Introduction
Undeniably, primordial Egyptians’ mathematics is one of the earliest kinds of mathematics which had a great influence of the entire traditions of mathematics that followed later. In this context, the term “Egyptian math” is used to refer to math that has been written using the Egyptian language. The work of Egyptians represents one of the civilizations that began taking advantage of the benefits of mathematics as well as numbers; which is evident based on the fact that the results of this early mathematics are still noticeable in the immense architectural accomplishments of these individuals. Notably, the Egyptians most used two mathematical texts: the Rhind papyrus which dates back to c. 1650 BC and the Moscow papyrus which dates back to c. 1890 BC.
General overview of Egyptian Math
For a long time, Egyptian math has had a poor reputation until recently. This has been attributed to a limitation of availability of prime sources, in comparison to the immense collections of cuneiform texts of math that were created in Mesopotamia. Notably, Egyptian math was mainly produced in the cities. The papyrus on which most of the work was written could be effectively stored in a dry environment, preferable in the desert regions of Egypt. However, most of the cities where math was common in Egypt were situated along Nile River; hence, most of the records of written work were destroyed within a short period due to the fact that the papyrus could not be effectively stored in a damp environment, (David, 2006). As such, most records on the impacts of math in Egyptian social, economic, as well as cultural life are presumed lost.
Studies indicate that primordial Egyptians’ mathematics had two unique characteristics. The first characteristic is that almost all mathematical advancement in this country was undertaken during the early centuries during which their civilization took place; precisely during the Archaic Period. The second characteristic is that, there were no simplifications in all parts of their math. Studies indicate that the Egyptian math lacked general rules or rather theorems. Instead, there were specific rules as well as descriptions of certain procedures instead of proofs, (Gilings, 2004).
Important names and dates
Egyptian’s mathematicians forms part of the most famous people in who have contributed in various ways in the evolution of mathematics to what it is lately. Among the key people in this category of scholars is Ahmes. He was born in 1680 BC and died in 1620 BC. Ahmes is well known for writing the Rhind Papyrus which is the source of most information about Egyptian mathematics. Diophantus is another Egyptian scholar who made major contributions to math. He was born about 200 and died about 284. He is best known as the “Father of Algebra” which originates from his work; Arithmetica, which was mainly solving of algebraic equations as well as the numbers theory. The ‘Arithmetica’ is a term that is used to refer to a set of approximately 130 problems that gives solutions of a numerical nature to indeterminate equations as well as determinate equations.
The third popular Egyptian mathematician is Heron of Alexandria, who was commonly referred to as “Hero”. He was born about 10 and died about 75 in Egypt. Heron is well known as one of the first geometers who significantly made major contributions in geometry. Actually, he was among the first people who came up with the formulae of calculating the area of a triangle. For instance, in his famous Book I of the Metrica, he asserted that, “if A is the area of a triangle with sides a, b and c and s = (a+ b + c)/2, then A2 = s (s-a) (s-b) (s-c)”. In Book II of Metrica, he reflected on various measurements of volumes of spheres, pyramids, cones, prisms as well as cylinders. He also did other several works both in mathematics as well as in mechanics. Lastly, is Pappus of Alexandria (ca 300), (Matheus, 1994). He contributed to the development of mathematics by writing about arithmetic methods, the axiomatic method, solid and plane geometry as well as mechanics. He produced one of the most resourceful geometric theorems which includes Pascal’s hexagon Theorem and the Pappus Theorem. Based on these theorems, he came to be known as the “Father of Projective Geometry”.
Egyptian numerals
Notably, in principle, Egyptian numerals resemble “Roman numerals”, in which various symbols are used to represent meticulous units that are summed together. In most cases, ancient Egyptian texts were written in either Hieratic or hieroglyphs. In this case, hieroglyph is used to denote small pictures which represent words. Moreover, the number system was represented in base ten. A simple stroke was used to represent number 1, number 2 by two strokes, and so on. On the other hand, numbers, ten, a hundred, one thousand, ten thousand, and a million had their specific hieroglyphs. The number ten was represented by a limp for cattle, a hundred by a coiled rope, a thousand by a lotus flower, ten thousand by a finger, a hundred thousand by a frog, and lastly, a million was depicted by a god with lifted hands which is a sign of adoration, (Helaine and Ubiratan, 2001).).
