Transcript Numbers
The Historical development of
number and number systems
BY LAM TRAN
Egyptians (3000-1000 B.C.)
Two numeration systems
Improved tally system “Hieroglyphics”
Their systems were based on groupings of 10
Add and Double
Used their numeration system for measurement
Babylonians (2000-200B.C.)
Number system based on grouping of 60
Position System
Writings was on clay tablets
Biggest Problem was spacing between the position
Towards the end they used dot to separate their
numbers
Maya (300 B.C.) & Romans
Similar to Babylonians
Similar to the Egyptian
No problems with
system
Larger numbers were
written by putting a bar
over
Subtractive device
spacing difficulty
Number grouping based
on 20
An odd use of 18
Place Value- Zero
Place value started with the Babylonians with their use of
their dot.
Based 10 place value system started with the Hindus(600
A.D.)
Hindu recognized zero as a number
Arabs (9th century) adopted the Hindus system
Indian Word Sunya- absence of quanity
Mahavira wrote that number multiplied by zero will
result in zero
Bhaskara declared a number divided by zero will have
infinite quanity
Zero (cont.)
Even in 16th and 17th century some mathematicians
still didn’t consider zero as a number
Thomas Harriot began to use this idea in solving
algebraic equations
Descartes popularized Harriot’s idea
18th century zero grew to a place holder to number
for algebraic equations
Fractions
Early use of fractions from Egyptian’s idea of “parts”
Babylonians extended their base sixty system to
include fractions
Greece used a system similar to Egyptian systems of
“parts”
Russian had a unit-fraction method
Chinese mathematicians thought about fractions
similar to our in their Nine Chapters on
Mathematical Art
Chinese avoid using improper fractions
Negative Numbers
Brahmagupta (7th Century), Indian mathematician,
recognized that negative number can be treated as
debt
Bhaskara ignore the negative roots because at the
time there wasn’t a clear understanding of negative
roots
Acceptance of negative numbers began in 17th
century
Descartes called negative roots “false roots”
Negative Numbers (cont.)
Isaac Newton began to call negative numbers less
than nothing
Euler treated negative numbers as debts and
interpret that product of two negative numbers is a
positive number
There were still doubters even in the higher ranks of
the mathematic community
The move to abstraction made negative numbers
more acceptable
Complex Numbers
Early times if the quadratic formula lead to square
root of a negative number then you have no solution
Cardano noticed this problem but didn’t know what
to do about it
Rafael Bombelli invented a new language to treat
these negative radicals
Bombelli’s work showed that sometimes the square
roots of a negative number can be used to find real
solutions
Complex Number (cont.)
Euler used complex numbers a lot, but didn’t resolve
the issue of what they were
Argand suggested to represent imaginary numbers
geometrically on a plane
Gauss proposed the same ideas as Argand and
showed it could be useful in mathematics
Questions?