The History of Numbers

Introduction Numbers serve two purposes Tools for Counting and Measuring Attempt to Understand the Unexplainable Natural versus Learned Counting Develop System & Method of Manipulation Linguistics to Communicate the System

Introduction Civilizations each developed their own system, each contributing to today’s understanding of numbers

Babylonian Numbers Some of the Earliest Devices to Record Calculations Clay Tablets in Iran of Base 10 Clay Tablets in Iraq of Base 60 Both Counting Systems are Still Present in Society Today

Egyptian Numbers Number System is not well evidenced, but their contribution is undeniable The Temple of Wasat was the World’s first University Educated 80,000 students at its peak Students included: ???

Egyptian Numbers Students included: Plato, Aristotle, Socrates, Euclid, Pythagoras, Hypocrates, Archimides, Euripides

Egyptian Numbers Left Little Written Evidence of Mathematics Rhind Papyrus (1650 BCE) Scroll 20’ x 1’ with 87 problems

Greek Numbers Which is more basic: Arithmetic or Geometry? Discrete or Continuous Universe Reality is Mathematical in Nature Irrational Numbers Presented a Philosophical Problem for the Greeks Thinking Based on Words and Abstract Diagrams

Greek Numbers By 500 BCE, they had a system based on the decimal and comprised of the 27 letters of their alphabet First nine letters represented the digits 1-9 Second nine represented the tens

Greek Numbers The last nine represented the hundreds Special sign for numbers higher than 900 There was no zero Numbers were nonpositional

Roman Numbers Roman numerals spread throughout Western Europe Started with stick numbers (I, II, III, IIII) Added six letter symbols (V, X, L, C, D, M) Addition & Subtraction were simple, but Multiplication & Division proved Complicated CCKCVI + DCL + MLXXX = ?

Roman Numbers The Abacus existed to provide place value Work vanished as it was performed, leaving no record of the process No way to check results other than to redo the calculation

Arabic Numbers In 830, Caliph al’Mamun founded the House of Wisdom in Baghdad Advancement during European Dark Ages Muslim world was reading translated works of the great Greek mathematicians

Arabic Numbers Arabic numerals were promoted by Fibonacci, but met opposition in Europe System had place value and zero

Mayan Numbers Employed a place value system with a base twenty counting system They used a dot to represent 1 and a horizontal line for 5 Larger numbers were represented by stacking symbols in columns Had a zero