When Was the First Known Instance of Negative Numbers

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When Was the First Known Instance of Negative
Numbers?
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Findings

• There are two ancient artifacts that contain
  negative numbers that may be the oldest.
• The Bakhshali manuscript from India
• The Nine Chapters on the Mathematical Arts from
  China
• The Nine Chapters appears to be the oldest
• The version we have of The Nine Chapters was
  written by Liu Hui in 263 CE

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• Huis text was copied from older texts, probably
  from Zhang Cang around 170 BCE
• Which was reconstructed from earlier works burned
  by the Qin Dynasty in 213 BCE
• Hard to tell when negative numbers were added
• Chinese update copies of old works with new
  methods giving no credit
• This causes some to believe the Bakhshali
  manuscript was first
• Parts of Huis version contain decimal usage
  that began in 200BCE until around 250 BCE
• The Nine Chapters contain ways to find the
  area of figures using black counting rods to
  denote negative numbers

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1st page of chapter 1
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Other Questions Why do we have negative
numbers? Who thought of negative numbers? For
what were negative numbers first used? What about
Eastern cultures allowed negative numbers to
exist before Western cultures? Why is it so hard
to date some ancient artifacts?
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Connections -         Help students understand
negative numbers -       Alleviate some of the
stress about negative numbers Show some
practical application of negative numbers
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 Why I picked this question I found the
question genuinely interesting. I dont see
negative numbers in my daily life so I was
curious as to how people came to them and when.
Negative numbers are frustrating for middle
school students because theyre abstract and I
wanted some background on their development to
see how people could come to need them so I might
see how to make students need them.
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Sources

• O'Connor, JJ Robertson, E F . Nine Chapters on
  the Mathematical Art. Retrieved July 15, 2008,
  from http//www-groups.dcs.st-nd.ac.uk/history/Hi
  stTopics/Nine_chapters.html
• O'Connor, JJ Robertson, E F. The Bakhshali
  manuscript. Retrieved July 15, 2008,
  http//www-groups.dcs.st-and.ac.uk/history/HistTo
  pics/Bakhshali_manuscript.html
• Wikipedia U.S. Retrieved July 14, 2008, from the
  Wikipedia Wiki http//en.wikipedia.org/wiki/Bakhs
  hali_Manuscript