# History of Number Systems

### Properties and Operations

## Future Classroom Use

There are so many ways teachers could use this information for learning purposes in their classrooms. In middle school students learn more in-depth about the operations and properties of numbers. In my future classroom I could present this information to my class and use it to create a project for them. I could have them create a parallel universe where they are the Egyptians and they get to create the beginning foundations of math. This project would create a variety of learning opportunities for the students as well as myself. I could also show them all the different number systems that were created and create fun activities worksheets where they work problems using the different number systems. These worksheets could be used for extra credit grades, because simple problems would be challenging.

## Timeline of the Number System

· 5000 BC

o A decimal number system is in use in Egypt.

· 3000 BC

o Hieroglyphic numerals in use in Egypt.

· 2000 BC

o Babylonians begin to use a sexagesimal number system for recording financial transactions. It is a place-value system without a zero place value.

· 400 BC

o Babylonians use a symbol to indicate an empty place in their numbers recorded in cuneiform writing. There is no indication that this was in any way thought of as a number

· 300 BC

o Maya & Romans create number systems similar to previous systems

· 1 AD

o Chinese mathematician Liu Hsin uses decimal fractions.

· 200 AD

o The Maya civilization of Central America uses an almost place-value number system to base 20.

o Diophantus of Alexandria writes *Arithmetica*, a study of number theory problems in which only rational numbers are allowed as solutions.

· 500 AD

o Decimal notation is used for numbers in India. This is the system on which our current notation is based.

· 600 AD

o Based 10 place value system started with the Hindus

o Hindu recognized zero as a number

o Brahmagupta uses zero and negative numbers, gives methods to solve quadratic equations, sum series, and compute square roots.

· 800 AD

o Arabs adopted the Hindus system

o Thabit ibn Qurra makes important mathematical discoveries such as the extension of the concept of number to (positive) real numbers, integral calculus, and theorems in spherical trigonometry, analytic geometry, and non-euclidean geometry.

· 900 AD

o Gerbert of Aurillac (later Pope Sylvester II) reintroduces the abacus into Europe and uses Indian/Arabic numerals without having a zero.

o Al-Uqlidisi writes *Kitab al-fusul fi al-hisab al-Hindi*, which is the earliest surviving book that presents the Hindu system.

· 1000 AD

o Ahmad al-Nasawi writes *al-Muqni'fi al-Hisab al-Hindi,* which studies four different number systems. He explains the operations of arithmetic, particularly taking square and cube roots in each system

· 1500 AD

o Vander Hoecke uses the + and - signs.

o Bombelli publishes the first three parts of his *Algebra*. He is the first to gives the rules for calculating with complex numbers.

· 1700 AD

o Zero grew to a place holder to number for algebraic equations