From 0 to Infinity in 26 Centuries Read Free Page A

tablets littered with Mesopotamian mathematics. It seems the Mesopotamians were able to use fractions, to work out the areas of rectangles and
triangles, and to solve quite complicated equations. My favourite fact is that many tablets found appear to have been maths homework! But maybe you need to be a maths teacher to appreciate that
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    A NCIENT E GYPTIAN M ATHEMATICS
    The Ancient Egyptians were a talented lot. In addition to building the pyramids, many of which are still standing over 4,000 years later, they also turned their hands to
committing the written word to papyrus, a paper-like material made from interwoven reeds. Papyrus was a much more forgiving material to write on than the clay tablets the Mesopotamians were using
further north. As such, unlike the Mesopotamians, the Ancient Egyptians were not limited to using a single symbol. However, because papyrus rots, especially if it gets wet, it does mean that a vast
majority of the writing of Ancient Egypt has been destroyed over time.
    Systems in place
    It also seems that the Egyptians were not limited to one writing system.
    Egypt is famous for its hieroglyphics – pictograms they carved on to their monuments, and which remained a complete mystery until French soldiers unearthed the Rosetta Stone in 1799.
    Hieroglyphics were the Ancient Egyptian equivalent of calligraphy – decorative writing for use only on wedding invitations and inscriptions. The Egyptians had another writing system called
hieratic, which they used for everyday stuff – a much easier and faster way to write script that scribes would then use for their calculations.
    Hieroglyphic numbers had symbols for 1, 10, 100, 1000, etc., which the Ancient Egyptians would combine to make the required number:

    So if an Egyptian wanted to refer to Rameses’ 1,234 chariots on his latest obelisk, he would have used the following symbols:

    Because they added up the symbols in order to generate a total, the Egyptians could write the symbols in any order and direction they pleased – a
handy tool when they wanted to be decorative.
    The hieratic number system was a little more complicated because it used different symbols for each unit, each ten, each hundred and each thousand. The symbols for 40 and 50, for example, bore
no relation to each other. It seems that this system relied on the fact that the scribes would be familiar with the symbols and would be able to perform calculations either in their heads, or by
converting to the hieroglyphic system for tricky sums.
    The business of numbers
    Three important sources of mathematical information were left behind from Ancient Egypt: the Rhind Papyrus, the Moscow Mathematical Papyrus and the Berlin Papyrus. All three
documents contained mathematical problems in arithmetic and geometry, alongside, interestingly, the first written information about pregnancy tests.
    From these three sources we have learned that the Egyptians used fractions. However, they only used fractions that had a numerator of 1 – that is, the number on the top of the fraction
could only be 1. They would talk about more complicated fractions by adding these unit fractions together. So, for example, they would think of ¾ as ½ + ¼. Although
slightly cumbersome, this method stood the test of time – unit fractions were still used by mathematicians in medieval times.
    The pyramid builders obviously had a pretty good grasp ofgeometry; the papyri contain detail about how they set about making these ancient structures. The pyramids were
made with stacks of stone blocks in layers, and the steepness of a pyramid depended on the size of the overlap between two layers – the larger the overlap, the steeper the pyramid. The
Egyptians devised a series of methods to work out what size of overlap was needed for different gradients. It has also been suggested the Egyptians had some idea of Pythagoras’ theorem (see here ), which would have enabled them to work out the third length of a