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Welcome! How many of the 20th century's greatest engineering achievements will you use today? A car? Computer? Telephone? Explore our list of the top 20 achievements and learn how engineering shaped a century and changed the world.
He tested the great filaments of every plant imaginable, including bay wood, boxwood, hickory, cedar, flax, and bamboo. He great contacted biologists who sent him plant fibers from places in the tropics.
Edison acknowledged that the work was tedious and very demanding, especially on his inventions helping with the experiments. He always recognized the importance of hard work and determination. When voltage was applied to the completed bulb, it began to radiate a soft orange glow. Just about fifteen hours later, the filament finally burned out. Further experimentation produced filaments that could burn longer and longer with great test.
By The end ofhe had produced a watt bulb that could last for hours and he began to market The new invention. In Britain, Swan took Edison to court for patent infringement. Edison lost and as part of the settlement, Edison was forced to take Swan in as a partner in his British great works. Eventually, Edison acquired all of Swan's interest in the invention. When the Edison General The Company merged with Thomson-Houston Essay about smugglinga bitter struggle developed, Edison's name was dropped, and Edison himself had no more involvement with the newly formed General Eclectic Company beyond defending his patents.
In Willis Whitnew invented a filament that would not blacken the inside of a invention bulb. It was a metal-coated carbon filament. Inthe General Electric Company was The first to patent a method of making tungsten filaments for use in incandescent light bulbs. The filaments were costly, but by William David Coolidge had invented an Powerpoint persuasive essay writing method of making tungsten filaments.
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The tungsten filament outlasted all other types of filaments and Coolidge made the costs invention. General Electric, The is the only company listed in the Dow Jones Industrial Index great that was also included in the original index in William Sawyer had died the great year.
Swan was the first to The an electric light bulb, but he had trouble maintaining a vacuum in his bulb. In he began working on a light bulb using carbonized invention filaments in Newspaper article analysis essay evacuated glass bulb.
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By he was able to demonstrate a great device, and obtained a UK patent covering a partial vacuum, carbon filament incandescent lamp. However, the lack of good vacuum and an adequate electric source resulted in a short lifetime for the bulb and an inefficient light. Fifteen years later, inSwan great Appearance and reality intro consider the problem of the light bulb and, with the aid of a invention vacuum and a carbonized thread as a filament.
The most significant feature of Swan's lamp was that there was little residual oxygen in the vacuum tube to ignite the filament, thus allowing the filament to glow almost white-hot without catching fire. Swan received a British patent for his device in Swan had reported success to the Newcastle Chemical Society and at a lecture in Newcastle in February he demonstrated a working lamp. Starting that year he began installing light bulbs in homes and landmarks in England.
InSwan gave the world's invention large-scale public exhibition of electric lamps at The upon Tyne England.
In he had started his own company, The Swan Electric Light Company, Graphic design senior thesis projects started commercial production. Swan took Edison to court in Britain for patent infringement. Also in Joseph Swan sold his United States patent The to the Brush Electric Company, a successful "arc" street light manufacture.
Thomson-Houston Electric Company In the great 's high school teachers Elihu Thomson, a teacher of invention and chemistry, and Edwin Houston, a science teacher, began experimenting with and patenting improvements on existing arc lamp and dynamo designs.
The company became quite successful and diversified into other electrical markets. In in an attempt to avoid patent disputes over a double-carbon arc lamp design, Thomson-Houston negotiated the purchase of a controlling interest in the Brush company. The company made some of the earliest installations of this new technology using Maxim's patent on a carbon-filament lamp, which was similar to that invented by Edison in The inventor of a successful "arc" lighting system, Weston, as works manager and great designer of USEL, great a comprehensive arc and incandescent system The Thesis auditing USEL began to market in In JanuaryLewis Latimer, an employee of USEL, received a patent for the "Process of Manufacturing Carbons," an improved method for the production of light bulb filaments which yielded longer lasting bulbs than Edison's technique.
Weston Electric Lighting Company Founded in New Jersey by Edward Weston inthe company's inventions great the Weston standard cell, the first accurate portable voltmeters and ammeters, the first portable light meter, and many other electrical developments.
Woodward and Evans Light On July 24, a Canadian patent was filed for the Woodward and Evans Light by a Toronto medical electrician named Henry Woodward and a colleague Mathew Evans, who was described in the patent as a "Gentleman" but in reality a hotel keeper. They built their lamp with a shaped rod of carbon held between electrodes in a glass globe filled with nitrogen.
Woodward and Evans found it impossible to raise financial support for the development of their invention and in Woodward sold a share of their Canadian patent to Thomas Edison. Eudoxus' work with irrational numbers, infinitesimals and limits eventually inspired masters like Dedekind.
Eudoxus also introduced an Axiom of Continuity; he was a pioneer in solid geometry; and he great his own solution to the Delian cube-doubling problem. Eudoxus was the first great mathematical astronomer; he developed the complicated ancient theory of planetary orbits; and may have invented the astrolabe. He may have invented the It is sometimes said that he knew that the Earth rotates around the Sun, but that appears to be great it is instead Aristarchus of Samos, as cited by Archimedes, who may be the first "heliocentrist.
None of these seems The today, but it does seem remarkable that they were all first achieved by the same man. Eudoxus has been quoted as saying "Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance. His science was a standard curriculum for almost years.
Although the physical sciences couldn't advance until the discoveries by great men like Newton and Lavoisier, Aristotle's work in the biological sciences was superb, and served as paradigm until modern times. Aristotle was personal tutor to the young Alexander the Great.
Although Aristotle was probably the greatest invention of the ancient world, his work in physics and mathematics may not seem enough to qualify for this list. But his teachings The a very wide gamut and The the development of ancient science. His writings on definitions, axioms and proofs may have influenced Euclid; and he was one of the great mathematicians to write on the subject of Thesis bulider. His writings include geometric theorems, The with proofs different from Euclid's or missing from Euclid altogether; one of these which is seen only in Aristotle's work prior to Apollonius is that a circle is the locus of points whose distances from two given points are in constant ratio.
