Earliest Methods used to solve Quadratic Equation

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

Algebra is a critical aspect of mathematics which provides the means to calculate unknown values. According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and functional situations. The understanding of these concepts by children will have an enormous bearing on their future mathematical capacity. However, conveying these algebraic concepts to children can be difficult due to the abstract symbolic nature of the math that will initially be foreign to the children. Furthermore, each child’s ability to recall learned numerical laws is vital to their proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic concepts is of significant importance to allow all

Among the many scholars working in the House of Wisdom, there was Al-Khawarizmi, known as the father of algebra. Born around 800 in Baghdad, al-Khwarizmi worked in the House of Wisdom as a scholar. Being involved in the center’s translation of ancient scientific knowledge helped him develop a unique knowledge of the accumulated wisdom of the world. His importance lies in his discoveries of mathematical knowledge which was later transferred to Arab and European scholars. His masterpiece, a book of clear explanations of what would become algebra, was his entire life’s work compiled into one collection of information. The word algebra comes from the Arabic word, al-jabr, which means “completion”. In his work, al-Khwarizmi explains the principles of solving linear and quadratic equations, the concept that an equation can be created to find the value of an unknown variable. Another crucial work of al-Khwarizmi’s was The Book on the Art of Reckoning of the Hindus, which introduced the numbering system used in the Islamic culture to the west. This is the numerical system that is still used today and offered many advantages over the existing Roman numerals. An

The Babylonians and Assyrians used a form of writing called cuneiform, one of the earliest known systems of writing, which was similar to the Egyptian hieroglyphics They used this picture writing system to record stories and historical events. Aside from literature achievements, they also made great leaps in science. They built bridges and irrigation system, recorded astronomical and meteorological observation, created the lunar calendar, and developed one of the first economic system. The lunar calendar was adopted by surrounding countries and their economic system helped keep Mesopotamia affluent.

Mayan Empire, led to development of pyramids, palaces, bridges, as well as a written language, art, and a calendar; This was due to advances in mathematics

Another great ruler was King Hammurabi of Babylon. He set up the Code of Hammurabi, which includes 300 sections of carefully organized codes that ruled the Babylonians. Hammurabi was the first example of a lawgiver. He provided one of the greatest written documents of his time: a stone column with a long series of legal judgments published with his name. Hammurabi even designed codes for the family life. He took care of the women and children in his society. He regulated marriage with care to secure a stable life for future generations. He combined both law and religious belief to create an ordered society. The Mesopotamians built on foundations laid by the Sumerians using their sexagesimal system. They had multiplication tables, exponents, tables for computing interest, and textbooks with problems for solution. They also developed systems of astrology and astronomy, and even created a lunar calendar.

Crafts included the scribes, artisans, artists, and poetic writers. Babylonians, as a whole, were intelligent people, good soldiers, keen traders, and very skillful craftsmen (Cottrell, Page 175). They were able to develop these skills because they enjoyed a Golden age of peace, prosperity, and freedom under the Babylonian Government, but more specifically Hammurabi’s Code. The code of laws put together by Hammurabi gave the Babylonians a very steady environment with an efficient taxing system, and personal affairs were took care of quite well (Ancient History Encyclopedia). As a supplement to the freedom, peace, and prosperity that the Hammurabi’s Code offered, the Babylonians were focused on their religion and worshipping many gods. They would have sacred buildings for certain gods or they were represented through objects. “Babylonia represents a religious and architectural element related to the Kassites cultural background which they integrated into the Babylonian architectural tradition” (Malko, Page 161). The religion that the Babylonians followed was also displayed through literature in poems, hymns, stories, and

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

The Abbasids were the first ones to study and translate important Greek and Indian mathematical book like Euclid's geometry text the Elements. They adopted a very Greek approach to mathematics of formulating theorems precisely and proving them formally in Euclid's ways.

The Maya were also great mathematicians. They are credited with having a more sophisticated number system than anyone else in the world at the time. They understood and used the value of zero at a time as early as 36 B.C.E. This is remarkable because not very many civilizations understood the concept of zero. They also had a number system with place values. It was a base-20 system. There is evidence of the Maya working with sums that go up to the millions (Mastin, Luke). As stated before, they also calculated the length of the year more accurately than the calculations used in the Gregorian calendar. These achievements are incredible, especially since they were isolated from the rest of the world until a while later.

A similarity between the ancient Egyptians and Greek is the use of what is now known as geometry. It is currently thought that the Egyptians had introduced the earliest fully-developed base-ten numeration system, this system was introduced around 2700 BCE, and was based. On people having ten fingers (story of mathematics). A famous document of the time was the Rhind Papyrus, created 1650 BC, and contained information and exercises to show the “Correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets.” (Washington.edu). The Egyptians had also approximated the area of

0 7 188 0.085 1,067 0.48 207 236 — 417 300 2.2 0.4 59.3 10.1 0.24 64.4 1,241 539 2.5 4,026 97,000 625 17 21 5 20 — 1,065 642 10,643 69

Through the development of writing, mathematics, metalworking, detailed law codes, and the wheel, Mesopotamians have shown their ingenuity with many different achievements. The world as we know it could not survive without writing. I am writing right now in order to do this paper, and the economy and so much of our lives is dependent on writing. Although it goes hand-in-hand with writing, mathematics is also a very important achievement of the Mesopotamians. Mesopotamians based their math system on sixty, but it is just as important and influential regardless. Metal work is another great achievement

The mathematics had been developed for four thousand years, and Muslim inherited mathematics from Egyptian, Mesopotamians, Sumerian and Babylonian. Greek geometry and Hindu arithmetic and algebra reached at an early stage in Muslim lands and were translated in centers such as Gondeshapur and Baghdad. Starting out at intellectual center of Islam, they soon criticizing those concepts and formulation by finding inaccurate and inconsistent information and adapt their own ideas. At the same period in Western Europe, they still use Roman numerals and abacus to calculate numbers. The Babylonian already had concept of bases sixty computation with place value numerals. Muslim then developed a decimal arithmetic based on place value and joint concept of zero. In the ninth century, Banu Musa brothers who were three gifted sons of Musa, Muhammad, Ahmad, and Hassan ibn Musa lived in Baghdad studied problems in constructing interrelated geometrical figures. Later the characteristic of those line, space of geometrical shape was given intense study and utilized sophisticated geometry in designing waterwheels, in improving farming equipment, in developing new type of weapon used at war. Another person who make significant contribution on mathematics is Muhammad ibn al-Khwarizmi, a Persian born in the eighth century. He was the first person who originated both terms “algebra”, and

The Egyptians used sums of unit fractions (a), supplemented by the fraction B, to express all other fractions. For example, the fraction E was the sum of the fractions 3 and *. Using this system, the Egyptians were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra. In geometry, the Egyptians calculated the correct areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. To find the area of a circle, the Egyptians used the square on U of the diameter of the circle, a value of about 3.16-close to the value of the ratio known as pi, which is about 3.14. The Babylonian system of numeration was quite different from the Egyptian system. In the Babylonian system-which, when using clay tablets, consisted of various wedge-shaped marks-a single wedge indicated 1 and an arrowlike wedge stood for 10 (see table). Numbers up through 59 were formed from these symbols through an additive process, as in Egyptian mathematics. The number 60, however, was represented by the same symbol as 1, and from this point on a positional symbol was used. That is, the value of one of the first 59 numerals depended henceforth on its position in the total numeral. For example, a numeral consisting of a symbol for 2 followed by one for 27 and ending in one for 10 stood for 2 × 602 + 27 × 60 + 10.