# egyptian_math by ashrafp

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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.

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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

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