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The Mayan was a great Mesoamerican culture
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that had settled in Central America from 2000 BC
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to around 900 CE.
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They had a sophisticated number system.
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This allowed them to have precise astronomical measurements,
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and to develop accurate calendar calculations.
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They are also believed to be the first civilisation to have the concept of Zero.
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But how does the number system work?
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Well, to answer that question we can start by analyzing our current number system.
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Our number system is written using base 10. Because it is base 10,
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we need ten symbols to represent any real number that we desire to write down.
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We know perfectly well those symbols. Those are the following:
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The order in which we arrange two or more of these symbols to represent a number
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is relevant, for example, it is not the same to be 19 years old than to be 91 years old.
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This happens because a position that a digit-symbol has on a number will give to it its different value
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for example, the digit 1 in the first position of a number stands for the number 1.
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But if the same digit goes to the second position, now the value is 10.
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And if we move again the digit to the third position, now its value will be 100,
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and so on...
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As you can see, when you move a digit-symbol one position,
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you multiply by 10 the value the digit had in its previous position.
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This is why, for instance, the number 7042, can be broken into this:
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Notice that we had summed the position value of each digit that formed the number 7042.
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Using power notation and setting that any number to the power of zero is one
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we have an alternative way to express this number.
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Now let us go back in space-time to analyze the Mayan system.
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The Mayan used a vigecimal number system
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this means that instead of representing the numbers in base 10 as we do,
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they had a number representation based on base 20.
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Remember how our number system has ten symbols because it is based in base 10.
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Well, since the Mayan number system is based in base 20,
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they used 20 symbols to represent any number.
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It's very useful to memorize the value in base 10,
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of each one of these Mayan symbols.
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What difference to you see between the symbols that we use in the base 10 numerical system,
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and Mayan number system symbols?
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That's right! The symbols used in base 20, only use
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three different objects to form the whole set of twenty symbols.
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The dot which stands for a rock, the line which stands for a stick,
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and this little graphic that stands for a shell.
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We have now all the elements we need to learn to read Mayan numbers
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and to know their value in base 10.
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What difference to you see between the arrangement of the symbols?
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Good answer! Now the symbols are in a column.
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When you move a symbol from bottom to top,
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the value of the symbol is multiplied by 20 with the correct position exponent.
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Now you know how to transform a number represented in Mayan number system,
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to a number with the same number represented in base 10.
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Let us analyze an example of how to transform a number represented in base 10,
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to a number represented in the Mayan numerical system.
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For instance, 1455,
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which in base 10 needs four digit positions to be represented.
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It turns out that it only takes three vertical digit positions to represent this number
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in the Mayan number system.
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We have now all the tools needed to know how to do Mayan arithmetic.
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See you in the next session to learn how to sum, subtract, multiply and
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divide with Mayan numbers.