The Historical development of
number and number systems
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
Maya (300 B.C.) & Romans
 Similar to Babylonians
 Similar to the Egyptian
 No problems with
 Larger numbers were
written by putting a bar
 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
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
 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
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
 Bhaskara ignore the negative roots because at the
time there wasn’t a clear understanding of negative
 Acceptance of negative numbers began in 17th
 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
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
Related flashcards

General topology

14 cards


77 cards

Mesh networking

12 cards

Create Flashcards