# Africa’s Contribution to Mathematics

### Cheikh Anta Diop on the Contributions of Africa to Mathematics

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. Archimedes, a Greek who studied his craft in Alexandria, Egypt, lived from 287 BC – c. 212 BC., and is credited with (1) discovering the area and tangents to the curve traced by a point moving with uniform speed along a straight line which is revolving with uniform angular speed about a fixed point. This curve, described by r = a in polar coordinates, is now called the “spiral of Archimedes.” He is also credited with (2) exacting the numerical value of pi, (3) principles of leverage, and (4) inventing the so-called “Archimedes Screw” (more on that later).

The tomb of Archimedes is famous for it depicts his famous diagram, a sphere in a cylinder of the exact height and diameter. Archimedes had allegedly proved that the volume and surface area of the sphere would be two thirds that of the cylinder.

Archimedes greatest so-called "discovery"

However, Archimedes stole this so-called discovery – and many others – from the texts he studied in Egypt. Cheikh Anta Diop wrote in Civilization or Barbarism that “…Archimedes did not even have the excuse of an honest scholar who would rediscover an established theorem, without knowing that it had been discovered two thousand years before him by his Egyptian predecessors. The other “borrowings” in which he indulged himself during and after his trip to Egypt, without ever citing the sources of his inspiration, show clearly that he was perfectly conscious of his sin, and that hereby he was being faithful to a Greek tradition of plagiarism.”

He goes on to say “It is remarkable that the Romans, who had less contact with the Egyptians, have contributed practically nothing to the exact sciences, geometry in particular.”

### 1. Egyptians discovered mathematical formulas for determining cylindrical surface values two millenia before Archimedes, and 2. Archimedes failed to truly discover pi, whereas the Egyptians had discovered the value as early as 3,000 B.C.

We know this thanks to an Egyptian mathematical papyrus that was written in 1700 B.C. The Rhind Mathematical Papyrus consists of reference tables and a collection of 20 arithmetic and 20 algebraic problems. The problems start out with simple fractional expressions, followed by completion (sekhem) problems and more involved linear equations (aha problems).

In the opening paragraphs of the papyrus, Ahmes presents the papyrus as giving “Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries…all secrets”. He continues with:

This book was copied in regnal year 33, month 4 of Akhet, under the majesty of the King of Upper and Lower Egypt, Awserre, given life, from an ancient copy made in the time of the King of Upper and Lower Egypt Nimaatre. The scribe Ahmose writes this copy.

Problems 41 – 46 of the Rhind Papyrus show how to find the volume of both cylindrical and rectangular based granaries. In problem 41 the scribe computes the volume of a cylindrical granary. Given the diameter (d) and the height (h), the volume V is given by:

In modern mathematical notation (and using d = 2r) this clearly equals The quotient 256/81 approximates the value of pi as being ca. 3.1605.

Archimedes, however, failed to discover pi. Cheikh Anta Diop writes:

“Archimedes does not explicitly calculate the value of 3.1416 (the value of pi). He shows that the ratio of the circumference to the diameter lies between 3.1/7 and 3.10/71. The next best approximation was found by the Babylonians, and their calculation was (incorrectly) a whole number (3) or else 3.8!

### 3. The Egyptians invented the scale – the worlds first rigorous scientific application of the theory of leverage.

Archimedes is credited with saying “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” The Egytians not only knew the power of the lever, they used them in both simple and complex ways. Levers like the shadoof, a lever with unequal arms, was used to raise heavy building blocks, and to water gardens.

An Egyptian using the shadoof to water a garden. This is the lever that Archimedes claimed would allow him to

Archimedes published a treatise entitled On the Equilibrium of Planes or of Their Center of Gravity – which would deal with the equilibrium of a lever. But once again, his treatise was a useless plagiarism of a problem that the Egyptians had already solved more than 2,000 years before Archimedes was born. It should be noted that while the Egytians used this technology for peacful purposes, Archimedes used it to create weapons of war.

### 4. The Archimedes Screw predates Greek history, and was old news that was in regular use in Egypt by the time Archimedes came along.

Cheikh Anta Diop writes:

“…Archimedes would not invent the continuous screw, the spiral, in Sicily, but during a trip to Egypt where this screw was invented, evidently, centuries before the birth of Archimedes.”

Euclid of Alexandria, was a Greek mathematician who is often referred to as the “Father of Geometry”, was as much a fake as Archimedes. A second Egyptian papyrus, the Moscow Mathematical Papyrus, asks for a calculation of the surface area of a hemisphere. Solving this problem requires extensive and mature knowledge of geometry. The text of problem 10 runs like this: “Example of calculating a basket. You are given a basket with a mouth of 4 1/2 . What is its surface? Take 1/9 of 9 (since) the basket is half an egg-shell. You get 1. Calculate the remainder which is 8. Calculate 1/9 of 8. You get 2/3 + 1/6 + 1/18. Find the remainder of this 8 after subtracting 2/3 + 1/6 + 1/18. You get 7 + 1/9. Multiply 7 + 1/9 by 4 + 1/2. You get 32. Behold this is its area. You have found it correctly.”

The solution amounts to computing the area as

The 14th problem of the Moscow Mathematical calculates the volume of a frustum.

Problem 14 of the Moscow papyrus states that a pyramid has been truncated in such a way that the top area is a square of length 2 units, the bottom a square of length 4 units, and the height 6 units, as shown. The volume is found to be 56 cubic units, which is correct.

The text of the example runs like this: “If you are told: a truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top: You are to square the 4; result 16. You are to double 4; result 8. You are to square this 2; result 4. You are to add the 16 and the 8 and the 4; result 28. You are to take 1/3 of 6; result 2. You are to take 28 twice; result 56. See, it is of 56. You will find it right”

The solution to the problem indicates that the Egyptians knew the correct formula for obtaining the volume of a truncated pyramid:

In addition to the above, the Moscow and the Rhind Papyrus shows us that the Egyptians knew were intimate with algebra and knew how to rigorously calculate the square root, irrational numbers, the so-called Pythagorean theorem, the quadrature of a circle, trigonometry (used to calculate the slope of a pyramid using sine, cosine, tangent, and cotangent), and the surfaces of triangles, circles, rectangles, and trapezium. Remember, this is all 2,000+ years before the white, so-called father of geometry was born.

The key takeaway is this: from early in education, the world is taught that western civilization originated everything of value to the world. Not only is this untrue, but it should be said that the west learned everything they knew of value from Africa. The real origins of Christianity, mathematics, architecture, medicine, and literature originated with the Black man and woman.

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### One Response to Africa’s Contribution to Mathematics

1. Nelson Ojijo on May 24, 2012 at 9:02 am

Just one question: Does the period of these mathematical discoveries in Egypt coincide in any way with the period when the Jews were slaves in Egypt? If not, I will agree that “The real origins of Christianity, mathematics, architecture, medicine, and literature originated with the Black man and woman”.