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Rope - 3-4-5 triangle Does it Produce a Right Angle...

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Rope-Stretcher's Triangle One practical value of any triangle is its rigidity . A triangular frame is rigid, while a four-sided one will collapse. Another imortant use is for triangulation , for locating things as in surveying and navigation, and this property takes us back to the very origins of geometry, in ancient Egypt. The Origins of Geometry Geometry means earth measure . Geo + Metry. According to the Herodotus the Nile flooded its banks each year, obliterating the markings for fields. He wrote, " This king divided the land . . . so as to give each one a quadrangle of equal size and . . . on each imposing a tax. But everyone from whose part the river tore anything away . . . he sent overseers to measure out how much the land had become smaller, in order that the owner might pay on what was left . . . In this way, it appears to me, geometry originated, which passed thence to Greece. The Rope-stretcher's Triangle One tool they may have used is a rope knotted into 12 sections stretched out to form a
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Unformatted text preview: 3-4-5 triangle. Does it Produce a Right Angle? According to the Pythagorean theorem, In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. The converse of is also true, If the square of one side of a triangle equals the sum of the squares of the other two sides, then we have a right triangle. For the 3-4-5 triangle; 5 2 = 3 2 + 4 2 25 = 9 + 16 It checks, showing a rope knotted like this will give a right angle. The rope-stretcher's triangle is also called the 3-4-5 right triangle, the Rope-Knotter's triangle, and the Pythagorean triangle. Project: Use a long knotted rope to make a rope-stretcher's triangle. Use it outdoors to lay out a right angle on some field. Then continue, making three more right angles to form a square. How accurate is your work? Did you come back to the starting point?...
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