The left symbol represents linen and the symbol next to it represents alabaster vessels. The numerals below them mean that he has offerings of pieces of linen and alabaster vessels. On the right below the table we see offerings of pieces of bread, jars of beer, antelopes and oxen. The rest of the text refers to even more offerings. The Egyptians used a technique called "repeated doubling" to compute their products. The technique is most easily explained through an example.
Suppose we wish to compute 11 X We first find several easy multiples of What if we want to multiply by a fraction? In this case repeated halfing may be the answer. For more about fractions, see below. A similar method can be used for division. Suppose we wish to divide by 5.
The we can work backwards and look at multiples of 5 until we reach The rest of the fractions were always represented by a mouth super-imposed over a number. When working with fractions the Egyptians expressed all their fractions as a sum of unit fractions.
The Egyptian mathematicians did not memorize all these fractions. The Rhind mathematical papyrus for instance contains some tables showing what these decompositions were. The most common example is someone computing different rations of grain. In more recent times some of the thinking about the origins of the glyphs has changed: " In older literature about Egyptian mathematics these signs are often interpreted as hieratic versions of the hieroglyphic parts of the eye of yhe Egyptian god Horus.
However, texts from the early third millennium as well as depictions in tombs of the Old Kingdom, which show the same signs, prove that the Eye of Horus was not connected to the origins of the hieratic signs. But no matter where the glyphs came from, the fact remains that the Egyptians computed these fractions. Problem 80 from the Rhind mathematical papyrus is a wonderful example to look at. It contains quite a few of the mathematical topics we have discussed.
According to Clagett [1] the problem translates to:. The word for square root is written with a sign that represents either a corner or more likely a right angle. The name was kenbet in Egyptian. The underlying idea may well be that a right angle with equal arms is the root in a sense of the square area. Paraphrased from Gunn and Peet via Clagett. Several ancient sources mention square roots [1].
The Moscow Mathematical Papyrus uses the fact that the square root of 16 is 4 twice, and the fact that the square root of is 10 once. Berlin Papyrus which dates to roughly the same time period as the Moscow Papyrus uses the fact that the square root of is It is not known how these square roots were computed.
The results are used in the problems, but no justification is given. It is possible likely? Sadly no such table has ever been found however. The Ancient Egyptians took measurements in several different ways. Some measuring sticks have actually been found in tombs. An interesting example is for instance the measuring rod from the tomb of Maya - Tutankhamen's treasurer - which was found in Saqqara. However, the annual Nile floods could quite easily wash away land, so the king dispatched surveyors to see by how much a tenant's land had been reduced and lowered the taxes accordingly.
In addition, the Nile floods made establishing boundary markers impossible, because the inundations would soon wash them away, so the surveyors were often called upon to mediate in any boundary disputes. To support the idea that the Egyptians were fine mathematicians, a number of papyruses proved to be a guide to solving problems in arithmetic and geometry. This papyrus, alongside hieroglyphics, showed that the Egyptians used a decimal system of numbers, although it was not positional like our modern system, which meant that they did not need a symbol for zero, much like the Roman system of numbers.
The Egyptians could add and subtract using this system of numbers, but division and multiplication were time consuming and difficult and relied upon doubling or halving, as with a computer binary system.
The Egyptians used trial and error techniques to arrive at solutions to problems, and had little interest in looking for formulae or complex interrelationships between sets of numbers.
The formulas that the Egyptians developed gave them ways to estimate the areas and volumes of shapes and solids, which, whilst not perfectly accurate, were a close enough approximation for their purposes. The Egyptian mathematicians understood a little algebra and were capable of solving linear equations, and could solve simple quadratic equations by using a series of guesses to find the closest answer, a brute force method that was used for many centuries afterwards.
What we know about Egyptian mathematics is scanty and incomplete. Sadly, most of the Egyptian records were stored on papyrus, which, apart from the problem of degradation, may have been amongst the Egyptian mathematical texts burned during the fire at the Library of Alexandria. Therefore, we only have a few manuscripts to reveal the skill of the Egyptian mathematicians, alongside a few hieroglyphic records and Greek sources. The Rhind papyrus discovered by Henry Rhind, in the 19th century, dates from BCE and is filled with problems and solutions, also including a section on fractions.
This seems a little unwieldy but is actually straightforward to use once you are used to it. The Moscow papyrus, also dating from around BCE and discovered by Golonischev, contained further problems showing how to calculate the volume of a truncated pyramid and work out the surface area of half a sphere.
Certainly, it was accurate enough for most practical uses. These techniques were used in the building of the pyramids and other monuments, and the Egyptians devised a measuring system over the centuries.
Their standard of measurement was the cubit, around In terms of using mathematics everyday, the Egyptians were masters and devised some sophisticated techniques. Their mathematicians were so skilled that great Greek mathematicians such as Thales and Pythagoras learned techniques in Egypt.
The Egyptians did not see any need to discover axioms or find relationships between sets of numbers, and were happy to use brute force and trial and error methods to solve problems. In many ways, we still use these methods today: When a supercomputer is used to discover prime numbers to calculate a few more decimal places for Pi, it uses force to perform huge numbers of calculations every second. Martyn Shuttleworth Jan 20, Egyptian Mathematics.
Retrieved Nov 14, from Explorable. The text in this article is licensed under the Creative Commons-License Attribution 4. That is it. You can use it freely with some kind of link , and we're also okay with people reprinting in publications like books, blogs, newsletters, course-material, papers, wikipedia and presentations with clear attribution. Menu Search. Menu Search Login Sign Up.
You must have JavaScript enabled to use this form. Sign up Forgot password. Leave this field blank :. Search over articles on psychology, science, and experiments.
0コメント