History of Math Numbers vs Numerals Number Definition

History of Math Numbers vs. Numerals

Number Definition Numeral Definition 1: A symbol or word, or a group of either of these, showing how many or which one is a series. Definition: A figure, letter, or word, or a group of any of these, expressing a number Definition 2: An idea corresponding to a quantity. What is the difference between these two words?

6, 000 BC African civilization in region between Uganda and Zaire 1957: A Belgion archeologist discovered a bone in a place called Ishango near the river Nile. The bone is over 8000 years old. Notching represented quantities

Ishango: By Lake Edward

Oldest Table of Prime Numbers Microscopic examination showed 6 month lunar calendar represented.

1) What is the sum of each row? 2) What is the pattern in row (a)? 3) What do you notice is true about all of the numbers in row (b)? 4) What is the pattern for the numbers in row (c)?

3000 B. C. Quipu: Pre. Incan Civilization in Caral

Pre-Incan and Incan Empire The Quipu is a system of knotted cords thought to represent quantities

Since most of the Incas were wiped out and the Spanish thought the Quipu was idolatrous, they enthusiastically exterminated knowledge of how to use the Quipu

Written Numerals • Ancient civilizations tried to model numbers • Tick marks and knots • Ancient Numerals • not efficient for “large” numbers • Led to new inventions for numerals

Mesopotamia Writing started as early as 4000 BCE Used Cuneiform as a form of writing to measure numbers. Cuneiform scribes wrote with a triangular stylus that was plunged into wet clay forming different indentations depending on the angle of the plunge The tablets typically did not show procedures, but recorded arithmetic results

Radix Number System This system allows a lower number symbol to modify the meaning of the symbol for a larger number. A radix occurs when a new symbol is introduced and represents the set of next smaller symbols. “radix” typically refers only to systems with a fixed radix called the base. What is a type of Radix system? Roman Numerals

Measuring using numbers The Chinese have the current earliest claim to measuring quantities using numbers Ping-Ti Ho studied Yangshoa pottery(around 4500 BCE)which was used to make markings to measure pots, or volume. This actually might be among the earliest examples of written numbers, because there were symbols similar to Roman numerals

Measuring Time All civilizations needed a way to measure time…why?

Resources • An Introduction to the History of Mathematics by Howard Eves • Writing – Ancient History Encyclopedia (www. ancient. eu) • Quipus Knots Index, Inca Empire (incas. homestead. com/quipu) • Quipu of Secrets: A different kind of string theory (www. core 77. com) • A History Of Numerals (www. math. buffalo. edu) • Ishango Bone (www. sudaneseonline. com)