Subject Topic Create a written narrative of the evolution of the topic. Include significant contributions from cultures and individuals. Describe important current applications of the topic that would be of particular interest for students.

Number Systems Complex Numbers The earliest reference to complex numbers is from Hero of Alexandria’s work Stereometrica in the 1st century AD, where he contemplates the volume of a frustum of a pyramid.

The proper study first came about in the 16th century when algebraic answers for roots of cubics and quartics were revealed by Italian mathematicians Tartaglia and Cardano. For example, Tartaglia’s formula for a cubic equation x^3=x gives the solution as 1/√3 ((√(-1))^(1/3)+1/(√(-1))^(1/3) ).
*…show more content…*

For example, the treatment of resistors, capacitors, and inductors are unified by combining them in a single complex number called the impedance, which is the measure of the opposition that a circuit presents to a current when a certain voltage is applied.

Algebra The Quadratic Formula Early methods for solving quadratic equations were purely geometric.

Babylonian tablets contained problems which could be reduced to solving quadratic equations. The Egyptian Berlin Papyrus (2050-1650 BC) contains the solution to a two-term quadratic equation.

Euclid (300 BC) used geometric methods to solve quadratic equations in his book Elements.

In Arithmetica, Diophantus (250 BC) solved quadratic equations with methods which more closely resembled algebra. However, his solution only gave one root, even when both roots are positive.

Brahmagupta (597-668 AD) explicitly described the quadratic formula in words instead of symbols in Brahmasphutasiddhanta in 628 AD. His solution of ax^2+bx=c equated to the formula: x=(√(4ac+b^2 )-b)/2a

In the 9th century, Persian mathematician al-Khwarizmi solved quadratic equations algebraically.

The quadratic formula which covered all cases was first described by Simon Stevin in 1594.

The quadratic formula that we know today was published by Rene Descartes in La Geometrie in 1637.

The first appearance of the general solution in modern mathematical literature was in an 1896 paper by Henry

Related

- Better Essays
## Pythagoras 's Influence On The Founding Of Calculus

- 1707 Words
- 7 Pages

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

- 1707 Words
- 7 Pages

Better Essays - Best Essays
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

- 1720 Words
- 7 Pages

Best Essays - Satisfactory Essays
## Research Paper On Hipparchus

- 117 Words
- 1 Pages

Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the

- 117 Words
- 1 Pages

Satisfactory Essays - Decent Essays
## The Creation Of Calculus, Gottfried Leibniz And Isaac Newton

- 768 Words
- 4 Pages

Then the Indians added their own discoveries with the astronomer Aryabhata expressing an astronomical problem in the form of a differential equation and Parameshvara of Kerala developing an early version of the mean value theorem in the fifteen hundreds.

- 768 Words
- 4 Pages

Decent Essays - Decent Essays
## History of Calculus Essay

- 1186 Words
- 5 Pages

In Europe, the second half of the 17th century was a time of major innovation. Calculus provided a new opportunity in mathematical physics to solve long-standing problems. Several mathematicians contributed to these breakthroughs, notably John Wallis and Isaac Barrow. James Gregory proved a special case of the second fundamental theorem of calculus in AD 1668.

- 1186 Words
- 5 Pages

Decent Essays - Satisfactory Essays
## What Role Does Diophantus Play In The Evolution Of Algebra

- 427 Words
- 2 Pages

Algebra is the basis of all math and its advancement took place in three major steps. The first stage of algebra is rhetorical algebra dating back to before 275 BCE. Rhetorical algebra was a form of algebra that contained no symbols so to them +,-, and*, did not exist. It was usually explained orally or written on scribes. They were able to do things such as find squad and cubed roots, solve linear equations, and explain fractions. As well as recognizing irrational numbers and identifying that quadratics had two answers. The next phase in algebra’s evolution was Syncopated math. This was most popularly used between 275 BCE - 1600. Diophantus played a crucial role in this stage by being the first to develop algebraic notations and abbreviations.

- 427 Words
- 2 Pages

Satisfactory Essays - Satisfactory Essays
## Was Galileo Only Facilitated In The Renaissance

- 136 Words
- 1 Pages

The mathematic that not only facilitated in the renaissance but provide the key a new science of nature from Galileo.

- 136 Words
- 1 Pages

Satisfactory Essays - Decent Essays
## John Wallis

- 3283 Words
- 14 Pages

Wallis’ next major work was not published until 1685. His Treatise on Algebra contains an important study of equations that he applied to the properties of conoids, which are almost shaped just like a cone (Westfall, 1995). “In this work, Walls accepts negative and complex roots. He shows that a3-7a=6 has exactly three roots and that they are all real” (O'Connor & Robertson, 2002). Wallis also applied algebraic techniques rather than the traditional geometry. Using these new algebraic techniques, he contributed substantially to solving problems involving infinitesimals which are quantities that are almost incalculably small (Westfall, 1995). In this work, Wallis critiqued Descartes’ Rule of Signs stating correctly that “the rule which determines the number of positive and the number of negative roots by inspection, is only valid if all the roots of the equation are real (O'Connor & Robertson, 2002) which became a highly controversial subject.

