright brothers began by accumulating and mastering all the important information on the subject, designed and tested their own models and gliders, built their own engine, and, when the experimental data they had inherited appeared to be inadequate or wrong, they conducted new and more thorough experiments. The Wrights decided that earlier attempts at flight were not successful because the plans for early airplanes required pilots to shift their bodies to control the plane. The brothers decided that it would be better to control a plane by moving its wings.

First trip to Kitty Hawk
The Wright brothers proceeded to fly double-winged kites and gliders in order to gain experience and to test the data they had. After consulting the U.S. Weather Bureau, they chose an area of sand dunes near the small town of Kitty Hawk, North Carolina, as the site of their experiments. In September 1900 they set up camp there.

The Wrights's first device failed to fly as a kite because it was unable to develop sufficient lift (upward force). Instead, they flew it as a free glider. They kept careful records of their failures as well as of their successes. Their own data showed conclusively that previous tables of information they had were greatly inaccurate.

Returning to Dayton in 1901, the Wright brothers built a wind tunnel (a tunnel wherein one can control the flow of wind in order to determine its effect on an object)—the first in the United States. This is where they tested over two hundred models of wing surfaces in order to measure lift and drag (resistance) factors and to discover the most suitable design. They also discovered that although screw propellers had been used on ships for more than half a century, there was no reliable body of data on the subject and no theory that would allow them to design the proper propellers for their airship. They had to work the problem out for themselves mathematically.

The Wrights, by this time, not only had mastered the existing body of aeronautical science but also had added to it. They now built their third glider, incorporating their findings, and in the fall of 1902 they returned to Kitty Hawk. They made over one thousand gliding flights and were able to confirm their previous data and to demonstrate their ability to control motions of the glider. Having learned to build and to control an adequate air frame, they now determined to apply power to their machine.

Powered flight
The Wright brothers soon discovered, however, that no manufacturer would undertake to build an engine that would meet their specifications, so they had to build their own. They produced one that had four cylinders and developed 12 horsepower (a unit that describes the strength of an engine). When it was installed in the air frame, the entire machine weighed just 750 pounds and proved to be capable of traveling 31 miles per hour. They took this new airplane to Kitty Hawk in the fall of 1903 and on December 17 made the world's first manned, powered flight in a heavier-than-air craft.

The first flight was made by Orville and lasted only 12 seconds, during which the airplane flew 120 feet. That same day, however, on its fourth flight, with Wilbur at the controls, the plane stayed in the air for 59 seconds and traveled 852 feet. Then a gust of wind severely damaged the craft. The brothers returned to Dayton convinced of their success and determined to build another machine. In 1905 they abandoned their other activities and concentrated on the development of aviation. On May 22, 1906, they received a patent for their flying machine.

The next step
The brothers looked to the federal government for encouragement in their venture, and gradually interest was aroused in Washington, D.C. In 1907 the government asked for bids for an airplane that would meet certain requirements. Twenty-two bids were received, three were accepted, but only the Wright brothers finished their contract.

The brothers continued their experiments at Kitty Hawk, and in September 1908, while Wilbur was in France attempting to interest foreign backers in their machine, Orville successfully demonstrated their contract airplane. It was accepted by the government. The event was marred by a crash a week later in which Orville was injured and a passenger was killed.

Wilbur's trip to France proved to be a success. In 1909 the Wright brothers formed the American Wright Company, with Wilbur taking the lead in setting up and directing the business. His death in Dayton on May 30, 1912, left Orville feeling depressed and alone. In 1915 he sold his rights to the firm and gave up his interest in manufacturing in order to turn to experimental work. He had little taste for the busy activity of commercial life.

After his retirement, Orville lived quietly in Dayton, conducting experiments on mechanical problems of interest to him, none of which proved to be of major importance. His chief public activity was service on the National Advisory Committee for Aeronautics (the government agency that came before the National Aeronautics and Space Administration, or NASA), of which he was a member from its organization by President Woodrow Wilson in 1915 until his death in Dayton on January 30, 1948.

The Wright Brothers helped found modern aviation through their curiosity, their inventiveness, and their unwillingness to give up their vision.

kalpana chawla

First Indian woman in space ...Born on 1962, in Karnal, India. Kalpana enjoyed flying, hiking, back-packing, and reading.

Kalpana completed her Graduation from Tagore School, Karnal, India, in 1976. Bachelor of science degree in aeronautical engineering from Punjab Engineering College, India, 1982. Master of science degree in aerospace engineering from University of Texas, 1984. Doctorate of philosophy in aerospace engineering from University of Colorado, 1988.

Also she held a Certificated Flight Instructor's license with airplane and glider ratings, Commercial Pilot's licenses for single- and multi-engine land and seaplanes, and Gliders, and instrument rating for airplanes. She enjoyed flying aerobatics and tail-wheel airplanes.

In 1988, Kalpana Chawla started work at NASA Ames Research Center in the area of powered-lift computational fluid dynamics. Her research concentrated on simulation of complex air flows encountered around aircraft such as the Harrier in "ground-effect."

