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Oyster Shells and Troubled Mathematicians

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Oyster Shells. and. Troubled Mathematicians. Kelly Browning. Jenn Bozzo. Emilie Erler. Jen Worth ... French mathematician Lazare Carnot, a member of the Academy ... – PowerPoint PPT presentation

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Title: Oyster Shells and Troubled Mathematicians


1
Oyster Shells and Troubled Mathematicians
  • Kelly Browning
  • Jenn Bozzo
  • Emilie Erler
  • Jen Worth

2
Thats right troubled mathematicians
  • Negative numbers were once totally ignored by
    mathematicians until many years into the 1800s!
  • A 17th century mathematician, Rene Descartes
    called negative numbers false because they
    represented numbers less than nothing.
  • French mathematician Lazare Carnot, a member of
    the Academy of Science and famous mathematician
    once stated " to really obtain an isolated
    negative quantity, it would be necessary to cut
    off an effective quantity from zero, to remove
    something of nothing impossible operation. "
    Geometry of Position, 1803
  • And so negative numbers were deemed as absurd,
    inadequate, false and completely disregarded.
  • Of course, there were a few exceptions

3
The Exceptions
  • Negative numbers were used in India to represent
    debts, even though some mathematicians in India
    still deemed negative numbers as inadequate.
  • The Chinese used a table with red and black rods
    as manipulatives to represent positive and
    negative numbers. Generally, red equaled
    positive numbers and black equaled negative
    numbers. However, this was very auxiliary
    because their problems and answers mention no
    negative numbers.
  • In the 1200s, Fibonacci would use negative
    numbers financially to represent a loss rather
    than a gain.
  • Throughout Islamic text there were rules for
    adding and subtracting numbers.

4
Still of No Use
  • Even when European mathematicians began to
    acknowledge negative numbers because of their
    appearance in Islamic texts, the negative numbers
    were still considered useless and meaningless.
  • Most did not even speak of negative numbers, but
    instead negative quantities.
  • Mathematicians argued that numbers can be only
    positive and that it is the quantities that can
    be negative or positive. A negative quantity is
    defined by an opposition to a positive quantity
    a path in a direction, a path in the contrary
    direction a profit, a debt...
  • Basically, when negative numbers were being used
    there was no justification of their rules or
    existence.
  • This was finally clarified in the 17th century by
    Leonhard Euler.

5
Negative Numbers Unsolvable?
  • While Greek mathematician Diophantus (circa
    200b.c.) was stating that an equation such as
    x3o was unsolvable, others were considering the
    concept of negative numbers to be true and
    recording their findings in manuscripts.
  • In Leonhard Eulers Complete Introduction to
    Algebra he reasoned the above unsolvable
    equation by saying, to cancel a debt signifies
    the same as giving a gift.

6
Negative Numbers Recognized Finally
  • Yes, during the 1800s negative numbers were
    getting considerable recognition.
  • At first, when negative numbers were written on
    text it was unclear the difference between the
    negative sign and the minus sign.

7
Negative Numbers Now
  • Negative has become a term in mathematics that
    means opposite.
  • The negative has the status of a number and rules
    were developed. The example below is for
    multiplication and notice that the negative sign
    means that it is the opposite of the positive A.
  • ( A) A
  • ( - A ) -A  
  • -( A ) -A           
  • -( - A ) A
  • And of course, negative could not exist without
    zero.

8
Is Zero Positive or Negative?
  • It is neither!
  • Psychologically, it is negative.
  • The concept of zero represents something that
    is not there, while zero as a number represents
    the lowest of all non-negative numbers
    (www.pantaneto.co.uk).
  • Can be non-negative or non-positive but not
    negative or positive

9
Is Zero a Number?
  • Yes!
  • Noun-A mathematical element that when added to
    another number yields the same number
  • Adjective-Indicating the absence of any or all
    units under consideration

10
Zero Has Many Meanings
  • By itself, it means nothing, zero quantity
  • Zero can be used as a place holder
  • The place value increases by one place value for
    each zero
  • There can be a zero slope for a graph
  • For a graph or number line, it is the point of
    origin
  • Zero is a point in geometry
  • Zero is false in a binary system

11
Where Did Zero Come From?
  • First civilization to use zero were the Maya
  • Used an empty oyster shell
  • Hindus used the zero symbol we know today

12
Other Civilizations
  • The Babylonians and Chinese didnt have a symbol
    for zero for a long time
  • Babylonians left a space, then had two slanted
    wedges
  • The Greeks questioned whether zero was a number
  • How can nothing be something?

13
Computations with zero
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Function of Trigonometry
  • Graphing

14
Interesting facts
  • Zero represents the operator
  • Modern numeral 0
  • Old-style fonts o
  • 0o C is the freezing point of water

15
  • RESOURCES
  • www.michielb.nl
  • mathforum.org
  • www.pantaneto.co.uk
  • en.wikipedia.org
  • http//nti.educa.rcanaria.es/penelope/uk_confboye.
    htmelements
  • History of Math, The Long History of Negative
    Numbers. Key Curriculum Press 1996. Pgs. 57-58.
  • Thanks for your attention
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