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Write my can be reached at For those students in its for possession school, and even some younger, we are familiar with the quadratic formula, "the opposite of b, plus or minus the square root of b squared minus 4ac, all divided by 2a". Where did this formula come from? Why did older civilizations need to solve equations of this form in the first place? The following article, taken from h2g2, explores the origins of precal homework help famous formula.

The types of research methods for thesis, or derivation, of a mathematical idea is usually as logical, deducible and precal homework help as possible. This brings about the common notion that its historical development is similarly as continuous, logical and rectilinear: one mathematician picking up an idea where another mathematician left it. Using the quadratic formula as an example, it will essay on holiday which you like the most shown that the historical development of mathematics is not at all rectilinear.

Instead, parallel developments, interconnections and confluences can be found, which - to complicate precal homework help stuff even further - are also interrelated apa dissertation citation proquest social, cultural, political and religious it personal statement. The so-called quadratic formula has been derived sample awa essays the course of a few millennia to its current form, which is taught to most of us in school.

This Entry will strictly concentrate on the historical development of the quadratic formula. Some mathematical background may be of use to fully understand the described development, however the maths used in this Entry will be kept at a necessary minimum. Egyptian, Chinese and Babylonian engineers were really smart people - they knew how the area of a square scales with the length of its side. They precal homework help that it's possible to store nine times more bales of hay if the side of the square loft is tripled.

They also found out how to calculate the area of more complex designs like rectangles and T-shapes and so on. However, they didn't know how to calculate the sides of the shapes - the length of the sides, starting from a given area - which was often what their clients really needed. And so, this is the original problem: a certain shape 1 must be scaled with a total area, precal homework help in the end what's needed is lengths of the sides, or walls to make a working floor plan. The first aspect that biology degree dissertation led to the quadratic equation was the recognition that it is connected to a very pragmatic problem, which in its turn demanded a precal homework help and dirty' solution.

We have to note, in this context, that Egyptian precal homework help did not know equations and numbers like we do nowadays; it is instead descriptive, rhetorical and sometimes very hard to follow. It is known that the Egyptian wisemen precal homework help, scribes and priests were aware of this shortcoming - but they came up with a way to circumvent open access dissertations and theses (pqdt open) problem: instead of learning an operation, or a formula that could calculate precal homework help sides from the area, they precal homework help the area for all possible sides and shapes clivage gauche droite dissertation squares precal homework help rectangles and made a look-up table.

This method works much like we learn the multiplication tables by heart in school instead of doing the operation proper. So, if someone wanted a loft with a certain shape and a certain capacity precal homework help store bales of papyrus, the engineer would go to his table and find the most fitting design. The engineers did not have time to calculate all shapes and sides to michelle obama thesis pdf their own table. Instead, the table they precal homework help was a reproduction of a master look-up table.

The copyists did not know if the stuff they were copying made sense or not as they didn't know anything about maths. So, obviously, sometimes errors crept in, and copies of the copies were known to be less trustworthy 2. These tables still exist, and it is possible to see where errors crept in during the copying of precal homework help documents. The Egyptian method worked fine, but a more general solution - without the need for tables - seemed desirable. That's where the Babylonian geeks come into play. Babylonian maths had a big advantage over the precal homework help used in Egypt, namely they used a precal homework help that is pretty much like the one we use today, albeit on a hexagesimal basis, or base Addition and multiplication were a lot easier to perform with this system, so the engineers around BC could always double-check the values in their tables.

By BC they found a more general experience in college essay called 'completing the square' to solve generic problems involving areas. There precal homework help no indications that these people used a specific mathematical procedure to find out the solutions, so probably some educated guessing was involved. Around the same time, or a bit later, this method also appears in Chinese documents. The Chinese, like the Egyptians, also did not use a numeric system, but a double checking of essays on effective leadership mathematical operations was made astonishingly easy by argumentative essay format ap lang widespread use of the abacus.

The first attempts to find a more general formula to solve quadratic equations can be tracked back to geometry and trigonometry top-bananas Pythagoras BC in Croton, Italy and Euclid BC in Alexandria, Egyptwho used a strictly geometric approach, and found a general procedure to solve the quadratic equation. Pythagoras noted that the ratios between the area of a square and the respective simone lachmayer dissertation of the side - the square root - were not always integer, precal homework help he refused to allow for proportions other than rational.

Euclid went even further and found out that this proportion might also not be rational. He concluded that irrational numbers exist. Euclid's opus Elements covered more or less all transition words for writing a paper mathematics needed for precal homework help applications from a theoretical point of view. However, it didn't use the same notation with formulas and how to write history essays like we use precal homework help. For that reason it was not possible to calculate the square root of any number by handhelp on essay writing order to precal homework help a good approximation for the exact value of the root, which is what the architects and engineers were after.

Because all theoretically relevant at least maths seemed to be complete 3 but otherwise useless, the many wars occurring in Europe, and also the early Middle Ages turned the mathematical world in Europe silent until the 13th Century. In this period mathematics also suffered a big shift, going from a pragmatic science to a more mystical, philosophical discipline.

Hindu mathematics has used the decimal system the one we precal homework help at least since Precal homework help. One of the most important influences on Hindu mathematics was that it was widely used in commerce. The average Hindu merchant was pretty fast in simple maths. If essay on trees are life had a debt the numbers would be negative, if someone had a credit the numbers precal homework help be online assignment. Also, if someone had neither credit, nor debt, the numbers would add up to zero. Zero is an important number in the history of mathematics, and its relatively late precal homework help is due to essay in urdu dehshat gardi fact that many cultures had difficulty of conceiving 'nothing'.

The concept of 'nothing', like in 'shunya', the void, or the concept of 'equilibrium', was already anchored in Hindu culture. Around AD the general solution for the quadratic equation, this time using numbers, was devised by a Hindu mathematician called Brahmagupta, who, among other things, used irrational numbers; he also precal homework help two roots in the solution. The final, complete solution as we know it today came around AD, by another Hindu mathematician called Baskhara 4. Baskhara was the first to recognise that any positive number has two square roots. The algebra precal homework help by him was entirely rhetorical, and he rejected negative solutions.

With the Renaissance in Europe, academic attention came back to original precal homework help problems. By Girolamo Cardano, who was a typical Renaissance scientist ie, interested in alchemyoccultism and suchlikeand one of the best algebraists of his time, compiled the works related to the quadratic equations - that is, he blended Al-Khwarismi's solution with the Euclidean geometry. He was possibly not the first or only one, but the most precal homework help. In his mainly rhetorical works he allows for the existence of complex, or imaginary numbers - that is, roots of negative numbers. Get Directions. Math Enrichment and Accelerated Programs in Pflugerville. Did you know Mathnasium offers enrichment programs for students?

Mathnasium is where students in Precal homework help Success in the Spring Semester. The Spring Semester is underway and classrooms are gearing up Toggle navigation. Grade Level school year --None-- K 1 2 3 4 5 6 7 8 9 10 11 How did you hear about us? Consent to receive precal homework help text messages and calls is not required to purchase other goods or services.

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