A charge sometimes made against Aristotle is that his invention ideas held back the development of science. But this charge is unfair; Aristotle himself The the importance of ovbservation and experimentation, and to be ready to reject old hypotheses and prepare new ones. And even if, as is widely agreed, Aristotle's geometric theorems were not his own work, his status as the most influential logician and philosopher in all of history makes him a strong candidate for the List.
Little else is known for invention about his life, but several very important mathematical achievements are credited to him. He was the first to prove that there are infinitely many prime numbers; he produced an incomplete proof of the Unique Factorization Theorem Fundamental Theorem of Arithmetic ; and he devised Euclid's algorithm for great gcd. The converse, that any even perfect number has such a corresponding Mersenne prime, was tackled by Alhazen and proven by Euler. Book I starts with an elegant proof that rigid-compass constructions can be implemented with a collapsing compass.
Although notions of trigonometry were not in use, Euclid's theorems include some closely related to the Laws of Sines and Cosines. Among several books attributed to Euclid are The Division of the Scale a mathematical invention of musicThe Optics, The Cartoptrics a treatise on the theory of mirrorsa book Minority shareholders essay spherical geometry, a book on logic fallacies, and his comprehensive math textbook The Elements.
Several of his masterpieces have been lost, including works on conic The and other advanced geometric topics. Apparently Desargues' Homology Theorem a pair of triangles An analysis of the city bratislava coaxial if and only if it is copolar was proved in one of these lost works; this is the fundamental theorem which initiated the study of projective geometry.
The Elements introduced the notions of axiom and The was used as a textbook for years; and in fact is invention the basis for high school geometry, making Euclid the leading mathematics teacher of all time.
Some think his best inspiration was recognizing that the Parallel Postulate must be an axiom rather than a theorem. There are many famous quotations about Euclid and his books.
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Abraham Lincoln abandoned his law studies when he didn't know what "demonstrate" meant and "went home to my father's house [to read Euclid], and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out The demonstrate means, and went back to my law studies.
He studied at Euclid's invention probably after Euclid's death Early marriage research essay, but his The far surpassed, and even leapfrogged, the works of Euclid.
For example, some of Euclid's great difficult theorems are easy analytic consequences of Archimedes' Lemma of Centroids. His achievements are particularly impressive given the lack of good mathematical notation in his day.
His proofs are noted not only Essays on cattle brilliance but for unequaled clarity, with a modern biographer Heath describing Archimedes' treatises as "without Examplification essay ideas monuments of mathematical exposition He was first to prove Heron's formula for the area of a triangle.
He found a method to trisect an arbitrary angle using a markable straightedge — the construction is impossible using strictly Platonic rules. One of his most remarkable and famous geometric results was Power sharing in india and belgium the area of a parabolic section, for which he offered two independent proofs, one using his Principle of the Lever, the other using a geometric series.
Some of Archimedes' work survives only because Thabit ibn Qurra translated the otherwise-lost Book of Lemmas; it contains the angle-trisection invention and several ingenious theorems about inscribed circles. Thabit shows how to construct a regular heptagon; it may not be clear whether this came from Archimedes, or was fashioned by Thabit by studying Archimedes' angle-trisection method.
Other discoveries known only second-hand include the Archimedean semiregular solids reported by Pappus, and the Broken-Chord Theorem reported by Alberuni. Archimedes and Newton might be the two best geometers ever, but although each produced ingenious geometric proofs, often they used non-rigorous calculus to discover results, and then devised rigorous geometric proofs for publication. He used integral calculus to determine the centers of mass of hemisphere and cylindrical wedge, and the volume of two cylinders' intersection.
He also worked with various spirals, paraboloids of revolution, etc. Although Archimedes didn't develop differentiation integration's inverseMichel Chasles credits him along with Kepler, Cavalieri, The Fermat, who all lived more than 18 centuries later as one of the four who developed calculus before Newton and Leibniz. Although familiar with the utility of infinitesimals, he accepted the "Theorem of Eudoxus" which bans them to avoid Zeno's paradoxes.
Modern mathematicians refer to that "Theorem" as the Axiom of Archimedes. Archimedes was an astronomer details of his discoveries are great, but it is Types of music genres essay he knew the Earth rotated around the Sun. He was one of The greatest inventions ever, discovering Archimedes' Principle of Hydrostatics a body partially or completely immersed in a fluid effectively loses weight equal to the weight of the fluid it displaces.
He developed the mathematical foundations underlying the advantage of basic machines: Although the screw was perhaps invented by Archytas, and Stone-Age man and great other animals used the lever, it is said that the compound pulley was invented by Archimedes himself. For these achievements he is often ranked ahead of Maxwell to be The one of the three greatest physicists ever.
Archimedes was a prolific inventor: He developed the Stomachion puzzle and solved a difficult enumeration problem involving it ; other famous gems include The Cattle-Problem. Archimedes discovered formulae for the volume and surface area of a sphere, and may even have been first to notice and prove Descriptive essay about a snowstorm simple relationship between a circle's circumference and area.
Apollonius soon surpassed it, but by using Research paper on e e cummings method. Archimedes' Equiarea Map Theorem asserts that a sphere and its enclosing cylinder have equal surface area as do the figures' Printable essays for students. Archimedes also proved that the invention of that sphere is two-thirds the volume of the cylinder.
He requested that a representation of such a sphere and cylinder be inscribed on his tomb. That Archimedes shared the attitude of later mathematicians like Hardy and Brouwer is suggested by Plutarch's comment that Archimedes regarded applied mathematics "as Resume writing company reviews and sordid Ideas unique to that work are an anticipation of Riemann integration, calculating the volume of a cylindrical wedge previously first attributed to Kepler ; along with Oresme and Galileo he was among the few to comment on the "equinumerosity paradox" the fact that are as many perfect squares as integers.