In 1993 Kalpana Chawla joined Overset Methods Inc., Los Altos, California, as Vice President and Research Scientist to form a team with other researchers specializing in simulation of moving multiple body problems. She was responsible for development and implementation of efficient techniques to perform aerodynamic optimization.

In December 1994, she was selected by NASA and reported to the Johnson Space Center in March 1995 as an astronaut candidate in the 15th Group of Astronauts. After completing a year of training and evaluation, she was assigned as crew representative to work technical issues for the Astronaut Office EVA/Robotics and Computer Branches.

In November, 1996, Kalpana Chawla was assigned as mission specialist and prime robotic arm operator on STS-87. She flew on STS-87 (1997) and STS-107 (2003) and has logged 30 days, 14 hours and 54 minutes in space.

STS-107 Columbia (January 16 to February 1, 2003), The 16-day flight was a dedicated science and research mission. Working 24 hours a day, in two alternating shifts, the crew successfully conducted approximately 80 experiments. The STS-107 mission ended abruptly on February 1, 2003 when Space Shuttle Columbia and her crew perished during entry, 16 minutes prior to scheduled landing.

Thomas Alva Edison

Thomas Alva Edison was born on February 11, 1847 in Milan, Ohio; the seventh and last child of Samuel and Nancy Edison. When Edison was seven his family moved to Port Huron, Michigan. Edison lived here until he struck out on his own at the age of sixteen. Edison had very little formal education as a child, attending school only for a few months. He was taught reading, writing, and arithmetic by his mother, but was always a very curious child and taught himself much by reading on his own. This belief in self-improvement remained throughout his life.

Work as a Telegrapher

Edison began working at an early age, as most boys did at the time. At thirteen he took a job as a newsboy, selling newspapers and candy on the local railroad that ran through Port Huron to Detroit. He seems to have spent much of his free time reading scientific, and technical books, and also had the opportunity at this time to learn how to operate a telegraph. By the time he was sixteen, Edison was proficient enough to work as a telegrapher full time.

First Patent

The development of the telegraph was the first step in the communication revolution, and the telegraph industry expanded rapidly in the second half of the 19th century. This rapid growth gave Edison and others like him a chance to travel, see the country, and gain experience. Edison worked in a number of cities throughout the United States before arriving in Boston in 1868. Here Edison began to change his profession from telegrapher to inventor. He received his first patent on an electric vote recorder, a device intended for use by elected bodies such as Congress to speed the voting process. This invention was a commercial failure. Edison resolved that in the future he would only invent things that he was certain the public would want.

Marriage to Mary Stilwell

Edison moved to New York City in 1869. He continued to work on inventions related to the telegraph, and developed his first successful invention, an improved stock ticker called the "Universal Stock Printer". For this and some related inventions Edison was paid $40,000. This gave Edison the money he needed to set up his first small laboratory and manufacturing facility in Newark, New Jersey in 1871. During the next five years, Edison worked in Newark inventing and manufacturing devices that greatly improved the speed and efficiency of the telegraph. He also found to time to get married to Mary Stilwell and start a family.

Move to Menlo Park

In 1876 Edison sold all his Newark manufacturing concerns and moved his family and staff of assistants to the small village of Menlo Park, twenty-five miles southwest of New York City. Edison established a new facility containing all the equipment necessary to work on any invention. This research and development laboratory was the first of its kind anywhere; the model for later, modern facilities such as Bell Laboratories, this is sometimes considered to be Edison's greatest invention. Here Edison began to change the world.

The first great invention developed by Edison in Menlo Park was the tin foil phonograph. The first machine that could record and reproduce sound created a sensation and brought Edison international fame. Edison toured the country with the tin foil phonograph, and was invited to the White House to demonstrate it to President Rutherford B. Hayes in April 1878.

Srinivasa Ramanujan

Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras. When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. In December 1889 he contracted smallpox.

When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898. At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series.

Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic. The following year, not knowing that the quintic could not be solved by radicals, he tried (and of course failed) to solve the quintic.

It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics, but the style of the book was to have a rather unfortunate effect on the way Ramanujan was later to write down mathematics since it provided the only model that he had of written mathematical arguments. The book contained theorems, formulae and short proofs. It also contained an index to papers on pure mathematics which had been published in the European Journals of Learned Societies during the first half of the 19^th century. The book, published in 1856, was of course well out of date by the time Ramanujan used it.

By 1904 Ramanujan had begun to undertake deep research. He investigated the series ∑(1/n) and calculated Euler's constant to 15 decimal places. He began to study the Bernoulli numbers, although this was entirely his own independent discovery.

Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in Kumbakonam which he entered in 1904. However the following year his scholarship was not renewed because Ramanujan devoted more and more of his time to mathematics and neglected his other subjects. Without money he was soon in difficulties and, without telling his parents, he ran away to the town of Vizagapatnam about 650 km north of Madras. He continued his mathematical work, however, and at this time he worked on hypergeometric series and investigated relations between integrals and series. He was to discover later that he had been studying elliptic functions.

