Physics Project _1_ The History of Zero by hcj

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									Physics Project #1:
The History of Zero
      Jacob Suydam
      Quan Nguyen
   Jonathan De La Cruz
                 Life Before Zero
n   Ancient Attitudes
    n   Math was not used for abstract concepts that it is
        used for today. Ancient civilians only concerned
        themselves with concrete ideals
    n   They did not really have to worry about “zero”
        objects or negative numbers when doing math.
                  Life Before Zero
n   Babylonia
    n   Had a place holder
        system without zero for
        over 1000 years.
    n   Until 400BC, they did
        not distinguish between
        2106 and 216. (it was all
        contextual)
    n   Place holder was a
        wedge ('') instead of a
        zero. (ex. 21 '' 6)
              Life Before Zero
n   Other placeholders existed, often varying in
    the amount of “hooks”, depending on cultural
    influence.
n   One universal occurrence: The placeholder
    would never be on the end. (216 '' for 2160
    never existed, it was interpreted based on
    context.)
Life Before Zero
        n   The Greeks
            n   Did not make use of
                placeholders, as most
                mathematical thought
                went towards geometry
                (Did not need to name
                their numbers)
            n   Merchants were the only
                ones who recorded
                numbers, and did not
                need a new notation.
                 Invention of Zero
n   The Mayans:
n   By 665 CE (AD) the
    Mayans used a place-value
    number system to base 20
    with a symbol for zero.
    However their use of zero
    goes back further than this
    and was in use before they
    introduced the place-valued
    number system. This is a
    remarkable achievement but
    sadly did not influence other
    peoples.
Invention of Zero
         n   India
         n   Zero was used as a
             placeholder and as an
             empty value.
         n   Aryabhata (500AD)
             n   Used the word “kha” for
                 position, which was later
                 the word for zero
         n   First recorded usage of
             zero would be in
             876AD.
                   Invention of Zero
n   Rules of Zero:
n   Brahmagupta:
    n   Laid the rules for addition,
        subtraction and multiplication
        of zero, but was confused by
        division.
    n   Zero + a negative = a
        negative; zero + a positive = a
        positive.
    n   Zero + zero = zero.
    n   Zero – a negative = a positive;
        zero – a positive = a negative.
    n   Zero – zero = zero.
    n   Zero x anything = zero.
Invention of Zero
         n   Popularizing Zero:
         n   al-Khwarizmi’s book: On the
             Hindu Art of Reckoning.
              n   First in what is now Iraq to use
                  zero.
         n   Indian ideals spread to China,
             along with zero.
              n   Ch’in Chiu-Shao’s Mathematical
                  treatise in nine sections.
              n   Zhu Shijie’s Jade mirror of four
                  elements.
         n   Fibonacci is credited for bringing
             Indian ideals to Europe, but only
             treated it as a sign, not a number
             necessarily.
                  Impact of Zero
n   In society, zero represents an empty value.
    (Absence of value or nothing)
n   After the creation of zero, it was used to be a
    simple placeholder. Now it is a number of its
    own.
    n   Evolved from its placeholder position into its
        current meaning as conceptual idea of nothing.
                  Impact of Zero
n   We are now able to distinguish between the
    uses of zero in conversations based on context.
    n   Ex: We know that if somebody tells us the price of
        a slice of pizza is “two fifty", we know that they
        mean $2.50. However if the context changes to the
        cost of a speaker system, and somebody tells us
        the price is “two fifty”, we assume it means $250.
            Importance of Zero
n   With zero, the existence of negative and
    decimal numbers is possible, which is
    important to concepts such as temperature.
n   Zero is a “origin point” on some scales,
    allowing for a balanced start. (Neither positive
    or negative.)
n   Zero is also important to rounding, which may
    require rounding to the nearest tens or higher,
    numbers that need zero.
                 References
n   http://www.helium.com/items/295891-the-
    importance-of-zero-in-mathematics
n   http://www.gap-
    system.org/~history/HistTopics/Zero.html
n   http://www.mediatinker.com/blog/archives/00
    8821.html

								
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