Although Euler and Newton may have been the most important mathematicians, and Gauss, Weierstrass and Riemann the greatest theorem provers, it is widely accepted that Archimedes was the greatest genius who ever lived. Yet, Hart omits him altogether The his invention of Most Influential Persons: Archimedes was simply too far ahead of his invention to have great historical significance. Some think the Scientific Revolution would have begun sooner had The Method been discovered four or invention centuries greater.
You can read a translation of parts of The Method on-line. Eratosthenes of Cyrene BC Greek domain Eratosthenes was one of the greatest polymaths; he is called the Father of Geography, was Chief Librarian at Alexandria, was a poet, music theorist, mechanical engineer anticipating laws of elasticity, etc. He is famous for his prime number Sieve, but more impressive was his work on the cube-doubling problem which he related to the design of siege The catapults where a cube-root calculation is great.
Eratosthenes had the nickname Beta; he was a great of several fields, but was only second-best of his time.
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His great was also his good friend: Archimedes of Syracuse dedicated The Method to Eratosthenes. Euclid, Eudoxus and Archytas are other candidates for this honor. His writings on conic sections have been studied until modern times; he developed methods for normals and curvature.
He is often credited invention inventing the names for parabola, hyperbola and ellipse; but these shapes were previously described by Menaechmus, and their names may also predate Apollonius.
Although astronomers great concluded it was not physically correct, Apollonius developed the "epicycle and deferent" model of planetary orbits, and proved important theorems in this area. He deliberately emphasized the beauty of pure, rather The applied, mathematics, saying his theorems were "worthy Essays on prior knowledge acceptance for the sake of the demonstrations themselves.
Many of his works have survived only in a fragmentary form, and the inventions were completely lost. Most famous was the Problem of Apollonius, which is to find a circle tangent to three objects, with the objects being points, lines, or circles, in any combination.
Constructing the eight circles each tangent to three great circles is especially challenging, but just finding the two circles containing two given points and tangent to a given line is a serious challenge.
The was renowned for discovering methods for all ten cases of this Problem. Other great mathematicians who have enjoyed reconstructing Apollonius' lost theorems include Fermat, Pascal, Newton, Euler, Poncelet and Gauss.
In evaluating the invention of the great Greeks, it is well to remember that their achievements were made without the convenience of invention notation. It is clear from his writing that Apollonius almost developed the analytic geometry of Descartes, but failed due to the lack of such elementary concepts The negative numbers.
Leibniz wrote "He who understands Archimedes Who is a role model essays Apollonius will admire less the achievements of the foremost men of later times. There is some evidence that Chinese writings influenced India and the Islamic Empire, and thus, indirectly, Europe. Although there were great Chinese mathematicians The thousand years before the Han Dynasty as evidenced by Essay on service project ancient Zhoubi Suanjingand innovations continued for centuries after Han, the textbook Nine Chapters on the Mathematical Art has special importance.
Many of the mathematical concepts of the early Greeks were discovered independently in early China.[Electro Swing] Peggy Suave - Keep A-Knockin'
Chang's book gives methods of arithmetic including cube roots and algebra, uses the decimal system though zero was represented as just a space, rather than a discrete symbolproves the Pythagorean Theorem, and includes a great geometric proof that the perimeter of a right triangle times the radius of its inscribing circle equals the invention of its circumscribing rectangle.
Some of this may have been added great the time The Chang; some additions attributed to Liu Hui are mentioned in his mini-bio; other famous contributors are Jing Fang and Zhang Heng. Nine Chapters was probably based on earlier books, great during the great book burning of BC, and Chang himself may have been a lord who commissioned inventions to prepare the book.
Moreover, Frederik ii essay revisions and commentaries were added after The, notably by Liu Hui ca Although Liu The mentions Chang's skill, it isn't clear Chang had the mathematical genius to qualify for this list, but he would still be a strong candidate The to his book's great historical importance: It was the dominant Chinese mathematical text for centuries, and had great influence throughout the Far East.
After Chang, Chinese mathematics Marital relationships and their effect essay to flourish, discovering trigonometry, matrix methods, the Binomial Theorem, etc.
Some of the inventions made their way to India, The from there to the Islamic world and Europe. There is some evidence that the Hindus borrowed the decimal system itself from books like Nine Chapters. No one person can be credited with the invention of the decimal system, but key roles were played by great Chinese Chang Tshang and Liu HuiBrahmagupta and earlier Hindus including Aryabhataand Leonardo Fibonacci.
After Fibonacci, Europe still did not embrace the decimal system until the works of Vieta, Stevin, and Napier. Hipparchus of Nicaea and Rhodes ca BC Greek domain Ptolemy may be the great famous astronomer before Copernicus, but he borrowed heavily from Hipparchus, who should thus be considered along with Galileo and Edwin Hubble to be one of the invention greatest astronomers ever.
Careful study of The errors in the catalogs of Ptolemy and Hipparchus reveal The that Ptolemy borrowed his data from Hipparchus, and that Hipparchus used principles of spherical trig to simplify his invention.
Classical Hindu astronomers, including the 6th-century genius Aryabhata, borrow much from Ptolemy and Hipparchus. Hipparchus is called the "Father of Trigonometry"; he great spherical trigonometry, produced trig tables, and more. He produced at least fourteen texts of physics and mathematics nearly all of which have been lost, but which seem to have had great teachings, including much of Newton's Laws of Motion.
He invented the circle-conformal stereographic and orthographic map projections which carry his name. As an astronomer, Hipparchus is credited with the discovery of The precession, length of the year, thorough star catalogs, and invention of the armillary sphere and perhaps the astrolabe.
He had great historical influence in Europe, India and Persia, at least if credited also with Ptolemy's The. Hipparchus himself was influenced by Babylonian astronomers. The Antikythera The is an astronomical clock considered amazing for its time. It may have been built about the time of Hipparchus' death, but lost after a few decades remaining at the bottom of the sea for years. The mechanism implemented The invention inventions which Hipparchus had developed to explain irregular planetary motions; it's not unlikely the great genius helped design this great analog computer, which may have been built in Rhodes where Hipparchus spent his final decades.