In 1906 Ramanujan went to Madras where he entered Pachaiyappa's College. His aim was to pass the First Arts examination which would allow him to be admitted to the University of Madras. He attended lectures at Pachaiyappa's College but became ill after three months study. He took the First Arts examination after having left the course. He passed in mathematics but failed all his other subjects and therefore failed the examination. This meant that he could not enter the University of Madras. In the following years he worked on mathematics developing his own ideas without any help and without any real idea of the then current research topics other than that provided by Carr's book.

Continuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908. At this stage he became seriously ill again and underwent an operation in April 1909 after which he took him some considerable time to recover. He married on 14 July 1909 when his mother arranged for him to marry a ten year old girl S Janaki Ammal. Ramanujan did not live with his wife, however, until she was twelve years old.

Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society. He devoloped relations between elliptic modular equations in 1910. After publication of a brilliant research paper on Bernoulli numbers in 1911 in the Journal of the Indian Mathematical Society he gained recognition for his work. Despite his lack of a university education, he was becoming well known in the Madras area as a mathematical genius.

In 1911 Ramanujan approached the founder of the Indian Mathematical Society for advice on a job. After this he was appointed to his first job, a temporary post in the Accountant General's Office in Madras. It was then suggested that he approach Ramachandra Rao who was a Collector at Nellore. Ramachandra Rao was a founder member of the Indian Mathematical Society who had helped start the mathematics library. He writes in

A short uncouth figure, stout, unshaven, not over clean, with one conspicuous feature-shining eyes- walked in with a frayed notebook under his arm. He was miserably poor. ... He opened his book and began to explain some of his discoveries. I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense. ... I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches.

Ramachandra Rao told him to return to Madras and he tried, unsuccessfully, to arrange a scholarship for Ramanujan. In 1912 Ramanujan applied for the post of clerk in the accounts section of the Madras Port Trust. In his letter of application he wrote [3]:-

I have passed the Matriculation Examination and studied up to the First Arts but was prevented from pursuing my studies further owing to several untoward circumstances. I have, however, been devoting all my time to Mathematics and developing the subject.

Despite the fact that he had no university education, Ramanujan was clearly well known to the university mathematicians in Madras for, with his letter of application, Ramanujan included a reference from E W Middlemast who was the Professor of Mathematics at The Presidency College in Madras. Middlemast, a graduate of St John's College, Cambridge, wrote [3]:-

I can strongly recommend the applicant. He is a young man of quite exceptional capacity in mathematics and especially in work relating to numbers. He has a natural aptitude for computation and is very quick at figure work.

On the strength of the recommendation Ramanujan was appointed to the post of clerk and began his duties on 1 March 1912. Ramanujan was quite lucky to have a number of people working round him with a training in mathematics. In fact the Chief Accountant for the Madras Port Trust, S N Aiyar, was trained as a mathematician and published a paper On the distribution of primes in 1913 on Ramanujan's work. The professor of civil engineering at the Madras Engineering College C L T Griffith was also interested in Ramanujan's abilities and, having been educated at University College London, knew the professor of mathematics there, namely M J M Hill. He wrote to Hill on 12 November 1912 sending some of Ramanujan's work and a copy of his 1911 paper on Bernoulli numbers.

Hill replied in a fairly encouraging way but showed that he had failed to understand Ramanujan's results on divergent series. The recommendation to Ramanujan that he read Bromwich's Theory of infinite series did not please Ramanujan much. Ramanujan wrote to E W Hobson and H F Baker trying to interest them in his results but neither replied. In January 1913 Ramanujan wrote to G H Hardy having seen a copy of his 1910 book Orders of infinity. In Ramanujan's letter to Hardy he introduced himself and his work [10]:-

I have had no university education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at mathematics. I have not trodden through the conventional regular course which is followed in a university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as 'startling'.

Hardy, together with Littlewood, studied the long list of unproved theorems which Ramanujan enclosed with his letter. On 8 February he replied to Ramanujan the letter beginning:-

I was exceedingly interested by your letter and by the theorems which you state. You will however understand that, before I can judge properly of the value of what you have done, it is essential that I should see proofs of some of your assertions. Your results seem to me to fall into roughly three classes:
(1) there are a number of results that are already known, or easily deducible from known theorems;
(2) there are results which, so far as I know, are new and interesting, but interesting rather from their curiosity and apparent difficulty than their importance;
(3) there are results which appear to be new and important...

Ramanujan was delighted with Hardy's reply and when he wrote again he said [8]:-

I have found a friend in you who views my labours sympathetically. ... I am already a half starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university of from the government.

Indeed the University of Madras did give Ramanujan a scholarship in May 1913 for two years and, in 1914, Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration. Setting this up was not an easy matter. Ramanujan was an orthodox Brahmin and so was a strict vegetarian. His religion should have prevented him from travelling but this difficulty was overcome, partly by the work of E H Neville who was a colleague of Hardy's at Trinity College and who met with Ramanujan while lecturing in India.

