Early Number Systems PDF
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This document presents a lesson on early number systems, tracing their evolution from tallying and notches to the development of hieroglyphic systems and later Greek alphabetic numerals. It details methods like tallying with stones or shells, and the use of knots and cords (quipus) for numerical representations. The material highlights significant milestones in the history of number systems and their practical applications.
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Early Numbers System Mathematics Root Term From the Greek wordmathemata ormathema which means “subject of instructions” or “ to learn/ study”. Began classical Greece during the years 600 to 300 BC. Mathematics Definitions The group of sciences dealing with quantities, magnitu...
Early Numbers System Mathematics Root Term From the Greek wordmathemata ormathema which means “subject of instructions” or “ to learn/ study”. Began classical Greece during the years 600 to 300 BC. Mathematics Definitions The group of sciences dealing with quantities, magnitudes, and forms, and their relationships, attributes; by the use of numbers and symbols. Early Number System And Symbols By The Egyptian NUMBER The fundamental abstraction. Tallying Term tally comes from the french verb tailler means “to cut”. The idea in tallying is to match the collection to be counted with some easily employed set of object. ---- In that case of early ancestors these were shells or stones. Sheep set instance could be counted by driving them one by one through a narrow passage while dropping a pebble for each. As the rock was gathered in for the night, the pebbles were moved from one pile to another until all the sheep had been accounted for. NOTCHES AS TALLY MARKS Bone artifacts bearing incased markings seem to indicate that people of old stone age had devised a system of tallying by groups. Example: Shinbone From a young wolf found in Czechoslovakia in 1937; about 7 inches long and have 55 deeply cut notches. Notches bones were interpreted as hunting tallies & incisions were thought represent kills. ISHANGO BONES Discovered in 1960 at Ishango. It is reported to be between six and nine thousand years old. A method of tallying has been used in many different times & places involves the notches stick. The acceptance of tally sticks as a promissory notes or bills of exchange reached its highest level of development in the British exchequer tallies, which formed an essential part of the government records from the twelfths century onward. KNOTS AS NUMBERS Inthe new world, the number string is best illustrated by the knotted cords called QUIPUS. QUIPUS made of up of a thick main cord a crossbar of which where attached cord of different lengths and colors. represents numerical value used: figure-eight knot standing for 1. long knot denoting one of the values 2 through 9. single knot also indicating 1. NUMBER RECORDING OF EGYPTIANS The History of HERODOTUS HERODOTUS (Circa 485-430 B.C) - born at Halicarnassus. - He was involve in political troubles in his home city and force to be exile to the island of Jamos and then to Athens. The three principle journey of Herodotus: 1.perhaps as a merchant. 2.collecting materials 3. recording his impressions. In the black sea > Herodotus sailed all the way up the west coast to the Greek community at the mouth of the Dnieper river now Ukraine. In Egypt > He ascend the Nile river from its delta to somewhere near as one, exploring the pyramids along the way. In thurium > He seems to have passed the last year of his life involve almost entirely on finishing “ the history of Herodotus” HIEROGLYPHIC REPRESENTATION OF THE PAST As early as 3500 B.C. the Egyptians had a fully developed number system that would allow counting to continue in definitely with only the introduction from time to time of a new symbol. This hieroglyphic system of writing is a picture scripts in which each character represented a concrete object. The significance of which may still be recognizable in any cases. HIEROGLYPHIC SYMBOLS Egyptian Hieratic Numeration The Egyptian invented papyrus. Papyrus was made by cutting lengthwise strip of the stem of the reed like papyrus plant which is abundant in the Nile delta marshes. They wrote a brush like pen and ink made up colored earth or charcoal that can mixed with gum and water. The symbols were written in a cursive or free running hand so that at first sight their forms bore little resemblance to the orl hieroglyphics is called hieratic (sacred). Hieratic symbols The Greek Alphabetic Numeral System Around the 5th century B.C, the Greek of lonia also developed a ciphered numerical system, but with a more extensive set of symbols to be memorized. Greek Alphabetic System Example: THANK YOU & GODBLESS!