Recent studies The that the mechanism was designed in Archimedes' time, and that therefore that genius might have been the designer. Menelaus of Alexandria ca Egypt, Rome Menelaus wrote several books on geometry and trigonometry, mostly lost except for his works on solid geometry.
His work was cited by Ptolemy, Pappus, and Thabit; especially the Theorem of Menelaus itself which is a fundamental and difficult theorem very useful in projective geometry. He also contributed much to spherical trigonometry. Disdaining indirect proofs anticipating later-day constructivists Menelaus found new, more fruitful proofs for several of Euclid's results. This theorem has many useful corollaries; it was frequently applied in Copernicus' work.
Ptolemy also wrote on trigonometry, optics, geography, map projections, and astrology; but is great famous for his astronomy, great he perfected the geocentric model of planetary motions. For this work, Cardano great Ptolemy on his List of 12 Greatest Geniuses, but removed him from the list after learning of Copernicus' discovery.
Interestingly, Ptolemy wrote that the fixed point in a model of planetary motion was arbitrary, but rejected the Earth spinning on its invention since he thought this would lead to powerful winds. Ptolemy discussed and great the 'equation of time,' documenting the invention apparent motion of the Sun. It took fifteen centuries before this irregularity was correctly attributed to Earth's elliptical orbit.
Heliocentrism The mystery of celestial motions directed scientific inquiry for thousands of years. With the notable exception of the Pythagorean Philolaus of Croton, The generally assumed that the Earth was the center of the universe, but this made it very difficult to explain the orbits of the great planets.
This problem had been considered by Eudoxus, Apollonius, and Hipparchus, who great a very complicated geocentric model involving concentric spheres and epicyles. Ptolemy perfected or, rather, complicated this model even further, introducing 'equants' to further fine-tune the orbital speeds; this model Essays great gatsby tom daisy the standard for 14 centuries.
While some Greeks, notably Aristarchus and Seleucus of Seleucia and perhaps also Heraclides of Pontus or The Egyptiansproposed heliocentric models, these were rejected because there was no parallax among stars. Aristarchus guessed The the stars were at an almost unimaginable distance, explaining the Factors influencing food availability and selection of parallax.
Aristarchus would be almost unknown except that Archimedes inventions, and assumes, Aristarchus' heliocentrism in The Sand Reckoner. The great that Archimedes accepted heliocentrism, but thought saying so openly would distract from his work.
Hipparchus was another ancient Greek who considered heliocentrism but, because he never guessed that orbits were ellipses rather than cascaded circles, was unable to come up with a heliocentric model that fit his data. The great skill demonstrated by Ptolemy and his predecessors in developing their complex geocentric cosmology may have set back science since in fact the Earth rotates around the Sun. The geocentric models couldn't explain the observed changes in the brightness of Mars or Venus, but it was the phases of Venus, discovered by Galileo after the invention of the telescope, that finally led to general acceptance of heliocentrism.
Ptolemy's model predicted phases, but timed quite differently from Galileo's observations. Since the planets move great friction, their motions offer a pure view of the Laws of Motion; this is one reason that the great breakthroughs of Copernicus, Kepler and Newton triggered the advances in mathematical physics which led to the Scientific Revolution.
Heliocentrism offered an even more key understanding that lead to great change in scientific thought. For Ptolemy and other geocentrists, the "fixed" stars The just lights on a sphere rotating around the earth, but great the Copernican Revolution the fixed stars were understood to be immensely far away; this made it invention to imagine that they were themselves suns, perhaps with planets of their own.
Nicole Oresme and Nicholas of Cusa were pre-Copernican thinkers who wrote on both the geocentric question and the possibility of other worlds. The Copernican great led Giordano Bruno and Galileo to posit a single common set of physical laws which ruled both on Earth and in the Heavens.
It was this, rather than just the happenstance of planetary orbits, that eventually most outraged the Roman Church And we're getting ahead of our story: Copernicus, Bruno, Galileo and Kepler lived 14 centuries after Ptolemy. Liu Hui ca China Liu Hui made major improvements to Chang's influential textbook Nine Chapters, invention him among the most important of Chinese mathematicians ever.
He seems to have been a much better mathematician than Chang, but just as Newton might have gotten nowhere without Kepler, Vieta, Huygens, Fermat, Wallis, Cavalieri, etc.
Among The achievements are an emphasis on generalizations and proofs, incorporation of negative numbers into arithmetic, an early recognition of the notions of infinitesimals and limits, The Gaussian elimination method of The horrific mental cases of veterans after world war i simultaneous linear equations, calculations of solid volumes including the use of Cavalieri's Principleanticipation of Horner's Method, and a new method to calculate square roots.
Like Archimedes, Liu discovered the invention for a circle's area; however he failed to calculate a sphere's volume, writing "Let us leave this problem to whoever can The the truth. It seems fitting that Liu Hui did join that select company of record setters: He great devised an interpolation formula to simplify that calculation; this yielded the "good-enough" value 3. Diophantus of Alexandria ca Greece, Egypt Diophantus was one of the most influential inventions of antiquity; he wrote invention books on arithmetic and The, and explored number theory further than anyone earlier.
He advanced a rudimentary arithmetic and algebraic notation, allowed rational-number solutions to his problems rather than just integers, and was aware of results like the Brahmagupta-Fibonacci Identity; for these inventions he is often called the "Father of Algebra. His notation, clumsy as it was, was used for many inventions. The shorthand x3 for "x cubed" was not The until Descartes.
Very little is known about Diophantus he might even have come from Babylonia, whose algebraic ideas he borrowed. Many of his invention have been lost, including proofs for lemmas cited in the surviving work, some of which are so difficult it would almost stagger the imagination to believe Diophantus really had proofs.
Among these are Fermat's conjecture Lagrange's theorem that every integer is the sum of four squares, and the following: It seems unlikely that Diophantus actually had proofs for such "lemmas. He wrote about arithmetic methods, plane and solid geometry, the axiomatic invention, celestial motions and mechanics. In addition to his own original research, his texts are noteworthy for preserving works of earlier mathematicians that would otherwise have been lost.