Ramanujan sailed from India on 17 March 1914. It was a calm voyage except for three days on which Ramanujan was seasick. He arrived in London on 14 April 1914 and was met by Neville. After four days in London they went to Cambridge and Ramanujan spent a couple of weeks in Neville's home before moving into rooms in Trinity College on 30^th April. Right from the beginning, however, he had problems with his diet. The outbreak of World War I made obtaining special items of food harder and it was not long before Ramanujan had health problems.

Right from the start Ramanujan's collaboration with Hardy led to important results. Hardy was, however, unsure how to approach the problem of Ramanujan's lack of formal education. He wrote [1]:-

What was to be done in the way of teaching him modern mathematics? The limitations of his knowledge were as startling as its profundity.

Littlewood was asked to help teach Ramanujan rigorous mathematical methods. However he said ([31]):-

... that it was extremely difficult because every time some matter, which it was thought that Ramanujan needed to know, was mentioned, Ramanujan's response was an avalanche of original ideas which made it almost impossible for Littlewood to persist in his original intention.

The war soon took Littlewood away on war duty but Hardy remained in Cambridge to work with Ramanujan. Even in his first winter in England, Ramanujan was ill and he wrote in March 1915 that he had been ill due to the winter weather and had not been able to publish anything for five months. What he did publish was the work he did in England, the decision having been made that the results he had obtained while in India, many of which he had communicated to Hardy in his letters, would not be published until the war had ended.

On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (the degree was called a Ph.D. from 1920). He had been allowed to enrol in June 1914 despite not having the proper qualifications. Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England.

Ramanujan fell seriously ill in 1917 and his doctors feared that he would die. He did improve a little by September but spent most of his time in various nursing homes. In February 1918 Hardy wrote

Batty Shaw found out, what other doctors did not know, that he had undergone an operation about four years ago. His worst theory was that this had really been for the removal of a malignant growth, wrongly diagnosed. In view of the fact that Ramanujan is no worse than six months ago, he has now abandoned this theory - the other doctors never gave it any support. Tubercle has been the provisionally accepted theory, apart from this, since the original idea of gastric ulcer was given up. ... Like all Indians he is fatalistic, and it is terribly hard to get him to take care of himself.

On 18 February 1918 Ramanujan was elected a fellow of the Cambridge Philosophical Society and then three days later, the greatest honour that he would receive, his name appeared on the list for election as a fellow of the Royal Society of London. He had been proposed by an impressive list of mathematicians, namely Hardy, MacMahon, Grace, Larmor, Bromwich, Hobson, Baker, Littlewood, Nicholson, Young, Whittaker, Forsyth and Whitehead. His election as a fellow of the Royal Society was confirmed on 2 May 1918, then on 10 October 1918 he was elected a Fellow of Trinity College Cambridge, the fellowship to run for six years.

The honours which were bestowed on Ramanujan seemed to help his health improve a little and he renewed his effors at producing mathematics. By the end of November 1918 Ramanujan's health had greatly improved. Hardy wrote in a letter [3]:-

I think we may now hope that he has turned to corner, and is on the road to a real recovery. His temperature has ceased to be irregular, and he has gained nearly a stone in weight. ... There has never been any sign of any diminuation in his extraordinary mathematical talents. He has produced less, naturally, during his illness but the quality has been the same. ....

He will return to India with a scientific standing and reputation such as no Indian has enjoyed before, and I am confident that India will regard him as the treasure he is. His natural simplicity and modesty has never been affected in the least by success - indeed all that is wanted is to get him to realise that he really is a success.

Ramanujan sailed to India on 27 February 1919 arriving on 13 March. However his health was very poor and, despite medical treatment, he died there the following year.

The letters Ramanujan wrote to Hardy in 1913 had contained many fascinating results. Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function. On the other hand he had only a vague idea of what constitutes a mathematical proof. Despite many brilliant results, some of his theorems on prime numbers were completely wrong.

Ramanujan independently discovered results of Gauss, Kummer and others on hypergeometric series. Ramanujan's own work on partial sums and products of hypergeometric series have led to major development in the topic. Perhaps his most famous work was on the number p(n) of partitions of an integer n into summands. MacMahon had produced tables of the value of p(n) for small numbers n, and Ramanujan used this numerical data to conjecture some remarkable properties some of which he proved using elliptic functions. Other were only proved after Ramanujan's death.

In a joint paper with Hardy, Ramanujan gave an asymptotic formula for p(n). It had the remarkable property that it appeared to give the correct value of p(n), and this was later proved by Rademacher.

Ramanujan left a number of unpublished notebooks filled with theorems that mathematicians have continued to study. G N Watson, Mason Professor of Pure Mathematics at Birmingham from 1918 to 1951 published 14 papers under the general title Theorems stated by Ramanujan and in all he published nearly 30 papers which were inspired by Ramanujan's work. Hardy passed on to Watson the large number of manuscripts of Ramanujan that he had, both written before 1914 and some written in Ramanujan's last year in India before his death.