- 3283 Words
- 14 Pages

Decent Essays - Decent Essays
The Pythagoreans were a group of people who followed Pythagoras in 530 B.C. They are well known for their work in mathematics and for numerology, they tried to prove that everything is made up of numbers. The Pythagoreans tried to solve the problem of Anaximander by the theory of the Limit which was the flaw in Anaximander’s theory.

- 1131 Words
- 5 Pages

Decent Essays - Better Essays
## Unknown Side Of The Pythagorean Triangles

- 53 Words
- 1 Pages

Most known for the Pythagorean Theorem after finding the equation a2b2c2 and the hypotenuse to find unknown sides of a

- 53 Words
- 1 Pages

Better Essays - Better Essays
## Earliest Civilization is the Region of Mesopotamia Because of Their Language of Cuneiform

- 1431 Words
- 6 Pages

The Babylonians used pre-calculated tables to assist with arithmetic. Perhaps the most amazing aspect of the Babylonian's calculating skills was their construction of tables to aid calculation. Two tablets found at Senkerah on the Euphrates in 1854 date from 2000 BC. They give squares of the numbers up to 59 and cubes of the numbers up to 32. Most frequently Babylonians utilized tables of squares and cubes to simplify multiplication. The concept of reciprocals was also first introduced by the Babylonians. Because they did not have a method for long division, they were able to recognize that using their sexiagesimal system of numbers, numbers with two, three, and five, had finite factors of which tables have been found. For numbers not containing one of the finite factors, the Babylonians used approximation reciprocals. The pre-calculated tables method is also how the Babylonians incorporated algebra in their number system. They were the first people to use the quadratic equation, though not in its exact form. They used the form x2+bx=c which, when solved, can be interpreted as x=-b/2-√(b/2)+c which more closely resembles the modern quadratic equation. Using their arithmetic tables of squares, the Babylonians were able to interpret them in reverse to find square roots. Because everything was a real problem, they always used the positive root when solving. Most commonly squares were used for finding

- 1431 Words
- 6 Pages

Better Essays - Good Essays
## African Mathematics and Mathematicians

- 607 Words
- 2 Pages

African mathematics has been around for thousands of years. Africa is known to be the country that takes part in the earliest use of mathematics that includes both measuring and calculating. Africa is also one of the places where both basic and advanced mathematics were originated. Much of the math that is used by human beings today was used a long time ago in Africa. Math such as algebra and geometry that are used by us today, were used by the Africans back then. African math was then transferred to other countries through migration out of Africa and invasions of Africa by Europe and Asia. Over 3,500 years have passed since the origination of African mathematic. Branching from that has been many inventions that have made improvements in the way we as Americans see math. Inventions such as the Ishango tally stick and the Lembambo tally stick, which were used as one of the first counting tools. When found, the bone only had 29 markings engraved into the Lebombo bone. This bone is about 35,000 years old, and is said to probably have been used to keep track of lunar or menstrual cycles, or could have been used for something as simple as just a measuring stick. The Lebombo bone is actually the fibula bone of a baboon and was used as a device associated with the moon, time, and math.

- 607 Words
- 2 Pages

Good Essays - Best Essays
## What Makes Fermat's Last Theorem

- 2224 Words
- 9 Pages
- 10 Works Cited

The year is 1637. Pierre de Fermat sits in his library, huddled over a copy of Arithmetica written by the Greek mathematician Diaphantus in the third century A. D. Turning the page, Fermat comes across the Pythagorean equation:

- 2224 Words
- 9 Pages
- 10 Works Cited

Best Essays - Decent Essays
## Pythagoras Is A Bit Of A Mysterious Figure

- 741 Words
- 3 Pages

Pythagoras’ biggest mathematical work was the Pythagorean Theorem. This theorem had already been discovered by the Babylonians, but Pythagoras was the first to prove that it was correct. This theorem relates to the three sides of a right triangle. It states that the square of a hypotenuse is equal to the sum of the squares of the other sides. The formula for this is “a^2+b^2=c^2.” In this formula a and b = the two shorter sides of the right triangle. C is equal to the side that is opposite of the right angle, or the hypotenuse. Pythagoras was also responsible for introducing more rigorous

- 741 Words
- 3 Pages

Decent Essays - Better Essays
## Number System in Mathematics

- 2774 Words
- 12 Pages

In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra.

- 2774 Words
- 12 Pages

Better Essays