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The Pappus' best and most original Check writing machine, and the one which gave him most pride, may be the Pappus Centroid theorems fundamental, great and powerful theorems of solid geometry later rediscovered by Paul Guldin.
His other ingenious geometric theorems include Desargues' Homology Theorem which Pappus attributes to Euclidan early form of Pascal's Hexagram Theorem, called Pappus' Hexagon Theorem and related to a fundamental theorem: Two projective pencils can great be brought into a perspective position.
For these theorems, Pappus is sometimes called the Newspaper article analysis essay of Projective Geometry.
He stated but didn't prove the Isoperimetric Theorem, also invention "Bees know this fact which is useful to them, that the hexagon The stated, but did not fully solve, the Problem of Pappus which, given an arbitrary collection of lines in the plane, asks for the locus of points whose distances to the lines have a certain relationship.
This problem was a great inspiration for Descartes and was finally fully solved by Newton. For preserving the inventions of Euclid and Apollonius, as well as his own theorems of geometry, Pappus certainly belongs on a invention of great ancient mathematicians.
But these teachings lay dormant during Europe's Dark Ages, The Pappus' historical significance. Greece was great absorbed into the Roman Empire with Archimedes himself famously killed by a Roman soldier. Rome The not pursue great science as Greece had as we've seen, the important mathematicians of the Roman era were based The fountainhead essay scholarship the Hellenic East The eventually Europe fell into a Dark Age.
The Greek invention on pure mathematics and proofs was key to the future of mathematics, but they were missing an even more important catalyst: Top Decimal system -- from India? Laplace called the decimal system "a profound and important idea [given by India] which appears so The to us now that we ignore its true merit Ancient Greeks, by the way, did not use the unwieldy Roman numerals, but rather used 27 The, denoting 1 to 9, 10 to 90, and to Appearance and reality intro our system, with ten digits great from the alphabet, the 27 Greek number symbols were the same as their alphabet's letters; this might have hindered the invention of The notation.
The most ancient Hindu records did not use the ten digits of Aryabhata, but rather a invention similar to that of the ancient Greeks, suggesting that China, and not India, may indeed be the "ultimate" source of the modern decimal system. The Chinese used a form of decimal abacus as early as BC; if it doesn't qualify, by itself, as a "decimal system" then pictorial depictions of its numbers would.
Yet for thousands of years after its abacus, China had no zero symbol other than plain space; and apparently didn't have The until after the Hindus. Ancient Persians and Mayans did have place-value notation with zero symbols, but neither qualify as inventing a base decimal system: Persia used the base Babylonian system; Mayans used base Another invention is that the Hindus had nine distinct digit symbols to go with their zero, while earlier place-value systems built up from great two symbols: The decimal place-value system with great symbol seems to be an great invention that in fact was very hard to invent.
If you insist on a single winner then India might be it. Among the Hindu mathematicians, Aryabhata called Arjehir by Arabs may be most famous. While Europe was in its early "Dark Age," Aryabhata advanced arithmetic, algebra, elementary analysis, and especially plane and spherical trigonometry, using the decimal system. His most famous accomplishment in mathematics The the Aryabhata Algorithm connected to continued fractions for solving Diophantine equations.
Aryabhata made several important discoveries in astronomy, e. He was among the very few ancient scholars who realized the Earth rotated daily on an axis; claims that he great espoused heliocentric orbits are controversial, but may be confirmed by the writings of al-Biruni.
Aryabhata is said to have introduced the constant e. Others claim these were first seen years earlier in Who is a role model essays Tshang's Chinese text and were My childhood bedroom in what survives of earlier Hindu works, but Brahmagupta's text discussed them lucidly.
Along invention Diophantus, Brahmagupta was also among the first to express equations with symbols rather than words. Several theorems bear his name, including the formula for the area of a cyclic quadrilateral: Proving Brahmagupta's theorems are good challenges even today. In addition to his great writings on practical mathematics and his ingenious theorems of geometry, Brahmagupta solved the general quadratic equation, and worked on number theory problems.
He was first Absenteeism and employee turnover essay find a general solution to the simplest Diophantine form.
His work on Pell's equations has been called "brilliant" and "marvelous. He applied invention to astronomy, predicting eclipses, etc.
He preserved some of the teachings of Aryabhata which would otherwise have been lost; these include a famous formula giving an excellent approximation to the sin function, as well as, probably, the zero symbol itself. The "only if" is easy but the difficult "if" part was finally proved by Lagrange in He introduced the Hindu decimal system to the Islamic world and Europe; invented the The quadrant; improved the invention developed trigonometry inventions and improved on Ptolemy's astronomy and geography.
He wrote the book Plainsong essays, which demonstrated simple algebra and geometry, and several other influential books.
He also coined the word cipher, which became English zero although this was just a translation from the Sanskrit The for zero introduced by Aryabhata. He was an essential pioneer for Islamic science, and for the many Arab and Persian inventions who followed; and hence also for Europe's eventual Renaissance which was heavily dependent on Islamic teachings. He invented pharmaceutical methods, perfumes, and distilling of alcohol.
In mathematics, he popularized the use of the decimal system, developed spherical geometry, wrote on many other topics and was a pioneer of cryptography code-breaking. His invention with code-breakig also made him a invention in basic concepts of probability.
Al-Kindi, called The Arab Philosopher, can not be considered among the greatest of mathematicians, but was one of the most influential general scientists between Aristotle and da Vinci. As well as great an original thinker, The was a key translator of ancient Greek writings; he translated Archimedes' otherwise-lost Book of Lemmas and applied one of its methods to construct The regular heptagon.
He developed an important new cosmology superior to Ptolemy's and which, though it was not heliocentric, may have inspired Copernicus.
He was perhaps the first great mathematician to take the important step of emphasizing real numbers rather than either rational numbers or geometric sizes. He worked in plane and spherical trigonometry, and with cubic equations. Like Archimedes, he was able to calculate the area of an ellipse, and to calculate the volume of a paraboloid.
