... y respectively, then: Pythagorean Triples These are groups of three numbers, which satisfy the equation of Pythagoras' Theorem. For example: {3,4,5} {5,12,13} {7,24,25} {9,40,41} {11,60,61} Analysis Man's interest in geometrical patterns dates back to early prehistoric times. Examples have been found of plaited rushes to form rudimentary textile art. Additionally these arrangements have developed into clothing, tents and rugs. However, geometrical patterns have not been restricted solely to textiles. They have also formed a noticeable part of ancient architecture. Examples have been found on Mexican monuments and Peruvian architectural remains. This use of geometry to beautify their surroundings suggests that the ancients had the beginnings of later scientific geometry. The first being the ability to abstract, in other words being able to identify and duplicate the simple geometric shapes occurring naturally. The second, the ability to take a three-dimensional figure and represent it two dimensionally. Essentially these people were showing an understanding of the ...

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