The picture above is taken from a stamp issued by the Indian Post Office to celebrate the 75^th anniversary of his birth.

Nicolaus Copernicus

Nicolaus Copernicus is the Latin version of the famous astronomer's name which he chose later in his life. The original form of his name was Mikolaj Kopernik or Nicolaus Koppernigk but we shall use Copernicus throughout this article. His father, also called Nicolaus Koppernigk, had lived in Kraków before moving to Torun where he set up a business trading in copper. He was also interested in local politics and became a civic leader in Torun and a magistrate. Nicolaus Koppernigk married Barbara Watzenrode, who came from a well off family from Torun, in about 1463. They moved into a house in St Anne's Street in Torun, but they also had a summer residence with vineyards out of town. Nicolaus and Barbara Koppernigk had four children, two sons and two daughters, of whom Nicolaus Copernicus was the youngest.

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When young Nicolaus was ten years old his father died. His uncle Lucas Watzenrode, who was a canon at Frauenburg Cathedral, became guardian to Nicolaus and Barbara Koppernigk's four children.

Nicolaus and his brother Andreas remained in Torun, continuing their elementary education there. In 1488 Nicolaus was sent by his uncle to the cathedral school of Wloclawek where he received a good standard humanist education. After three years of study at Wloclawek he entered the University of Kraków (situated in what was then the capital of Poland). By this time Lucas Watzenrode was Bishop of Ermland and he envisaged a church career for both of his nephews. Andreas, Nicolaus's brother, entered the University of Kraków at the same time, and both their names appear on the matriculation records of 1491-92.

University education at Kraków was, Copernicus later wrote, a vital factor in everything that he went on to achieve. There he studied Latin, mathematics, astronomy, geography and philosophy. He learnt his astronomy from Tractatus de Sphaera by Johannes de Sacrobosco written in 1220. One should not think, however, that the astronomy courses which Copernicus studied were scientific courses in the modern sense. Rather they were mathematics courses which introduced Aristotle andPtolemy's view of the universe so that students could understand the calendar, calculate the dates of holy days, and also have skills that would enable those who would follow a more practical profession to navigate at sea. Also taught as a major part of astronomy was what today we would call astrology, teaching students to calculate horoscopes of people from the exact time of their birth.

While a student in Kraków, Copernicus purchased a copy of the Latin translation of Euclid's Elements published in Venice in 1482, a copy of the second edition of the Alfonsine Tables (which gives planetary theory and eclipses) printed in Venice in 1492, and Regiomontanus's Tables of Directions (a work on spherical astronomy) published in Augsburg in 1490. Remarkably Copernicus's copies of these works, signed by him, are still preserved.

It was while he was a student at Kraków that Copernicus began to use this Latin version of his name rather than Kopernik or Koppernigk. He returned to Torun after four years of study at Kraków but, as was common at the time, did not formally graduate with a degree. His uncle Lucas Watzenrode was still determined that Copernicus should have a career in the Church and indeed this was a profession which would allow security for someone wanting to pursue leaning. So that he might have the necessary qualifications Copernicus decided to go to the University of Bologna to take a degree in canon law. In the autumn of 1496 he travelled to Italy, entering the University of Bologna on 19 October 1496, to start three years of study. As a native German speaker he joined the "German Nation of Bologna University". Each student contributed to the "German Nation" an amount they could afford and the small contribution that Copernicus made indicates his poor financial position at that time.

While he was there his uncle put his name forward for the position of canon at Frauenburg Cathedral. On 20 October 1497, while in Bologna, Copernicus received official notification of his appointment as a canon and of the comfortable income he would receive without having to return to carry out any duties. At Bologna University Copernicus studied Greek, mathematics and astronomy in addition to his official course of canon law. He rented rooms at the house of the astronomy professor Domenico Maria de Novara and began to undertake research with him, assisting him in making observations. On 9 March 1497 he observed the Moon eclipse the star Aldebaran.

In 1500 Copernicus visited Rome, as all Christians were strongly encouraged to do to celebrate the great jubilee, and he stayed there for a year lecturing to scholars on mathematics and astronomy. While in Rome he observed an eclipse of the Moon which took place on 6 November 1500. He returned to Frauenburg (also known as Frombork) in the spring of 1501 and was officially installed as a canon of the Ermland Chapter on 27 July. He had not completed his degree in canon law at Bologna so he requested his uncle that he be allowed to return to Italy both to take a law degree and to study medicine. Copernicus was granted leave on 27 July 1501 [13]:-

... principally because Nicolaus promised to study medicine, and as a helpful physician would some day advise our most reverend bishop and also the members of the Chapter.

As this quotation indicates, the Cathedral Chapter liked his proposal to study medicine and provided the necessary funds. He set off again for Italy, his time going to Padua. Copernicus had another reason to return to Italy, which he almost certainly did not disclose, and that was to continue his studies of astronomy.