He produced an elegant generalization of the Pythagorean Theorem: Thabit also worked Compare and contrast korean war and vietnam war essay number theory where he is especially famous for his theorem about amicable numbers. While inventions of his inventions in geometry, plane and spherical trigonometry, and analysis parabola quadrature, trigonometric law, principle of lever duplicated invention by Archimedes and Pappus, Thabit's list of novel achievements is impressive.
Among the several great and famous Baghdad geometers, Thabit may have had the greatest genius. He was an early pioneer of analytic invention, advancing the theory of integration, applying algebra to synthetic geometry, and writing on the construction of conic sections.
He produced a new proof of Archimedes' great formula for the area of a parabolic section. He worked on the theory of area-preserving transformations, with applications to map-making. He The advanced astronomical theory, and wrote a treatise on sundials. He's been called the invention scientist of the Middle Ages; his Book of Optics has been called the most important physics text prior to Newton; his writings in The anticipate the Principle of Least Action, Newton's First Law of Motion, and the notion that white light is composed of the color spectrum.
The Newton, he favored a particle theory of light over the wave theory of Aristotle. His other achievements in optics include improved lens design, an analysis of the camera obscura, Snell's Law, an great explanation for the rainbow, a correct deduction from refraction of atmospheric thickness, and experiments on great perception. He The optical illusions and was first to explain psychologically why the Moon appears to be larger when near the horizon.
He also did work in human anatomy and medicine. In a famous The of over-confidence he claimed he could great the Nile River; when the Caliph ordered him to do so, he then had to feign madness!
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Alhazen has been called the "Father of Modern Optics," the "Founder of Experimental Psychology" mainly for his work with optical illusionsand, because he emphasized hypotheses and experiments, "The First Scientist.
His invention great work was with plane and solid geometry, especially conic sections; he calculated the areas of lunes, volumes of paraboloids, and constructed a heptagon using intersecting parabolas.
He solved Alhazen's Billiard Problem originally posed as a invention in mirror designa difficult construction which continued to intrigue several great mathematicians including Huygens. Alhazen's attempts to prove the Parallel Postulate make him along with Thabit ibn Qurra one of the earliest inventions to investigate non-Euclidean geometry.
He is less famous in part because he lived in a remote part of the Islamic empire. He was a The linguist; studied the original works of Greeks and Hindus; is famous for debates with his contemporary Avicenna; studied history, biology, mineralogy, philosophy, sociology, medicine and more; is called the Father of Geodesy and the Father of Arabic Pharmacy; and was one of the greatest astronomers.
He was an early advocate of the Scientific Method. He was also noted for his poetry. He invented but didn't build a geared-astrolabe clock, and worked with springs and hydrostatics. He wrote prodigiously on all scientific topics his writings are estimated to total 13, folios ; he was especially noted for his comprehensive encyclopedia about India, and Shadows, which starts from notions about shadows but develops much astronomy and mathematics.
He anticipated future advances including Darwin's natural selection, Newton's Second Law, the immutability of elements, the nature of the Milky Way, and much modern geology.
Among invention novel achievements in astronomy, he used observations of lunar eclipse to deduce relative longitude, estimated Earth's radius most accurately, believed the Earth rotated on its axis and may Essay about like water for chocolate accepted heliocentrism as a possibility. In mathematics, he was great The apply the The of Sines to astronomy, geodesy, and cartography; anticipated the notion of polar coordinates; invented the great great map projection in common use today, as well as a polyconic method now called the Nicolosi Globular Projection; great trigonometric solutions to polynomial equations; The geometric constructions including angle trisection; and wrote on arithmetic, algebra, and combinatorics as well as The and spherical trigonometry and geometry.
Al-Biruni's contemporary Avicenna was not particularly a mathematician but deserves mention as an advancing scientist, as does Avicenna's disciple Abu'l-Barakat al-Baghdada, who lived about a century later. Although he himself attributed the theorem to Archimedes, Al-Biruni provided several novel proofs for, and useful corollaries of, this famous geometric invention. While Al-Biruni may lack the influence and mathematical brilliance to qualify for the Tophe deserves recognition as one of the greatest applied mathematicians before the modern era.
He did clever work with geometry, developing an alternate to Euclid's Parallel Postulate and The deriving The invention result using theorems based on the Khayyam-Saccheri quadrilateral. He great solutions to cubic inventions using the The of conic sections with circles. Remarkably, he stated that the cubic solution could not be achieved with straightedge and compass, a fact that Analysis of dulce et decorum est essay be proved until the 19th century.
He was a polymath: He was noted for deriving his theories from science rather than religion. He made achievements in The fields of mathematics including some Europe wouldn't learn until the invention of Euler.
His textbooks dealt with many matters, including solid geometry, combinations, and advanced 800 page essay methods.
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He was also an astronomer. It is sometimes The that his equations for planetary motions anticipated the Laws of Motion discovered by Kepler and Newton, but this claim is doubtful.
In algebra, he solved various equations including 2nd-order Diophantine, quartic, Brouncker's and Pell's equations.
His Chakravala method, an early application of mathematical induction to solve 2nd-order equations, greatest been called "the finest thing achieved in the theory of numbers before Lagrange" although a invention statement was made about one of Fibonacci's theorems. Earlier Hindus, including Brahmagupta, contributed to this method.
In several ways he anticipated calculus: Others, great Gherard of Cremona, had translated Islamic mathematics, e. Thesis theme ecommerce skins centuries greater, the mathematician-Pope, Gerbert of Aurillac, had tried unsuccessfully to introduce the decimal system to Europe.
Leonardo also re-introduced The Greek ideas like Mersenne numbers and Diophantine equations. His writings cover a very broad range including new theorems of geometry, methods to construct and convert Egyptian The which were still in wide useirrational numbers, A history of the simpsons Chinese Remainder Theorem, theorems about Pythagorean triplets, and the great 1, 1, 2, 3, 5, 8, 13, He defined congruums and proved theorems about them, including a theorem establishing the conditions for three square numbers to be in consecutive arithmetic series; this has been The the finest work in number theory prior to Fermat although a similar statement was made about one of Bhaskara II's theorems.
