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Newton found science a hodgepodge of isolated facts and laws, capable of describing some phenomena, but predicting only a few. He left it with a unified system of laws that can be applied to an enormous range of physical phenomena, and that can be used to make exact predications. Newton published his works in two books, namely "Opticks" and "Principia."

Newton died in London on March 20, 1727 and was buried in Westminster Abbey, the first scientist to be accorded this honour. A review of an encyclopedia of science will reveal at least two to three times more references to Newton than any other individual scientist. An 18th century poem written by Alexander Pope about Sir Isaac Newton states it best: "Nature and Nature's laws lay hid in night: God said, Let Newton be! and all was light."

Unit 6

Student A

DARWIN'S FLOWERS

Most people are familiar with Charles Darwin's activities aboard the HMS Beagle and its famous journey to South America. He made some of his most important observations on the Galapagos Islands, where each of the 20 or so islands supported a single subspecies of finch perfectly adapted to feed in its unique environment. But few people know much about Darwin's experiments after he returned to England. Some of them focused on orchids.

As Darwin grew and studied several native orchid species, he realized that the intricate orchid shapes were adaptations that allowed the flowers to attract insects that would then carry pollen to nearby flowers. Each insect was perfectly shaped and designed to pollinate a single type of orchid, much like the beaks of the Galapagos finches were shaped to fill a particular niche. Take the Star of Bethlehem orchid (Angraecum sesquipedale), which stores nectar at the bottom of a tube up to 12 inches (30 centimeters) long. Darwin saw this design and predicted that a "matching" animal existed. Sure enough, in 1903, scientists discovered that the hawk moth sported a long proboscis, or nose, uniquely suited to reach the bottom of the orchid's nectar tube.

Darwin used the data he collected about orchids and their insect pollinators to reinforce his theory of natural selection. He argued that cross-pollination produced orchids more fit to survive than orchids produced by self-pollination, a form of inbreeding that reduces genetic diversity and, ultimately, survivability of a species. And so three years after he first described natural selection in "On the Origin of Species," Darwin bolstered the modern framework of evolution with a few flower experiments.

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Student B

THE FIRST VACCINATION

Until the stunning global eradication of smallpox in the late 20th century, smallpox posed a serious health problem. In the 18th century, the disease caused by the variola virus killed every tenth child born in Sweden and France. Catching smallpox and surviving the infection was the only known "cure." This led many people to inoculate themselves with fluid and pus from smallpox sores in the hopes of catching a mild case. Unfortunately, many people died from their dangerous self-inoculation attempts.

Edward Jenner, a British physician, set out to study smallpox and to develop a viable treatment. The genesis of his experiments was an observation that dairymaids living in his hometown often became infected with cowpox, a nonlethal disease similar to smallpox. Dairymaids who caught cowpox seemed to be protected from smallpox infection, so in 1796, Jenner decided to see if he could confer immunity to smallpox by infecting someone with cowpox on purpose. That someone was a young boy by the name of James Phipps. Jenner made cuts on Phipps' arms and then inserted some fluid from the cowpox sores of a local dairymaid named Sarah Nelmes. Phipps subsequently contracted cowpox and recovered. Forty-eight days later, Jenner exposed the boy to smallpox, only to find that the boy was immune.

Today, scientists know that cowpox viruses and smallpox viruses are so similar that the body's immune system can't distinguish them. In other words, the antibodies made to fight cowpox viruses will attack and kill smallpox viruses as if they were the same.

Unit 7

WHO CREATED THE QUADRATIC FORMULA?

x = [-b ± √(b2 - 4ac)]/2a

Through the use of non-linear equations, complex mathematical problems such as the trajectories of weapons fire can be solved ... but who created the quadratic formula that is used to solve the polynomial expressions that describe these types of phenomena. Man has been using complex mathematical principles for 1000s of years to solve its problems. The principles of mathematics were long applied primarily to pragmatic problems rather that being studied for their theoretical interest. From the years of about 2000 B.C. up until approximately 300 B.C., construction required solutions of this type.

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MATHEMATICAL PROBLEMS

Many problems related to calculating the area of buildings required to store items. There is evidence that engineers and construction workers in China, Egypt and Babylonia faced the same problems on a regular basis. They solved their problems by using lookup tables as a reference tool to reach the answers that they required for their building projects. In fact, most mathematicians up until the time of Euclid in 300 B.C. used either look-up tables to find the values that met their needs or they used a method called completing the square.

The Chinese were a bit quicker in calculating some of their own tables due to the rapid calculations that they could accomplish with the abacus. All of these lookup tables had the drawback of allowing error to creep into the tables in the copying process. All of these lookup tables would become obsolete in a few thousand years in the future by the quadratic formula. Little did the early engineers know that the men who created the quadratic formula would come from the parts of the world in which they lived.

WHO CREATED THE QUADRATIC FORMULA?

While most mathematicians before him had used lookup tables instead of trying to create a formula, Euclid was able to put forward a general equation that would calculate the square root of an area. This formula would give the length of sides required to provide the requested area. An extension of this general formula would include calculating the area and dimensions of a rectangular room or space.

While Euclid began the process, most of the further work done on the general form of the quadratic formula occurred between 700 A.D. and about 1100 A.D. in both India and in Islamic countries.

The precursor to what is known today as the quadratic formula, was derived by an Islamic mathematician named Mohammed bin Musa Al-Khwarismi. He derived the formula at about the same time as an Indian mathematician named Baskhara did.

Looking at how the formula was developed suggests that, to answer who created the quadratic formula you would have to cite both Baskhara from India and Al-Khwarismi from an area near Baghdad.

