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Ancient Africans Invented Geometry |
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In Ancient Egypt the Nile River overflowed its banks each year and dumped tons of mud over the farm land in the river valley. These fields had been laid out in different ways. Some had formed squares; others, rectangles; still others, triangles. After the water went down each farmer again marked out his field. Proper boundaries were of particular interest to the tax collectors because the amount of taxes depended upon the size of the land a farmer had; how much surplus produce was exchanged for personal gain; and how much was stored for future use.
Thus arose the need for a variety of math related operationsâ€"for land surveying to determine where one farmer's boundaries ended and the neighbor's began; for a system of weights and measures; for calculations like addition, subtraction, multiplication, and division; for the use of fractions; for finding the capacity of granaries; for running irrigation trenches; for carrying water by aqueducts; and for making records of all business transactions.
These math challenges, based upon African inventions, were probably accomplished by the fourth millennium BC. In marking out boundaries of the fields anew, the Egyptians learned something about squares, rectangles, triangles and the other figures which form the subject matter of geometry. Since this science had its beginning in a series of measurements of land, the Greeks put together two words to form "geometry"â€"meaning "measurement of the earth".
Geometry, like trigonometry and arithmetic, all have the syllable "met"â€"the root of the verb "to measure". Geometry's main elements are points, lines, and planes. All other figures are often defined in terms of these. Geometric ideas help to measure lengths, areas, and volumes of figures. To find the area of a square and then of a rectangle, they simply multiplied the width by the height. To find the area of a triangle, they multiplied the width by the height and divided by two. Eventually, these math operations came to embrace the relations of properties (e.g. between congruence and similarity).
They also served to determine the measurements of solids, surfaces, lines, and angles in such aspects as "space figures" and "spatial relations". Coordinate Geometry brings together numbers and geometric figures. Analytic Geometry applies algebraic ideas to geometric relations and quantities. In Hyper-geometry imaginary field quantities of more than three dimensions are considered through algebraic symbols. Topology is studying geometric properties that are unaffected by changes in the size or shape of a figure.
Geometry was so well known and so perfected by the Ancient Egyptians that monumental sculpture and architecture were created with geometric patterns, even in the Pre-Dynastic era (prior to 3200 BC). In contrast to the literature, there were also African approaches to logical proof of geometric statements.
African geometric patternsâ€"whether in weaving, wood carvings, or cloth dyingâ€"had meaning. From Africans discovering the circumference of a Circle is about three and a half times its diameter, the Sexigesimal System of numeration by which 60 is usedâ€"(e.g. 60 minutes equals one degree and 360 degrees make one circle) allowed for heaven and earth measurements in degrees.
The process developed for the observation and the measuring of circles resulted in a well established 360 day calendar (plus 5 holidays devoted to the gods) by 4236 BC--the oldest date known with certainty for a calendar in the history of mankind (Diop, African Origins, p91, 141, 136; Lumpkin, in van Sertima's Egypt, p325). Furthermore, by the Sexigesimal System corresponding to the stars of the Orion' Belt, the Sphinx (10,500 BC) was built in exact alignment (Bynum, African Unconscious p.109). This meant the circles of time and space were in accord, as two prospects of the same principle of number (Campbell, Oriental Myth p115).
Joseph A. Bailey, II, M.D.
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