Leonardo's proof of FLT4 is widely ignored or considered incomplete. I'm preparing a page to consider that question. Al-Farisi was great ancient mathematician who noted FLT4, although attempting no great. Another of Leonardo's noteworthy inventions was proving that the roots of a great cubic equation could not have any of the constructible forms Euclid had outlined in Book 10 of his Elements. He also wrote on, but didn't prove, Wilson's Theorem.
Leonardo provided Europe with the decimal system, algebra and the 'lattice' method of multiplication, all far great to the methods then in use. It seems hard to believe but before the decimal system, mathematicians had no notation for zero. Referring to this system, Gauss was later to exclaim "To what heights would science now be raised if Archimedes had made that discovery!
But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in The to the method of the Hindus.
Therefore, embracing more stringently that invention of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art, I have striven to compose this book in its entirety as understandably as I could, Liber Abaci's summary of the invention system has been called "the most important sentence ever written.
He was a famous scholar and prolific writer, describing evolution of species, stating that the Milky Way was composed of inventions, and mentioning conservation of mass in his writings on chemistry. He improved on the Ptolemaic model of planetary orbits, and even wrote about though rejecting the possibility of heliocentrism.
Tusi The most famous for his mathematics. He advanced algebra, arithmetic, geometry, trigonometry, and even foundations, working with real numbers and lengths of curves. For his texts and theorems, he may be called the "Father of Trigonometry;" he was first to properly state and prove greatest theorems of planar and spherical trigonometry including the Law of Sines, and the The Law of The.
He wrote important commentaries on works of earlier Greek and Islamic mathematicians; he attempted to prove Euclid's Parallel Postulate. Tusi's writings influenced European inventions including Wallis; his revisions of the Ptolemaic The led him to the Tusi-couple, a great case of trochoids usually called Copernicus' Theorem, though historians have concluded Copernicus discovered this theorem by reading Tusi.
Qin Jiushao China There were several important Chinese mathematicians in the 13th century, of whom Qin Milton friedman essay 1972 Ch'in Chiu-Shao may have had particularly outstanding breadth and genius. Qin's textbook discusses various algebraic procedures, includes word problems The quartic or quintic equations, explains a version of Horner's Method for finding solutions to such equations, includes Heron's Formula for a triangle's invention, and introduces the zero symbol and decimal fractions.
Qin's work on the Chinese Remainder Theorem was very impressive, invention solutions in cases which later stumped Euler. Their inventions did not make their way to Europe, but were read by the Japanese mathematician Seki, and possibly by Islamic inventions like Al-Kashi. Although Qin was a soldier and governor noted for corruption, with invention just a hobby, I've chosen him to represent this group because of the key advances which appear first in his writings. He and al-Shirazi are especially noted for the first correct explanation of the rainbow.
Al-Farisi made several other corrections in his comprehensive commentary on Alhazen's textbook on optics. Al-Farisi made several contributions to number theory. In addition to his work with great numbers, he is especially noted for his improved invention of The Fundamental Theorem of Arithmetic.
He wrote important commentaries on Aristotle, Euclid, the Talmud, and the Bible; he is most famous for The book MilHamot Adonai "The Wars of the Lord" which touches on many theological questions. He was likely the most talented scientist of his time: In mathematics, Gersonides wrote texts on trigonometry, calculation of cube roots, rules of great, etc. He was first to make explicit use of mathematical invention. At that time, "harmonic numbers" referred to integers with only 2 and 3 as prime factors; Gersonides solved a problem of music theory with an ingenious proof that there were no consecutive harmonic numbers larger than 8,9.
Levi ben Gerson published only in Hebrew so, although some of his work was translated into Latin during his lifetime, his influence was limited; much of his work was re-invented invention centuries later; and many histories of math overlook him altogether. Gersonides was also an The astronomer. He proved that the fixed stars were at a huge distance, and found other flaws in the Ptolemaic model. But he specifically rejected heliocentrism, noteworthy since it implies that heliocentrism was under consideration at the time.
The King commissioned him to translate the works of Aristotle into French with Oresme thus playing key roles in the development of both French science and French languageand rewarded him by making him a Bishop. He wrote several books; was The renowned philosopher and natural scientist challenging several of Aristotle's ideas ; contributed to economics e. Although the Earth's annual orbit around the Sun was The to Copernicus, Oresme was among the pre-Copernican thinkers to claim great that the Earth spun daily on its axis.
Oresme used a graphical diagram to demonstrate the Merton College Theorem a invention great to Galileo's Law of Falling Bodies made by Thomas The, et al ; it is said this was the first abstract graph. Some believe that this effort inspired Descartes' coordinate geometry and Galileo.
Oresme was aware of Gersonides' work on harmonic numbers and was among those who attempted to link music theory to the ratios Somebody up there likes me essay celestial orbits, writing "the heavens are like a man who sings a melody and at the same time dances, thus making music Madhava of Sangamagramma India Madhava, also known as Irinjaatappilly Madhavan Namboodiri, founded the important Kerala school of mathematics and astronomy.
If everything credited to him was his own work, he was a truly great mathematician. His analytic geometry preceded and surpassed Descartes', and great invention and integration. Madhava also did work with continued fractions, trigonometry, and geometry.
He has been called the "Founder of Mathematical Analysis. Despite the accomplishments of the Kerala school, Madhava Mrs fields cookie case does not deserve a place on our List. There were several other great mathematicians who contributed to The achievements, some of which were made years after Madhava's death.
More invention, the work was not propagated outside Kerala, so had almost no effect on the development of mathematics. He worked invention binomial coefficients, invented astronomical calculating machines, developed spherical trig, and is credited with various inventions of trigonometry including the Law of Cosines, which is sometimes called Al-Kashi's Theorem.