Both of these men realized that there were two answers to the quadratic formula, called "roots," but neither of them would allow for a negative root. They did allow both rational and irrational numbers to be used, however.

THE FORMULA MOVES TO EUROPE

This early version of the quadratic formula was carried to Europe in 1100 A.D. by a Jewish Mathematician / Astronomer from Barcelona named Abraham bar Hiyya. As the Renaissance raged on in Europe, interest and attention

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began to be focused on unique mathematical problems. Girolamo Cardano began to compile the work on the quadratic equation in 1545.

Cardano was one of the best algebraists of his time. He compiled the works of Al-Khwarismi and Euclidian geometry and blended them into a form that allowed for imaginary number. This inclusion also allowed for the existence of complex numbers.

Complex numbers are also called imaginary numbers and are primarily used for taking the square root of a negative number. This derivation and blending of mathematical knowledge resulted in the creation of the quadratic formula that we now recognize and use for calculating polynomial equations of powers of two.

THE IMPORTANCE OF THE FORMULA

The development of the quadratic formula and its solution took over 3000 years of work by mathematicians. Granted the work wasn’t done on a full time basis, but the formula was studied throughout this time and mathematicians did make significant progress over that period.

Looking back now and realizing how much time it took to come to an explicit mathematical derivation and solution to the quadratic formula, it is amazing that the ancient cultures were able to solve their problems without the aid of solutions like the formula.

Unit 8

A BRIEF HISTORY OF MAGIC SQUARES

Magic squares have a rich history dating to around 2200 B.C. A Chinese myth claimed that while the Chinese Emperor Yu was walking along the Yellow River, he noticed a tortoise with a unique diagram on its shell. The Emperor decided to call the unusual numerical pattern lo shu. The earliest magic square on record, however, appeared in the first-century book Da-Dai Liji.

Magic squares in China have been used in various areas of study, including astrology; divination; and the interpretation of philosophy, natural phenomena, and human behaviour. Magic squares also permeated other areas of Chinese culture. For example, Chinese porcelain plates on display in museums and private collections were decorated with Arabic inscriptions and magic squares.

Magic squares most likely traveled from China to India, then to the Arab countries. From the Arab countries, magic squares journeyed to Europe, then to Japan. Magic squares in India served multiple purposes other than the dissemination of mathematical knowledge. For example, Varahamihira used a fourth-order magic square to specify recipes for making perfumes in his book on seeing into the future, Brhatsamhita (ca. 550 A.D.). The oldest dated third-order magic square in India appeared in Vrnda's medical work Siddhayoga (ca. 900 A.D.), as a means to ease childbirth.

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Little is known about the beginning of research on magic squares in Islamic mathematics. Treatises in the ninth and tenth centuries revealed that the mathematical properties of magic squares were already developed among what were then Islamic Arabic-speaking nations. Further, history suggests that the introduction of magic squares was entirely mathematical rather than magical. The ancient Arabic designation for magic squares, wafq ala'dad, means "harmonious disposition of the numbers." Later, during the eleventh and twelfth centuries, Islamic mathematicians made a grand leap forward by proposing a series of simple rules to create magic squares. The thirteenth century witnessed a resurgence in magic squares, which became associated with magic and divination. This idea is illustrated in the following quotation by Camman, who speaks of the spiritual importance of magic squares:

"If magic squares were, in general, small models of the Universe, now they could be viewed as symbolic representations of Life in a process of constant flux, constantly being renewed through contact with a divine source at the center of the cosmos."

Considerable interest in magic squares was also evident in West Africa. Magic squares were interwoven throughout the culture of West Africa. The squares held particular spiritual importance and were inscribed on clothing, masks, and religious artifacts. They were even influential in the design and building of homes. In the early eighteenth century, Muhammad Ibn Muhammad, a well-known astronomer, mathematician, mystic, and astrologer in Muslim West Africa, took an interest in magic squares. In one of his manuscripts, he gave examples of, and explained how to construct, odd-order magic squares.

During the fifteenth century, the Byzantine writer Manuel Moschopoulos introduced magic squares in Europe, where, as in other cultures, magic squares were linked with divination, alchemy, and astrology. The first evidence of a magic square appearing in print in Europe was revealed in a famous engraving by the

German artist Albrecht Dürer. In 1514, Dürer incorporated a magic square into his copperplate engraving Melencolia I in the upper-right corner.

Chen Dawei of China launched the beginning of the study of magic squares in Japan with the import of his book Suan fa tong zog, published in 1592. Because magic squares were a popular topic, they were studied by most of the famous wasan, who were Japanese mathematics experts. In Japanese history, the oldest record of magic squares was evident in the book Kuchi-zusam, which described a 3-by-3 square.

During the seventeenth century, serious consideration was given to the study of magic squares. In 1687−1688, a French aristocrat, Antoine de la Loubere, studied the mathematical theory of constructing magic squares. In 1686, Adamas Kochansky extended magic squares to three dimensions. During the latter part of the nineteenth century, mathematicians applied the squares to problems in probability and analysis. Today, magic squares are studied in relation to factor analysis, combinatorial mathematics, matrices, modular arithmetic, and geometry. The magic, however, still remains in magic squares.

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Appendix 2: MINI-DICTIONARY

Unit 1

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THE NATIONAL TECHNICAL UNIVERSITY OF UKRAINE

"KYIV POLYTECHNIC INSTITUTE"

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Unit 2

IMPERIAL ENGLISH: THE LANGUAGE OF SCIENCE

Unit 3

THE MIND MACHINE?

Unit 4

Unit 5

THE PRINCIPAL ELEMENTS OF THE NATURE OF SCIENCE:

DISPELLING THE MYTHS

Unit 6

BEAUTY IN SCIENCE