Oyster Shells and Troubled Mathematicians

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Oyster Shells and Troubled Mathematicians

• Kelly Browning
• Jenn Bozzo
• Emilie Erler
• Jen Worth

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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

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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.

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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.

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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.

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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.

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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.

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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

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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

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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

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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

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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?

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Computations with zero

• Addition
• Subtraction
• Multiplication
• Division
• Function of Trigonometry
• Graphing

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Interesting facts

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

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• 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