The number system of the Egyptians was additive. For instance, huge numbers were depicted by a compilation of glyphs, whose value could be obtained by simply summing together the individual numbers, (Florian, 2007).It is also of importance to note that, solely, fractions of the form 1/n were used by the Egyptians, with an exception of 2/3 which is very commonly found in most math texts. In terms of pictures, ½ was represented by a portion of linen that was folded in two, 2/3 by a mouth with two strokes of different sizes, and the other fractions were portrayed by a mouth that was put on top of a number. Additionally, division and multiplication was also very common in the Egyptian mathematics. Multiplication in this case took the form of binary arithmetic. To be more precise, multiplication was made by recurring doubling of the specific number that is to be multiplied, as well as selecting which of the doublings to be summed together.
Egyptian algebra
The Egyptian algebra problems are found both in the Moscow math papyrus and Rhind math papyrus and also other various sources. Egyptian algebra encompasses both quadratic as well as linear equations; which are answered using a method that is consistent with their mathematical specificities. In most cases, algebra in this case involves solving for unknown values which are usually referred to as Aha, if the amount as well as other parts of it has been given. In solving the Aha problems, a method of false position (method of false assumption) technique is usually used, (Gilings, 2004).The soundness of this technique is verified by explicit authentication, which can be calculated, based on the assumption that verifications are confirmations for certain process, and not for wide-ranging methods. It is evident from studies that scribes used universal multiples to problems of fraction nature into problems via integers.
Egyptian Geometry
Arguably, geometry originated in Ancient Egypt before spreading to the other parts of the world. The origin of geometry in Egypt is attributed to the need to survey land. Due to frequent flooding of the Nile destroying land as well as property, surveys were undertaken frequent so as to evaluate the value of property for taxation purposes. Like other segments of Egyptian math, information on geometry is found in problems of geometrical nature in the Moscow papyrus and the Rhind papyrus, inscriptions on shrines, as well as other sources of written history of Egypt. From the mathematical texts, it is evident that the Egyptians knew how to calculate various volumes of pyramids and cylinders as well as geometric shapes, (Matheus, 1994). It is this information which formed the background of the architectural activities in Egypt such as the construction of the historical pyramids as well as temples. Moreover, foundations for cities were laid out by applying geometric knowledge.
In order to illustrate Egyptian geometry, various laws of calculating volumes and areas of solid objects and common planes are used. However, it should be noted that, as opposed to theoretical proof, these calculations are based on a trial and error outcomes as well as observations. For instance, according to the Moscow Papyrus; Sin order to get the volume of a pyramid, V= (h/3)a2 was used. In this case, h represents the height, “a” represents length. Another example is the calculation of the area of a triangle, using the formula A= 1/2bh; where ‘b’ is the base length, and ‘h’ the height, (David, 2006).
Conclusion
Ancient Egyptians are one of the famous individuals who made greater contributions to the development of mathematics. For a long time, Pharaoh’s surveyors applied various techniques in measuring buildings as well as land in the Egyptian history, which led to the introduction of a decimal numeric system. The two common mathematical texts in Egypt are the Moscow Papyrus and the Rhind Papyrus. It is believed that base 10 numeration system was established in Egypt much early in 2700 BC. Notably, in Egypt, symbols were used to denote various numbers like in the case of the “Roman numerical”. Nevertheless, the concept of place value had not been developed by then. It is also evident that the Egyptians had great knowledge in algebra and geometry. In fact, their knowledge of geometry can be experienced in their architectural activities such as the construction of pyramids as well as other structures such as temples. Moreover, even their cities were established on the basis of geometry. For instance, they were much aware that a triangle of sides measuring 3, 4 and 5 units comprised of a right triangle, even before Pythagoras coming with the same idea. Based on this knowledge, used they were able to lay down their stonework during construction of structures in ensuring exact right triangles. To-date, Egyptian mathematics is appreciated for the contributions it has made in the history of this subject.
References
David, E.R. (2006). Ancient Egyptian Mathematics: new perspectives on Old Sources. Mainz:
Johannes Gutenberg University.
Florian, C. (2007). A History of Elementary Mathematics. Dallas: Cosimo, Inc.
Gilings, J.R. (2004). Mathematics in the Time of the Pharaohs. Illinois: John Wiley & Sons.
Helaine, S and Ubiratan, A. (2001). Mathematics Across Cultures: The History of Non-Western
Mathematics. Boston: Springer.
Matheus, R.G. (1994). Pragmatism and Conservatism in the Egyptian Mathematics. Sao Paulo:
Sao Paulo University
