African Mathematics: From Bones to Computers by Mamokgethi Setati, Abdul Karim Bangura

By Mamokgethi Setati, Abdul Karim Bangura

This is often the 1st finished textual content on African arithmetic that may be used to handle a few of the tricky matters during this zone. those concerns contain attitudes, curriculum improvement, academic switch, educational fulfillment, standardized and different exams, functionality elements, pupil features, cross-cultural alterations and reviews, literacy, local audio system, social category and transformations, equivalent schooling, instructing equipment, wisdom point, academic directions and guidelines, transitional colleges, comparative schooling, different matters equivalent to physics and social experiences, surveys, expertise, academic examine, instructor schooling and skills, educational criteria, instructor effectiveness, lesson plans and modules, instructor features, guidelines, application effectiveness, application evaluate, African tradition, African historical past, Black reviews, classification actions, academic video games, quantity platforms, cognitive skill, international impression, and basic thoughts. What unifies the chapters during this booklet can seem quite banal, yet many mathematical insights are so visible and so primary that they're tough to take in, get pleasure from, and exhibit with clean readability. a number of the extra easy insights are remoted by means of debts of investigators who've earned their contemporaries' appreciate.

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The first two numeration systems appeared quite early in Egyptian history. The hieratic notation was used in both the Ahmes and Moscow Papyri, while the demotic variant was a popular adaptation of the hieratic notation and became important during the Greek and Roman periods of Egyptian history (Joseph 1991/2000:61). In the hieroglyphic system, characters represented objects, some easily recognizable. Special symbols were employed to represent each power of 10 from 1 to 107. A unit was therefore commonly written as a single vertical stroke; when written in detail, however, it was shown as a short piece of rope.

When Gerdes draws the oblique square (area C’) together with the squares with areas A and B, in such a way that the squares become “neighbors,” the Pythagorean proposition for the special case of the right triangle emerges. In essence, toothed squares may assume a heuristic value for the discovery of the Pythagorean proposition. In his first proof, Gerdes lets A’ and B’ be two arbitrary squares. He dissects A’ into nine little congruent squares and B’ into 16 congruent squares, and joins the 25 pieces together.

Indb 28 9/7/10 5:04 PM Geometry South of the Sahara 29 1 + 2 + 3 + 4 + 3 + 2 + 1 = 42, or, taking into account the visionary line: (1 + 2 + 3 + 4) + (3 + 2 + 1) = 42. It follows that (1 + 2 + 3) + (3 + 2 + 1) = 42 - 4, and 1 + 2 + 3 = (42 – 4)/2, Experimentation with other toothed squares, varying the number of teeth on each side, leads Gerdes to the following extrapolation: 1 + 2 + 3 + . . + (n - 1) = (42-n)/2, where n denotes a natural number bigger than 1. By counting all the unit squares of the toothed triangle, row by row, Gerdes finds 1 + 3 + 5 + 7.

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