ORIGINS OF MATHEMATICS

WHERE DID MATHEMATICS START????

As a math teacher students usually ask “ Who invented Math?” Or “Why was Math invented?”

Now we can express the development of mathematics and examples of the process in which the needs of society lead to the development of the math used in a specific time period. Once can stress how the needs of the eras change so does the complexity of the mathematical concepts.

THE BASIS OF COMPUTATION

o Who eats first, second, etc?

o What comes first, etc?

Dominance hierarchy

How many?

How much?

Quantity

Ordinals Cardinals

NEED

S F

OR

MATH

Counting Calculations Measurements

Lead to development of arithmetic facts

and geometry.

COUNTRIES WITH EVIDENCE OF MATH

India Egypt Mesopotamia China

All having the degree of antiquity, a pioneer in mathematical development, fertile lands, major rivers, strong centralized government and religious life.

COUNTING AND COMPUTING

Question is “ Was counting invented in one location and passed on? Or Did counting arise spontaneously around the world?”

Evidence show lots of similarities in the counting and tallying records. The following illustrations are examples of how counting in different artifacts and provide us with an idea of the similarities and possible purposes of the counting concept.

Ishango bone, oldest record of sequences of prime numbers or a six month lunar calendar. It is currently located at the Musee d’Histoire Naturelle in Brussels

Quipus (sometimes called talking knots) were recording devices used in the Inca Empire. A quipu usually consisted of colored, spun, and plied thread or strings from llama or alpaca hair, or cotton cords. Used to keep tracks of numerical records and it is said that some told their entire history.

Babylonian Tablet

Banking System

The double tally stick was used by the Bank of England. The amount was cut on a stick and the stick was then cut in half. The bank retained one piece called the foil and the other half was called the stock. It was the receipt issued by the bank. The holder was called a stockholder. When the holder returned the stock it was carefully checked against the foil. The owner would ten be paid. A written certificate was presented which later was referred to as the check.

Magic Square a type of permutation and seen throughout mathematical history. Earliest found in China and believed spread to Japan, India and the Middle East.

Sangrada Familia church in Barcelona, features a 4×4 magic square.The magic constant of the square is 33, the age of Jesus at the time of the Passion.

Counting on fingers was nearly universal among Indian tribes. oThe Zuni counted the second ten on their knuckles. oThe Bellacoola language shows evidence of subtraction.

16 = one man less four26= one man and two hands less four

SCOPE OF ANCIENT MATHEMATICS Number- ordinal vs. cardinal

Base- binary, ternary, decimal, sexagesimal

Arithmetic- addition, multiplication, etc

Geometry- area and volumes Number Theory- Pythagorean triples, primes,

etc

Algebra- solution of equation Dividing inheritances, computing logistic needs,

allocation of resources, determining volume and area

Reference:Allen, D.G. 2002. http://myutbtsc.blackboard.com/bbcswebdav/courses/CD_Math_5305

Ishango bone (n.d.). In Wikipedia. Retrieved August 29, 2011, from http://en.wikipedia.org/wiki/ishango_bone

Zuni. (n.d.) In Wikipedia. Retrieved August 29, 2011 from http://en.wikipedia.org/wiki/zuni_people