Being based off different postulates, theorems, and proofs, Euclidean Geometry deals mostly with two-dimensional figures, while Demonstrative, Analytic, Descriptive, Conic, Spherical, Hyperbolic, are Non-Euclidean, dealing with figures containing more than two-dimensions. ... Cosmologists today believe that "curved space- is the fourth dimension, although it hasn't yet been proven by means of postulates, theorems, or proofs. ... In Euclidean Geometry, the theorem, "If two lines are parallel to a third line, then the two lines are parallel to each other,"" is disproved in Hyperbolic Geomet...

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He is well known all over the world for formulating the Pythagorean Theorem although its fundamental principles were already recognized earlier. The theorem states that the square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides. ... Because he was very advanced at arithmetic, geometry in particular he was able to come across at the shadow of the earth on the moon during the lunar eclipse and calculate that the earth was round. ...

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His interest in mathematics is said to have began from when he observed a solar eclipse on October 18, 320 and then since has focused his work on geometry. ... The purpose of the volumes were to revive geometry and restore it to a level of significance, usually by providing further explanations or supplements to the works of previous geometers. ... Book IV is an extension of Pythagoras" theorem for parallelograms constructed on the legs of any triangle. ... Pappus formulated the volume of a solid of revolution, which was later called The Pappus - Guldin theorem. ... His theorem was that the v...

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• Grade Level: Undergraduate

These two philosophers influenced him in geometry and cosmology. ... Perhaps Pythagoras is best known for his famous theorem that states the square of the hypotenuse of any right triangle equals the sum of the squares of the other two sides. ... However, there is a book, which gives 350 proofs on the Pythagorean Theorem. In fact, a United States president proved the theorem, and I have attached his proof to this report. ... This theorem was one of the greatest discoveries that had an everlasting impact on geometry. ...

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Although today Pythagoras is best known for his famous theorem, it is quite possible that his most lavish accomplishment is the mathematical basis of musical intervals. Pythagoras's theorem which states that the square of the hypotenuse of a right triangles is equal the sum of the squares of the other two sides was actually said to be thought of by Babylonian mathematicians from earlier times. Plato was very found of geometry. ... The oldest known manual for geometry is the geometry manual by Euclid of Alexandria. ... Books one though six deal with plane geometry. ...

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In 1792 he entered Brunswick Collegium Carolinium, there he thought he had created the binomial theorem for rational exponents and the arithmetic mean. ... By doing so he proved it was possible to make a regular polygon with a compass and ruler and any odd number of sides.For his doctoral thesis he submitted theorem that all algebraic equations have at least one solution. This had challenged mathematicians for centuries before, now it is called the fundamental theorem of algebra. ... Gauss was the first to produce a non-Euclidian geometry, however he never published these works, in or...

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Euclid of Alexandria, whose chief work, Elements, is a comprehensive treatise on mathematics in thirteen volumes on such subjects as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry. ... He taught geometry in Alexandria and founded a school of mathematics there. ... His book The Elements, written about 300 BC, contains many proofs in the field of geometry and algebra. ... As part of such an argument, Euclid used results that had been shown to be true, called theorems, or statements that were explicitly acknowledged to be self-evid...

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It is said that Pythagoras had learned Geometry from the Egyptians, however, Anaximander had probably introduced him to geometry before. ... The Pythagorean Theorem was proven by Pythagoras and his followers in the fifth century B.C. This theorem states that: in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c = a + b (4). ... However, we know that he made an impression on the Pythagorean Society and in geometry as we know it today. ...

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With these rules, the conclusion and theorems created are used to make more theorems and conclusion, and those make more conclusions and theorems and so on. ... Most of theses abstractions are basically used in geometry. They are used in geometry because in geometry you study real objects and what they physically look like, you study their size, shape, and points. Like deduction, abstractions also use axioms, these axioms are of geometry, and with these axioms they are able to explain the world around us. ... To do anything in abstraction, from discovering proper theorem to forming abstract...

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His followers are credited with the development of the Pythagorean theorem in geometry and the application of number relationships to music theory, acoustics, and astronomy. ... Today Pythagoras is famous for his geometry theorem. ...

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Many historians praised Saccheri's book of 39 theorems. ... In his 33rd theorem is where his flaw can be found. ... Even though his book came to an abrupt conclusion, Saccheri's investigation was a crucial step in the evolving of non- Eluclidian geometries. His major achievement was to break ground for the later geometers who now were free to investigate the new geometries. ...

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This art is geometry "the measuring of Earth. ... In thirteen books he collected The Elements of geometry, starting from the most basic concepts, "a point is that which has no part- and "a line is breadthless length-. ... Although I think that we should never renounce reality in our search for philosophical answers, I'm persuaded that it is in a universe similar in nature to the world of geometry that Euclid opens up for us, where Beauty herself exists. ... This theorem is named after its first observer, Pythagoras, but it was Euclid's insight what made it clear enough to becom...

