Even before 77,000 BC when Africans invented writing, various African signs were used to indicate numbers. From Primitive Africans' elemental counting, measuring, and describing shapes of objects, their offspring used them in step-by-step reasoning and quantitative calculations to fashion the math science of structure, order, and relations. In the process, Ancient Egyptians applied a separate mark-a vertical line-for each number until they got to 10. To indicate 5, for example, they set down five marks; to indicate 7 they set down seven marks.

Their special sign for 10 resembled a capital U turned upside down, or two marks joined together at the top. Two of these signs standing side by side stood for the number 20. While cultivating numbers, shapes, and symbols, they devised rules for dealing with these things. One of those, Infinity, is symbolized as an 8 lying down. Rather than being a number, it conveys that something is endless. A giant step of math progress occurred when the Egyptians converted their hieroglyphic numerals into symbols and then arranged them into powers of 10. The resultant Decimal system consisted of repeating the symbols for numbers-ones, tens, hundreds, thousands-as many times as necessary to obtain the desired figure.

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Joseph A. Bailey, II, M.D.

They also invented the Commutative, Associative, and Distributive properties of Multiplication. Commutative means to change altogether, as in substitution, interchange, or exchange-in order to combine objects or sets of objects two at a time. Associative ("companion that joins with but retains some individuality") means independent grouping. If a+(b+c) = (a+b)+c, the operation indicated by + is associative. Distributive ("give out amongst in portions, shares, or units") relates to a rule that the same product results in multiplication when performed on a set of numbers, as when performed on members of the set individually. If  a  x  (b + c) = a  x  b + a  x  c, then x is distributive over + (see Lumpkin, in van Sertima  p326 for details).

Calculus deals with changing quantities and with motion. Its basic idea is one of "limit". Limits allow for the finding of the instantaneous rate of change (called the Derivative) of a function-which is like a formula. In Differential Calculus the focus is on changing rates of change (e.g. non-uniform velocities and accelerations). Integral Calculus is used to find the work done by a force and to solve geometric problems related to areas, volumes, the center of gravity of a mass, and the equations of curves. Similar principles were applied to Trigonometry (trigonon, triangle; metria, measurement)-the study of the relations among the angles and sides of triangles. Measurements can be made in terms of ratios of the sides of a triangle. The Ratio is the quotient of two numbers. The ratio of 12 to 18, or of 6 to 9 or of 2 to 3 is the same-i.e. 2/3.

In Pyramid Math (Osei, Issa & Faraji: The Origin of the Word Amen p64), Egyptians used different trigonometric lines, the tangent, sine, cosine, and cotangent in calculating the pyramids' slopes and cones. As a boy scout, to determine the height of a tall object (e.g. a tree), I used the Egyptian method of holding up a stick. If the shadow from the stick was the same length as the stick itself, then the shadow of the tree would also be as long as the tree is high. Since measuring the tree's shadow would give its height, the ratio of these two measurements would give a good idea as to the time of day.

To show its evolution, between 1900 and 1950 math knowledge doubled-and again from 1950 to 1960. Thus "New Math" arose with the aim of teaching great math ideas to elementary and high school students. Besides standing on the shoulders of the old, it is an up-dated version of basic math. Reference Bailey, Common Sense Inside African Tradition, Wingspanpress.com

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Joseph A. Bailey, II, M.D.