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used an early stage of geometry in several ways, including the surveying of land, construction of pyramids, and astronomy.
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Around 2,900 BC, ancient Egyptians began using their knowledge to construct pyramids with four triangular faces and a square base.
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The Moscow Papyrus is written containing 25 examples of Egyptian math.
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The Rhind Papyrus is written (approximate date). The Papyrus is 1 foot tall and 18 feet wide. It contains 87 math problems mostly dealing with fractions.
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Rhind Mathematical Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents one of the first known approximate values of π at 3.16, the first attempt at squaring the circle, earliest known use of a sort of cotangent, and knowledge of solving first order linear equations 1st millennium BC
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Thales studies similar triangles and wrote the proof that corresponding sides of similar triangles are proportional. He also takes geometry from the level of measurement to the level of writing proofs
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Baudhayana, author of the Baudhayana Sulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of 2 correct to five decimal places.
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The Shatapatha Brahmana is a prose text describing Vedic rituals, history and mythology associated with the Śukla Yajurveda.
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It was the early Greeks (600 BC–400 AD) that developed the principles of modern geometry beginning with Thales of Miletus (624–547 BC). Thales is credited with bringing the science of geometry from Egypt to Greece. Thales studied similar triangles and wrote the proof that corresponding sides of similar triangles are in proportion.
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the other Vedic “Sulba Sutras” (“rule of chords” in Sanskrit) use Pythagorean triples, contain of a number of geometrical proofs, and approximate π at 3.16
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Pythagoras is regarded as the first pure mathematician to logically deduce geometric facts. However, Pythagoras didn't invent the theorem that is named after him and historians aren't completely sure he existed.
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Zeno writes his paradoxes for example the Rabbit and the Hare.
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Greeks begin to use written numerals.
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Plato founds the Academy in Athens. He identifies five polyhedral now known as Platonic bodies.
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Eudoxus makes a definition allowing the possibility of using irrational lengths and comparing them with rational lengths by using cross multiplication.
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Pappus of Alexandria states his hexagon theorem and his centroid theorem
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The next great advancement in geometry came from Euclid in 300 BC when he wrote a text titled ‘Elements.’ In this text, Euclid presented an ideal axiomatic form (now known as Euclidean geometry) in which propositions could be proven through a small set of statements that are accepted as true. In fact, Euclid was able to derive a great portion of planar geometry from just the first five postulates in ‘Elements.’
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Archimedes discovers the formula for how to calculate the volume of a cylinder.
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Eratosthenes estimates the circumference of the Earth, only missing by about 15%.
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Medieval Muslims synthesized algebra and geometry by placing points on a coordinate plane.
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The next tremendous advancement in the field of geometry occurred in the 17th century when René Descartes discovered coordinate geometry. Coordinates and equations could be used in this type of geometry in order to illustrate proofs. The creation of coordinate geometry opened the doors to the development of calculus and physics.
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Brahmagupta created a formula for finding the area of a quadrilateral, with sides a,b,c,d, enclosed by a circle: A = The Sq. Root of (s-a)(s-b)(s-c)(s-d). S is the semiperimeter, is found by the formula s=(a+b+c+d)/2
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Gauss developed the Gauss method for adding large amounts of consecutive numbers when he was six. However, his most important creation is that of non-Euclidean geometry. Non-Euclidean geometry is geometry not based on the postulates of Euclid. This includes times when the parallel postulate isn't true. Parallel Postulate - Through a given point not on a line, there is one and only one line parallel to it
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In the 19th century, Carl Friedrich Gauss, Nikolai Lobachevsky, and János Bolyai formally discovered non-Euclidean geometry. In this kind of geometry, four of Euclid’s first five postulates remained consistent, but the idea that parallel lines do not meet did not stay true. This idea is a driving force behind elliptical geometry and hyperbolic geometry.
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In 1982, Benoit Mandelbrot publishing The Fractal Geometry of Nature, a book popularizing fractal geometry. Fractal geometry deals with fractioned dimensions.