Padua was famous for its medical school and while he was there Copernicus studied both medicine and astronomy. At that time astronomy was essentially astrology and, as such, considered relevant to medicine since physicians made use of astrology. In the spring of 1503 he decided formally to obtain his doctorate in Canon Law, but he did not return to Bologna but rather took the degree at the University of Ferrara. After receiving his doctorate, Copernicus stayed in Ferrara for a few months before returning to Padua to continue his studies of medicine. There is no record that he ever graduated from Padua.

When he returned to his native land, Copernicus was again granted leave from his official duties as a canon in the Ermland Chapter at Frauenburg. This was allow him to be physician to his maternal uncle Lucas Watzenrode, the Bishop of Ermland, but he carried out far more duties for his uncle than medical ones becoming essentially his private secretary and personal advisor. For about five years he undertook these duties and during this period he lived at Heilsberg Castle, a few miles from Frauenburg, the official residence of the Bishop of Ermland.

In 1509 Copernicus published a work, which was properly printed, giving Latin translations of Greek poetry by the obscure poet Theophylactus Simocattes. While accompanying his uncle on a visit to Kraków, he gave a manuscript of the poetry book to a publisher friend there. Lucas Watzenrode died in 1512 and following this Copernicus resumed his duties as canon in the Ermland Chapter at Frauenburg. He now had more time than before to devote to his study of astronomy, having an observatory in the rooms in which he lived in one of the towers in the town's fortifications.

Around 1514 he distributed a little book, not printed but hand written, to a few of his friends who knew that he was the author even though no author is named on the title page. This book, usually called the Little Commentary, set out Copernicus's theory of a universe with the sun at its centre. The Little Commentary is a fascinating document. It contains seven axioms which Copernicus gives, not in the sense that they are self evident, but in the sense that he will base his conclusions on these axioms and nothing else; see [79]. What are the axioms? Let us state them:

1. There is no one centre in the universe.

2. The Earth's centre is not the centre of the universe.

3. The centre of the universe is near the sun.

4. The distance from the Earth to the sun is imperceptible compared with the distance to the stars.

5. The rotation of the Earth accounts for the apparent daily rotation of the stars.

6. The apparent annual cycle of movements of the sun is caused by the Earth revolving round it.

7. The apparent retrograde motion of the planets is caused by the motion of the Earth from which one observes.

Some have noted that 2, 4, 5, and 7 can be deduced from 3 and 6 but it was never Copernicus's aim to give a minimal set of axioms. The most remarkable of the axioms is 7, for although earlier scholars had claimed that the Earth moved, some claiming that it revolved round the sun, nobody before Copernicus appears to have correctly explained the retrograde motion of the outer planets. Even when he wrote his Little Commentary Copernicus was planning to write a major work, for he wrote in it

Albert Einstein

Albert Einstein was born at Ulm, in Württemberg, Germany, on March 14, 1879.

Six weeks later the family moved to Munich and he began his schooling there at the Luitpold Gymnasium. Later, they moved to Italy and Albert continued his education at Aarau, Switzerland.

In 1896 he entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma, he acquired Swiss citizenship and, as he was unable to find a teaching post, he accepted a position as technical assistant in the Swiss Patent Office. In 1905 he obtained his doctor's degree.

During his stay at the Patent Office, and in his spare time, he produced much of his remarkable work and in 1908 he was appointed Privatdozent in Berne. In 1909 he became Professor Extraordinary at Zurich, in 1911 Professor of Theoretical Physics at Prague, returning to Zurich in the following year to fill a similar post. In 1914 he was appointed Director of the Kaiser Wilhelm Physical Institute and Professor in the University of Berlin. He became a German citizen in 1914 and remained in Berlin until 1933 when he renounced his citizenship for political reasons and emigrated to America to take the position of Professor of Theoretical Physics at Princeton. He became a United States citizen in 1940 and retired from his post in 1945.

After World War II, Einstein was a leading figure in the World Government Movement, he was offered the Presidency of the State of Israel, which he declined, and he collaborated with Dr. Chaim Weizmann in establishing the Hebrew University of Jerusalem.

Einstein always appeared to have a clear view of the problems of physics and the determination to solve them. He had a strategy of his own and was able to visualize the main stages on the way to his goal. He regarded his major achievements as mere stepping-stones for the next advance.

At the start of his scientific work, Einstein realized the inadequacies of Newtonian mechanics and his special theory of relativity stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field. He dealt with classical problems of statistical mechanics and problems in which they were merged with quantum theory: this led to an explanation of the Brownian movement of molecules. He investigated the thermal properties of light with a low radiation density and his observations laid the foundation of the photon theory of light.

In his early days in Berlin, Einstein postulated that the correct interpretation of the special theory of relativity must also furnish a theory of gravitation and in 1916 he published his paper on the general theory of relativity. During this time he also contributed to the problems of the theory of radiation and statistical mechanics.

