In Euclidean geometry it is stated that the sum of the angles in a triangle are equal to 180. ... 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 Geometry. ... Even though the lines do have some similarities, there are three theorems in Euclidean Geometry, which are false in Hyperbolic Geometry. ... However, in Hyperbolic Geometry it is possible for a square on the sphere to contain three right angles and one acute angle. ... This is a theorem in Euclidean Geometry, yet in Hyperb...

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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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Thales was said to have come up with these four basic principles. 1) a circle is bisected by its diameter. 2) The angles at the base of an isosceles triangle are equal. 3) two intersecting straight lines form two pairs of equal angles. 4) An angle inscribed in a semicircle is a right angle. ... 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 t...

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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-. ... In a rigorous, fast, and easily understandable way, XLVII proves that in a right-angled triangle the square of the hypotenuse, or diagonal, is equal to the sum of the squares on the remaining sides. This theorem is named after its first observer, Pythagoras, but it was Euclid's insight what made it clear enough to become the basis for a great number of further mat...

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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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Saccheri investigated the summit angles of a quadrilateral; his result depended on the postulate chosen. ... 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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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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In one particular result he was able to compute the maximum angle that a (paraboloid) ship could list before it capsized - and he did it without calculus! ... 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. ... This theory incorporates the idea that musical sounds have mathematical tones of energy which ultimately allow them to relate with patterns of proportion dealing with angles, shapes, and movements. ... 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 irrationa...

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Projecting further into the world of science, Euclid (circa 300 BC) a Greek mathematician was able to theorize and prove that two straight lines intersect each other, the vertical or opposite angles shall be equal. This is the currently known vertical angle theorem (Doc. 5, Euclid). ... His books were used as textbooks for over 2000 years and to date they're the basis of high school instruction in plane geometry. ... Hippocrates developed the Hippocratic oath, which all physicians beginning their careers must take and Euclid developed the vertical angles theorem. ...

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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. ... This he affected by circumscr...

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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 chemistry as a serious study. ... Let the angle of a prism be I and the deviation of the ray be &, the reflective index will be sin ½(I+&) cosec: 1/2I. ... He also calculated areas by antidifferentiation and t...

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Pythagoras was a famous mathematician that studied astronomy, logistics, and geometry. He came up with the Pythagorean Theorem. Euclid is considered the father of geometry, and reorganized a compilation of geometry proofs and created the most successful math textbook. ... The Romans also used different layers underneath the paving stone of a road at angle in order to allow rainwater to be drained. ...

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As a current Geometry student, Pythagoras, a famous and brilliant Greek mathematician, has helped many master the subject easily. He is well-known for his discovery of the Pythagorean Theorem, which shows the basic relationship of the sides of a right-angled triangle. ...

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In the 12th century, the Indian mathematician Bhaskara II developed an early derivative representing infinitesimal change, and he described an early form of "Rolle's theorem". ... James Gregory proved a special case of the second fundamental theorem of calculus in AD 1668.       ... The basic insight that both Newton and Leibniz had was the fundamental theorem of calculus.       ... Modern differential calculus on mean value theorem Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. ...

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At age thirteen, before Albert had studied geometry, his uncle Jakob taught him the pythagorean theorem: that the sum of the squares n the sides of a right-angled triangle is equal to the square on the hypotenuse. ...

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