MODULE 1
Unit 1.1
Read and translate the text using the dictionary:
(Part 1)
The history of mathematics cannot with certainty be traced back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into three periods, the distinctions between which are tolerably well marked. The first period is that of the history of mathematics under Greek influence, the second is that of the mathematics of the Middle Ages and the Renaissance, the third is that of modern mathematics.
The word "mathematics" comes from the Greek μάθημα (máthema) which means "science, knowledge, or learning"; μαθηματικός (mathematikós) means "fond of learning". Today, the term refers to a specific body of knowledge – the deductive study of quantity, structure, space and change.
While almost all cultures use basic mathematics (counting and measuring), new mathematical developments have been reported in relatively few cultures and ages. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments come to light only in a few locales. The most ancient mathematical texts come from ancient Egypt in the Middle Kingdom period of about 1300-1200 B.C., Mesopotamia in 1800 B.C., and ancient India circa 800-500 B.C. All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical developments after basic arithmetic and geometry.
Probably the earliest way of keeping a count was by some simple tally method, employing the principle of one-to-one correspondence. In keeping a count on sheep, for example, one finger per sheep could be turned under. Counts could also be maintained by making collections of pebbles or sticks, by making scratches in the dirt or on a stone, by cutting notches in a piece of wood, or by tying knots in a string. As the way of counting, people should learn how to mark the numbers. Each nation, therefore, used its peculiar marking of numbers.
Ancient Greece and the Hellenistic cultures of Egypt, Mesopotamia and the city of Syracuse increased mathematical knowledge. The first true evidence of mathematical activity in China can be found in numeration symbols on oracle bones, dated to about 1300 B.C., while the Han Dynasty in ancient China contributed the Sea Island Manual and The Nine Chapters on the Mathematical Art from the 2nd century B.C. to the 2nd century A.D. Hindu mathematicians from the 5th century and Islamic mathematicians from the 9th century made major contributions to mathematics.
One striking feature about the history of ancient and medieval mathematics is that bursts of mathematical development tended to be followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an ever increasing pace, and this continues to the present day.
(Part 2)
Long before the earliest written records, there are drawings that indicate knowledge of mathematics and of measurement of time based on the stars. For example, paleontologists have discovered ochre rocks in a cave in South Africa adorned with scratched geometric patterns dating back to 70,000 BC. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 BC and 20,000 BC, indicate early attempts to quantify time. Evidence exists that early hunters had the concepts of 'one', 'two', and 'many', as well as the idea of 'none' or 'zero', when considering herds of animals.
The Ishango Bone, found in the area of the headwaters of the Nile River (northeastern Congo), dates as early as 20,000 B.C. One common interpretation is that the bone is the earliest known demonstration of sequences of prime numbers and Ancient Egyptian multiplication. Predynastic Egyptians of the 5th millennium B.C. pictorially represented geometric spatial designs. It has been claimed that Megalithic monuments from as early as the 5th millennium B.C. in Egypt, and then subsequently England and Scotland from the 3rd millennium B.C., incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design, as well as a possible understanding of the measurement of time based on the movement of the stars. From circa 3100 B.C., Egyptians introduced the earliest known decimal system, allowing indefinite counting by way of introducing new symbols. Circa 2600 B.C., Egypt's massive construction techniques represent not only precision surveying but also suggest knowledge of the golden ratio.
The earliest known mathematics in ancient India dates back to circa 3000-2600 B.C. in the Indus Valley Civilization of North India and Pakistan, which developed a system of uniform weights and measures that used decimal fractions, a surprisingly advanced brick technology which utilised ratios, streets laid out in perfect right angles, and a number of geometrical shapes and designs, including cuboids, barrels, cones, cylinders, and drawings of concentric and intersecting circles and triangles. Mathematical instruments discovered include an accurate decimal ruler with small and precise subdivisions, a shell instrument that served as a compass to measure angles on plane surfaces or in horizon in multiples of 40–360 degrees, a shell instrument used to measure 8-12 whole sections of the horizon and sky, and an instrument for measuring the positions of stars for navigational purposes. The Indus script has not yet been deciphered. Archeological evidence has led some historians to believe that this civilization used a base-8 numeral system and possessed knowledge of the ratio of the length of the circumference of the circle to its diameter, thus a value of π.
Notes:
Hellenistic cultures – ancient Greek history, language, culture or ethical system, especially from the late 8th century B.C. to the death of Alexander the Great (323 B.C.)
Megalithic (monument) – a huge stone, especially one used in Neolithic monuments or in the construction work of ancient people
locale – local specific area (certain specific national or cultural medium in which the given program or system is functioning)