Milestones in the History of Mathematics - Assignment Example

1 Describe the system of rod numerals and its origin. Originally, the Ancient Chinese used the Rod numerals in doing computations. It was used before the invention of the abacus. Today, these can be seen in some Chinese markets in Hong Kong. Rod numerals or counting rods are short rods that are manipulated on top of a wooden table or counting board in doing the computations (Wikipedia). The way that a number is presented by counting rods is called the rod numeral system. The Chinese Rod Numeral System has only 9 numerals that can be represented in two ways depending on their position. It uses the decimal place value system for values greater than 10. The rods are placed in columns with the rightmost column representing the units, the next column representing the tens, then the nest representing the hundreds, and so on. Red rods represent the positive numbers while black rods represent the negative numbers. For example, the number 25 will have a representation using the rods where 5 will be placed in the rightmost column and 2 will be placed in the next column. An empty column represents zero (Chinese Rod Numerals (Counting Rods)). The rods were carried in a pouch and placed on a counting board which had compartments corresponding to the ones, tens, hundreds place and so on. Each compartment was split into two parts. The right part is for the heng (1 to 9) rods and the left part was for the tsangs (10 to 90) rods. Whole numbers are represented by combining these two types of rods. After the rods were placed in their rightful compartments, they were then manipulated by repositioning and reforming them as required by the arithmetic operation. 2.). Discuss the history of the symbol for zero. The first evidence of the existence of zero is from the Sumerian culture in Mesopotomia some 5,000 years ago (Wallin). This was in the form of cuneiform symbol for numbers where a slanted double wedge between two cuneiform symbols indicates an absence of a number or zero. Over time it became a positional notation form in the Babylonian Empire. From there the symbol arrived in India via the Greeks. The Ancient Greeks like the Babylonians did not a clear name for zero and the concept of zero still thrived as a positional notation form in their counting system. It was the Indians who began to understand zero as a symbol and as an idea. Brahmagupta, around 650 AD, was the first one who formalized arithmetic operations when using zero. He used dots under a number to indicate a zero. He was able to write in how many ways the zero can be achieved by the different arithmetic operations. Among his writings about zero, his conclusion on the division operation and zero was an error that was later proved and corrected much later by Isaac Newton. Zero reached Baghdad by 773 AD and would be developed in the Middle East by Arabian mathematicians who would base their numbers on the Indian system. Arab merchants brought the zero they found in India to the West. Mohammed ibn-Musa al-Khowarizmi was the first to formulate equations that equaled to zero or what we know now as algebra. By 879 AD, zero was written almost as we know it today, oval, but smaller compared to other numbers. The symbol we used was infused and its concept prospered. Zero took on a much more than a positional meaning and has played a vital part in the world of mathematics (Wallin). 3.) Discuss the value of pi with respect to the Chinese. The irrational number pi is a boggling number that can be computed up to an infinite number of decimal places. It is the ratio of the circumference of a circle to its diameter (Calculation of pi). The value of pi was first computed by independently by Archimedes and Ptolemy up to three and four decimal places respectively. For 1,450 years after that, there was no more greater accuracy on the value of pi achieved in the Western world. On the other side of the world, the Chinese had made great leaps in computing for the value of pi. Ancient mathematicians like calculated the value of pi by inscribing polygons inside the circles; by increasing the number of sides of the polygons and using the formula of the polygon's area that is very close to the circle to try and calculate for the value. Archimedes arrived at his value for pi using a 96-sided polygon. The Chinese found a value for pi following the same method and were said to be better than the previous mathematicians who originated the method. On the third century AD, Liu Hui first found a value for pi using a 192-sided polygon and then later improved the value using a 3,072-sided polygon. With this, Liu Hui was able to calculate 3.14159 for the value of pi. By this time, the Chinese were already ahead of the Greeks. In the 5th century AD, advanced values of pi emerged in China. Father and son mathematicians, Tsu Ch'ung-Chih and Tsu Keng-Chih, acquired an exact value for pi up to ten decimal places. Means of the applications were already lost, but records show that the circle used inscribing the polygon was 10 feet across. After nine hundred years later, Chao Yu Ch'in proved the value acquired by the Tsu father and son team by inscribing a 16,384 sided polygon to a circle. The Tsus' calculation of the pi had a lead for about 1,200 years thereafter. 4.) What is the "House of Wisdom" The House of Wisdom, located in the city of Baghdad, Iraq, was an institution for education and research founded by caliph al-Ma'mun. In this institution, talented scholars like Mohammed ibn Musa al-Khwarizmi and the Bana Musa brothers were recruited and sustained. It was a place where scholar-translators tried to translate into Arabic the important philosophical and scientific works of the ancient world, especially from Greece and Egypt. Various scholars of different religions from around the world gathered in the institution for the study of humanities and sciences, including mathematics, astronomy, medicine, zoology, chemistry, geography and as well as astrology and alchemy. The House of Wisdom was the greatest institution of education the medieval world has ever seen. Without the translations and researches that took place there, a great deal of the Greek, Latin and Egyptian knowledge would have been unknown to the world. The scholars gathered the greatest collection of knowledge in the world and built on it through their own discoveries (Whitaker 2004). 5.) Who is Omar Khayyam. Discuss his accomplishments. Omar Khayyam was a great Muslim mathematician. He showed how to express roots of cubic equations by line segments obtained by intersecting conic sections. Khayyam was an outstanding poet, mathematician, and astronomer. His work on algebra was known throughout Europe in the Middle Ages, and he also contributed to a calendar reform. Khayyam refers in his algebra book to Pascal's triangle. The algebra of Khayyam is geometrical, solving linear and quadratic equations by methods appearing in Euclid's Elements. Khayyam also gave important results on ratios giving a new definition and extending Euclid's work to include the multiplication of ratios. He poses the question of whether a ratio can be regarded as a number but leaves the question unanswered. Although Khayyam is best known today for his poetry and his contributions to mathematics were enormous. (Wikipedia) Works Cited Boyer, Carl B. and Merzbach, Uta C. A History of Mathematics. 2nd Ed. New York: John Wiley and Sons, Inc. 1991. "The Chinese Rod Numerals(Counting Rods)". Chinese History Timeline. Available at http://www.math.sfu.ca/histmath/China/Beginning/Rod.html Wikipedia-the free encyclodia. "Counting rods." Wikimedia. Available at http://en.wikipedia.org/wiki/Counting_rods Wallin N. "How was Zero Discovered". YaleGlobalOnline. Available at http://yaleglobal.yale.edu/about/zero.jsp "Calculation of pi" Available at http://www.chinapage.com/math/s9/pi.html Whitaker, B., 2004 23 September. "Centuries in the House of Wisdom." Guardian Unlimited. Available at http://www.guardian.co.uk/life/feature/story/0,13026,1310285,00.html Wikipedia, the free Encyclopedia. "Omar Khayyam." Available at http://en.wikipedia.org/wiki/Omar_Khayyam Read More