In the 1920's, Einstein embarked on the construction of unified field theories, although he continued to work on the probabilistic interpretation of quantum theory, and he persevered with this work in America. He contributed to statistical mechanics by his development of the quantum theory of a monatomic gas and he has also accomplished valuable work in connection with atomic transition probabilities and relativistic cosmology.

After his retirement he continued to work towards the unification of the basic concepts of physics, taking the opposite approach, geometrisation, to the majority of physicists.

Einstein's researches are, of course, well chronicled and his more important works include Special Theory of Relativity (1905), Relativity (English translations, 1920 and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works, About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later Years (1950) are perhaps the most important.

Albert Einstein received honorary doctorate degrees in science, medicine and philosophy from many European and American universities. During the 1920's he lectured in Europe, America and the Far East and he was awarded Fellowships or Memberships of all the leading scientific academies throughout the world. He gained numerous awards in recognition of his work, including the Copley Medal of the Royal Society of London in 1925, and the Franklin Medal of the Franklin Institute in 1935.

Einstein's gifts inevitably resulted in his dwelling much in intellectual solitude and, for relaxation, music played an important part in his life.

He married Mileva Maritsch in 1901 and they had two sons; their marriage was dissolved and in 1917 he married his cousin, Elsa Einstein, who died in 1936.

He died on April 18, 1955 at Princeton, New Jersey.

C.V. Raman

Born: November--7,1888
Died: November--21,1970
Achievements: He was the first Indian scholar who studied wholly in India received the Nobel Prize.

C.V. Raman is one of the most renowned scientists produced by India. His full name was Chandrasekhara Venkata Raman. For his pioneering work on scattering of light, C.V. Raman won the Nobel Prize for Physics in 1930.

Chandrashekhara Venkata Raman was born on November 7, 1888 in Tiruchinapalli, Tamil Nadu. He was the second child of Chandrasekhar Iyer and Parvathi Amma. His father was a lecturer in mathematics and physics, so he had an academic atmosphere at home. He entered Presidency College, Madras, in 1902, and in 1904 passed his B.A. examination, winning the first place and the gold medal in physics. In 1907, C.V. Raman passed his M.A. obtaining the highest distinctions.

During those times there were not many opportunities for scientists in India. Therefore, Raman joined the Indian Finance Department in 1907. After his office hours, he carried out his experimental research in the laboratory of the Indian Association for the Cultivation of Science at Calcutta. He carried out research in acoustics and optics.

In 1917, Raman was offered the position of Sir Taraknath Palit Professorship of Physics at Calcutta University. He stayed there for the next fifteen years. During his tenure there, he received world wide recognition for his work in optics and scattering of light. He was elected to the Royal Society of London in 1924 and the British made him a knight of the British Empire in 1929. In 1930, Sir C.V. Raman was awarded with Nobel Prize in Physics for his work on scattering of light. The discovery was later christened as "Raman Effect".

In 1934, C.V. Raman became the director of the newly established Indian Institute of Sciences in Bangalore, where two years later he continued as a professor of physics. Other investigations carried out by Raman were: his experimental and theoretical studies on the diffraction of light by acoustic waves of ultrasonic and hypersonic frequencies (published 1934-1942), and those on the effects produced by X-rays on infrared vibrations in crystals exposed to ordinary light. In 1947, he was appointed as the first National Professor by the new government of Independent India. He retired from the Indian Institute in 1948 and a year later he established the Raman Research Institute in Bangalore, where he worked till his death.

Aryabhata the Elder

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 to 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 15^th century. It is now thought by most historians thatNilakantha confused Aryabhata with Bhaskara I who was a later commentator on the Aryabhatiya.

We should note that Kusumapura became one of the two major mathematical centres of India, the other being Ujjain. Both are in the north but Kusumapura (assuming it to be close to Pataliputra) is on the Ganges and is the more northerly. Pataliputra, being the capital of the Gupta empire at the time of Aryabhata, was the centre of a communications network which allowed learning from other parts of the world to reach it easily, and also allowed the mathematical and astronomical advances made by Aryabhata and his school to reach across India and also eventually into the Islamic world.

As to the texts written by Aryabhata only one has survived. However Jha claims in [21] that:-

... Aryabhata was an author of at least three astronomical texts and wrote some free stanzas as well.

The surviving text is Aryabhata's masterpiece the Aryabhatiya which is a small astronomical treatise written in 118 verses giving a summary of Hindu mathematics up to that time. Its mathematical section contains 33 verses giving 66 mathematical rules without proof. The Aryabhatiya contains an introduction of 10 verses, followed by a section on mathematics with, as we just mentioned, 33 verses, then a section of 25 verses on the reckoning of time and planetary models, with the final section of 50 verses being on the sphere and eclipses.

There is a difficulty with this layout which is discussed in detail by van der Waerden in [35]. Van der Waerden suggests that in fact the 10 verse Introduction was written later than the other three sections. One reason for believing that the two parts were not intended as a whole is that the first section has a different meter to the remaining three sections. However, the problems do not stop there. We said that the first section had ten verses and indeed Aryabhata titles the section Set of ten giti stanzas. But it in fact contains eleven giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have been added and he identifies a small number of verses in the remaining sections which he argues have also been added by a member of Aryabhata's school at Kusumapura.

