The Historical development of number and number systems

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 -200 B. 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 (9 th 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 16 th and 17 th 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 � 18 th 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 (7 th 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 17 th 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 showed it could be useful in mathematics

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