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Egyptian Math “In ancient Egypt mathematics was used for measuring time, straight lines, the level of the Nile flooding, calculating areas of land, counting money, working out taxes and cooking. Math was even used in mythology - the Egyptians figured out the numbers of days in the year with their calendar. They were one of the ancient peoples who got it closest to the 'true year', though their mathematical skills. Math was also used with fantastic results for building tombs, pyramids and other architectural marvels.”1 Hieroglyphics The Egyptians invented two forms of writing. The first was called hieroglyphics. They wrote the hieroglyphics on the walls of their buildings and in their tombs. They were using these symbols before 3500 BCE. They are primarily carved on walls. They are made up of many symbols. The hieroglyph numerals actually have relatively few symbols. This is a base 10 system. They have different symbols of each placement, and when you want to increase the number in one place, you just write the appropriate symbols as many times as you need. The symbols for the placements are as follows: the 1s place is (a stick) the 10s symbol is (a heel bone) the 100s symbol is (a spiral) the 1000s is (a lotus flower) So if we are to write the number 1234, it would look like The number system is read from the top to bottom and from right to left. This was a very easy symbol system to remember, but it took a very long time to write. It takes 10 symbols to write was took 4 symbols in Hindu-Arabic numerals. 1 http://www.touregypt.net/featurestories/numbers.htm Hieratics So what was the second form of numerals in Egypt? Around 1800 BCE, hieratic numerals were invented. They were invented shortly after the invention of papyrus. These numbers were in base 10 as well, and there were more numerals but they were shorter to write on the papyrus. This diagram beside shows the symbols used on the papyrus. We can see that they are much like Hindu-Arabic numerals, having unique symbols from 1 to 9, and then differences at each new placement level. So what does 2765 look like in hieratic numbers? The number can also be written this way, The number can be read left to right and right to left. The Egyptians did not specify a positional system in hieratic numerals, so the numbers were written both ways! The Rhind papyrus, which has taught us much about Egyptian math, used hieratic numerals. It was written in 1650 BCE by a scribe named Ahmes. The Name Rhind comes from the last name of the man who discovered this papyrus. This papyrus records math equations and math problems. Fractions The Egyptians used fractions, but they are different than the ones we use in our class today. A fraction in hieroglyphics would use the symbol over the number of the denominator (the bottom number of the fraction in Hindu-Arabic numerals). This lets you know the number was a fraction and not an integer or whole number. An example of what a fraction looks like will follow, but first we need to know what was so unusual about these fractions? Well, the Egyptians always wrote their fractions in the form 1/n. This means that the numerator (the number on top in Hindu-Arabic fractions) was always the number one. The denominator could be any number, and this is how they could represent different values. So some of the fractions they could write were 1 2 , 1 3 , 1 4 , 1 5 and so on. So let’s look at a fraction in hieroglyphics. The fraction 1/8 would look like Another fraction, like 1/261 would look like Notice that the fraction sign is only over the top place number when there are too many symbols for the fraction symbol to go over. Also notice the fraction is read from right to left. There were a few special fractions which were used often in math work, and they developed unique symbols for these fractions. this is the ½ symbol this is the 2/3 symbol So how would we figure out how to write a fraction like ¾? We would have to find fractions in the 1/n form which add up to ¾. So for example ¾ = ½ + ¼. This may seem complicated, but for some problems you may find it easier to use the Egyptian fractions than the Hindu-Arabic ones! One of the rules with the fractions is that you can not have the same fraction repeated. Here is an example, if we have the fraction 2/7, we can not say this equals 1/7 + 1/7, it is illegal. We would have to express this fraction ¼ + 1 28 . How did I get this answer? Bonus points for showing my on your homework. Egyptians did multiply and divide numbers, but it was very complicated and involved adding various numbers together. Perhaps we could look at them another day. Sources: http://www.touregypt.net/featurestories/numbers.htm http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Egyptian_numerals.html http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fractions/egyptian.html http://www.ics.uci.edu/~eppstein/numth/egypt/why.html http://www.jimloy.com/egypt/fraction.htm