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. Let us examine some of these in a little more detail.

First we look at the system for representing numbers which Aryabhata invented and used in the Aryabhatiya. It consists of giving numerical values to the 33 consonants of the Indian alphabet to represent 1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100. The higher numbers are denoted by these consonants followed by a vowel to obtain 100, 10000, .... In fact the system allows numbers up to 10¹⁸to be represented with an alphabetical notation. Ifrah in [3] argues that Aryabhata was also familiar with numeral symbols and the place-value system. He writes in [3]:-

... it is extremely likely that Aryabhata knew the sign for zero and the numerals of the place value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value 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 place-value system and zero.

Next we look briefly at some algebra contained in the Aryabhatiya. This work is the first we are aware of which examines integer solutions to equations of the formby = ax + c and by = ax - c, where a, b, c are integers. The problem arose from studying the problem in astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to solve problems of this type. The word kuttaka means "to pulverise" and the method consisted of breaking the problem down into new problems where the coefficients became smaller and smaller with each step. The method here is essentially the use of the Euclidean algorithm to find the highest common factor of a and b but is also related to continued fractions.

Aryabhata gave an accurate approximation for π. He wrote in the Aryabhatiya the following:-

Add four to one hundred, multiply by eight and then add sixty-two thousand. the result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.

This gives π = ⁶²⁸³²/₂₀₀₀₀ = 3.1416 which is a surprisingly accurate value. In fact π = 3.14159265 correct to 8 places. If obtaining a value this accurate is surprising, it is perhaps even more surprising that Aryabhata does not use his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how he found this accurate value but, for example, Ahmad [5] considers this value as an approximation to half the perimeter of a regular polygon of 256 sides inscribed in the unit circle. However, in [9] Bruins shows that this result cannot be obtained from the doubling of the number of sides. Another interesting paper discussing this accurate value of π by Aryabhata is [22] where Jha writes:-

Aryabhata I's value of π is a very close approximation to the modern value and the most accurate among those of the ancients. There are reasons to believe that Aryabhata devised a particular method for finding this value. It is shown with sufficient grounds that Aryabhata himself used it, and several later Indian mathematicians and even the Arabs adopted it. The conjecture that Aryabhata's value of π is of Greek origin is critically examined and is found to be without foundation. Aryabhata discovered this value independently and also realised that π is an irrational number. He had the Indian background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit of discovering this exact value of π may be ascribed to the celebrated mathematician, Aryabhata I.

We now look at the trigonometry contained in Aryabhata's treatise. He gave a table of sines calculating the approximate values at intervals of 90°/24 = 3° 45'. In order to do this he used a formula for sin(n+1)x - sin nx in terms of sin nx and sin (n-1)x. He also introduced the versine (versin = 1 - cosine) into trigonometry.

Other rules given by Aryabhata include that for summing the first n integers, the squares of these integers and also their cubes. Aryabhata gives formulae for the areas of a triangle and of a circle which are correct, but the formulae for the volumes of a sphere and of a pyramid are claimed to be wrong by most historians. For example Ganitanand in [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V = Ah/2 for the volume of a pyramid with height h and triangular base of area A. He also appears to give an incorrect expression for the volume of a sphere. However, as is often the case, nothing is as straightforward as it appears and Elfering (see for example [13]) argues that this is not an error but rather the result of an incorrect translation.

This relates to verses 6, 7, and 10 of the second section of the Aryabhatiya and in [13] Elfering produces a translation which yields the correct answer for both the volume of a pyramid and for a sphere. However, in his translation Elfering translates two technical terms in a different way to the meaning which they usually have. Without some supporting evidence that these technical terms have been used with these different meanings in other places it would still appear that Aryabhata did indeed give the incorrect formulae for these volumes.

We have looked at the mathematics contained in the Aryabhatiya but this is an astronomy text so we should say a little regarding the astronomy which it contains. Aryabhata gives a systematic treatment of the position of the planets in space. He gave the circumference of the earth as 4 967 yojanas and its diameter as 1 581¹/₂₄yojanas. Since 1 yojana = 5 miles this gives the circumference as 24 835 miles, which is an excellent approximation to the currently accepted value of 24 902 miles. He believed that the apparent rotation of the heavens was due to the axial rotation of the Earth. This is a quite remarkable view of the nature of the solar systemwhich later commentators could not bring themselves to follow and most changed the text to save Aryabhata from what they thought were stupid errors!

Aryabhata 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. The Indian belief up to that time was that eclipses were caused by a demon called Rahu. His value for the length of the year at 365 days 6 hours 12 minutes 30 seconds is an overestimate since the true value is less than 365 days 6 hours.

Bhaskara I who wrote a commentary on the Aryabhatiya about 100 years later wrote of Aryabhata:-

Aryabhata 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.