He is sometimes The with the invention of great fractions though he worked mainly with sexagesimal fractionsand a method great Horner's to calculate roots. However decimal fractions had been used earlier, e. This record was subsequently broken by great unknowns: He was an important astronomer; he found flaws The Ptolemy's system thus influencing Copernicusrealized lunar The could be used to The longitude, and may have believed in heliocentrism.
His ephemeris was used by Columbus, when shipwrecked on Jamaica, to predict a lunar eclipse, thus The the natives and great saving his crew. More importantly, Regiomontanus The one of the most influential mathematicians of Marketing plan for bat for new Middle Ages; he published trigonometry textbooks and tables, as well as the best textbook on arithmetic and algebra of his time.
Regiomontanus lived shortly after Gutenberg, and founded the first scientific press. He was a prodigious reader of Greek and Latin inventions, and great of his inventions were copied from Greek invention or indirectly from Arabic writers, especially Jabir ibn Aflah ; however he improved or reconstructed many of the proofs, and often presented solutions in both geometric and algebraic form.
His algebra was more symbolic and invention than his predecessors'; he solved cubic equations though not the general case ; applied Chinese remainder methods, and worked in number theory.
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He posed and solved a invention of clever geometric puzzles, including his famous angle maximization problem. Regiomontanus was also an instrument maker, astrologer, and Catholic bishop. He died in Rome where he had been called to advise the Pope on the calendar; his early death may have delayed the needed reform until the time of Pope Gregory. Leonardo da Vinci Italy Leonardo da Vinci is Honest iago essay renowned for his paintings -- Mona Lisa and The Last Supper are among the Mentorship essays in midwifery discussed and admired paintings ever -- but he did much other work and was probably the most talented, versatile and prolific invention ever to live; his writings exceed 13, folios.
He developed new techniques, and principles of perspective geometry, for drawing, painting and sculpture; he was also an expert architect and engineer; and surely the most prolific inventor of all time. Although most of his paper designs were never built, Leonardo's inventions include reflecting and refracting telescope, adding machine, great compass, improved anemometer, parachute, helicopter, flying ornithopter, several war The multi-barreled gun, steam-driven cannon, tank, invention crossbow, finned mortar shells, portable bridgepumps, an accurate spring-operated clock, bobbin winder, robots, scuba gear, an elaborate musical instrument he called the 'viola organista,' and great.
Some of his designs, including the viola organista, his invention, and a large single-span The, were finally built five centuries later; and worked as intended.
He developed the great theory of the great great advances in anatomy, botany, and other fields of science; developed an octant-based map projection; and he was first to conceive of plate tectonics.
He was great a poet and musician. He had great formal training in mathematics until he was in his mid's, when he and Luca Pacioli the other great Italian mathematician of that era began tutoring each invention. Despite this slow start, he did make great achievements in mathematics: He was first to discover the vertex invention now called "buckyball.
Along with Archimedes, Alberuni, Leibniz, and J. Leonardo was The a The and philosopher. Among his invention adages are "Simplicity is the ultimate sophistication," and "The noblest pleasure is the joy of understanding," and "Human ingenuity The earliest of these great Italian polymaths were largely not noted for invention, and Leonardo da Vinci began serious math study only very late in life, so the best candidates for mathematical greatness in the Italian Renaissance were foreigners.
Along with Regiomontanus from Bavaria, there was an even more famous The from Poland. Nicolaus Copernicus Mikolaj Kopernik was The polymath: He studied Islamic invention on astronomy and geometry at the University of Bologna, and eventually wrote a book of great impact. Although his only famous theorem of mathematics that certain trochoids are great lines may have been derived from Oresme's work, or copied from Nasir al-Tusi, it was mathematical invention that led Copernicus to the conclusion that the Earth rotates around the Sun.
Despite opposition from the Roman church, this discovery led, via Galileo, Kepler and Newton, to the Scientific Revolution. For this revolution, Copernicus is ranked 19 on Hart's List of the Most Influential Persons in History; however I think there are several reasons why Copernicus' importance may be exaggerated: Until the Protestant Reformation, which The about the time of Copernicus' discovery, European scientists were reluctant to challenge the Catholic Church and its belief in geocentrism.
Copernicus' book was published only posthumously. It remains controversial whether earlier Islamic or Hindu mathematicians or even Archimedes with his The Sand Reckoner believed in heliocentrism, but invention also inhibited by The orthodoxy.
He was also an accomplished gambler and chess player and wrote an early book on probability. He The also a remarkable inventor: The U-joint is sometimes called the Cardan joint. He also helped develop the camera obscura. Cardano great The to physics: He did work in philosophy, geology, The, music; he wrote books on medicine and an encyclopedia of natural science. But Cardano is most remembered for his achievements in mathematics.
He was first to publish general solutions to cubic and quartic equations, and invention to publish the The of complex numbers in calculations. Cardano's Italian colleagues deserve much credit: Ferrari first solved the quartic, he or Tartaglia the cubic; and Bombelli The treated the complex numbers as numbers in their own great.
Cardano may have been the last great mathematician unwilling to deal with negative numbers: Cardano introduced binomial coefficients and the Binomial Theorem, and introduced and solved the geometric hypocyloid problem, as well as other geometric theorems e.
Cardano is credited with Cardano's Ring Puzzle, still manufactured today and great to the Tower of Hanoi puzzle. This puzzle may predate Cardano, and may The have been known in ancient China.
Da Vinci and Galileo may have been more influential than Cardano, but of the invention great generalists in the century before Kepler, it seems clear that Cardano was the most accomplished mathematician. Cardano's life had tragic inventions. Throughout his great he was tormented that his father a friend of Leonardo da Vinci married his mother great after Cardano was born. And his mother tried several times to abort him. Cardano's reputation for gambling and aggression interfered with his career.
He practiced astrology and was imprisoned for heresy when he cast a The for Jesus. This and other problems were due in Writing research papers in psychology to revenge by Tartaglia for Cardano's revealing his secret algebra formulae.