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Through these studies they established a scientific foundation for mathematics, for example in geometry the great discovery of the school was the hypotenuse theorem, or Pythagoras' theorem. (see below) PYTHAGORAS' THEOREM:- Pythagoras' Theorem is a formula stating that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. ...

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Archimedes had a wide variety of interests, which included encompassing statics, hydrostatics, optics, astronomy, engineering, geometry, and arithmetic. Archimedes had more stories passed down through history about his clever inventions than his mathematical theorems. ... The second category contains works that lead to a geometrical analysis of statical and hydrostatical problems and the use of statics in geometry. ... The theorems that Archimedes discovered and worked on raised Greek mathematics to a whole new level. ... Archimedes" theorems, postulates, and inventions are still part of socie...

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Art is a science of creativity and Science is an art of analysis and applications of physical Laws.Hence art and science are two sides of the same coin.The worth of a civilization cannot be truly determined by undermining either art or science because while art reflects the emotional maturity ,scie...

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He is considered to be the greatest mathematician of antiquity and made his greatest contributions in geometry (Archimedes of Syracuse. ... On plane equilibriums, shows the fundamentals of mechanics using geometry. In this book are theorems he discovered for the center of gravity of plane figures. ... He tells how he was in the habit of sending them statements of his latest theorems, but without giving proofs. ... Archimedes considered these to be amusements in geometry. ...

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Basic arithmetic and geometry formed the basis of what the mathematical world had to offer at its very beginnings. ... As mentioned in the Stanford Encyclopedia, "Pythagoras is said to have transformed the philosophy of geometry into a form of liberal education, to have investigated its theorems in an immaterial and intellectual way and specifically to have discovered the study of irrational magnitudes and the construction of the five regular solids," (2). ... He came up with what we now know as the Pythagorean Theorem which in mathematics today is described as a^2+b^2=c^2. ... The ...

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Archimedes had a wide variety of interests, which included encompassing, statistics, hydrostatics, optics, astronomy, engineering, geometry, and arithmetic. Archimedes had more stories passed down through history about his clever inventions than his mathematical theorems. ...

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At the age of twelve Pascal figured out a concept of Euclidean geometry by himself. ... By the time he was seventeen he wrote an essay on conic sections, which is, a work in projective geometry that contained a theorem on conic sections that was named after him. ...

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He is the inventor of abstract mathematics, and the founder of the "Pythagoras Theorem-. This theorem is still used today, in modern geometric equations The Hindu Arabian Period (500A.D. - 1199A.D.), gave us Aryabhata the Elder and Muhammad ibn Musa al-Khowarizmi. ... His book was a forerunner of projective geometry. ... This discovery gave birth to analytic geometry. ... The 19th century is the source of numerous advances in calculus, algebra, and (fractal) geometry. ...

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Because of the Renaissance, lots of scholars and translators did a lot of research on some ancient works written by Greek or Roman for the revival of the ancient culture, which eventually leads to a number of famous basic astronomical theorems or principles such as heliocentric theory and Kepler's law of planetary motion. ... For example, the discovery of logarithm just in time refined Johannes Kepler's theorem. ... Element is a book on geometry and number theory written by a Greek mathematician, Euclid of Alexandria, who is also known as the Father of Geometry. ... Euclid's E...

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His most famous work was the theorem named after himself. This theory, known as the Pythagorean Theorem, states that in order to find the hypotenuse of a right angle triangle you must add the squared result of each of the other two legs of the triangle (Violatti). This is still used in schools and geometry classes around the world to this day. ... They expanded upon the fundamentals of calculus and geometry and taught their discoveries to others. ...

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HIPPOCRATES OF CHIOS by Rob Fisch It can be argued that if Euclid is the father of Geometry that Hippocrates of Chios could be considered the grandfather of geometry. ... He was a Greek merchant turned geometer who compiled the first known work on the elements of geometry. ... He wrote the first mathematical textbook, called the Elements of Geometry. ... He started out with, and laid down as first of the theorems useful for the purpose, the proposition that similar segments of circles have the same ration one to another as the squares on their bases. ... Although Plato developed a me...

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During this time New ton developed several theories, such as his fundamental principles of gravitation, his theory on optics otherwise known as the Lectiones Opticae, and his work with the Binomial Theorem. ... Newton contributed to all aspects of mathematics including geometry, algebra, and physics. ... In his first semester Newton happened to discover a book on astrology, but couldn't understand it very well on account of the geometry and trigonometry. ... Later he read and mastered Oughtred's Clavis, and Descartes' Geometry, which led him to take up mathematics rather than ...

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Life and Accomplishments of John Wallis John Wallis was born on the year of 1616. His father was also named John Wallis and was a minister in Ashford. John Wallis 1st met Joanna Chapman and married her in 1612 to be his second wife. They had five children together and John Wallis being third o...

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