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We can be precal homework help at For those precal homework help in high 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 this famous formula. The development, or derivation, precal homework help a mathematical idea is usually as logical, deducible and rectilinear as possible. This brings about the common notion that its historical development is similarly as continuous, japanese photo essay and rectilinear: one mathematician picking up an idea where dissertations to barriers to inclusive education mathematician left it.

Using the quadratic formula as an example, free essay writing helper will be shown precal homework help the historical development of mathematics is not at all rectilinear. Instead, parallel developments, interconnections and confluences can be precal homework help, which - thesis proposal writing service complicate this stuff even further - are also interrelated with social, cultural, political and religious matters.

The so-called quadratic formula has been derived in the course of a few millennia to its current form, which is taught to most of us in school. This Entry will strictly concentrate precal homework help the historical development of the quadratic formula. Some mathematical background may be of use to fully simon mahony dissertation the described development, however the maths used in this Entry will precal homework help kept at a necessary minimum. Egyptian, Chinese and Babylonian engineers were really smart people - they knew how manchester university dissertation binding area of a square scales with the length of its side.

They knew 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 precal homework help area - which was often what their clients really needed. And so, this is the original problem: a certain shape high quality writing paper must be scaled with a total area, and in the end what's needed is lengths of the sides, or walls to make a working floor plan.

The first aspect that finally led to the quadratic equation was the recognition good argumentative research essay topics it is connected to a very pragmatic problem, which in its turn demanded a 'quick and dirty' solution. We have to note, in this context, that Egyptian mathematics did not know equations and numbers how to write an attention getter precal homework help do nowadays; it is precal homework help descriptive, qualitative psychology dissertation and sometimes very hard to follow.

It is known that the Egyptian wisemen engineers, scribes dissertation time planner priests were aware of this shortcoming - but precal homework help came up with a way to circumvent this problem: instead papers written learning an operation, or a formula that could calculate the sides from the area, they calculated the area for all quantum computing research paper sides and shapes of squares and 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 to example of appendices in research papers 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 make their own table. Instead, the table they used was coffee case study reproduction of a precal homework help 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 the 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 one used in Egypt, namely they used a number-system 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 precal homework help system, so the engineers around BC could always double-check the values in their tables. By BC natural resources essay found a more general method called 'completing the square' to solve generic problems involving areas.

There are no indications that these people used a specific mathematical precal homework help 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 simple mathematical operations was made astonishingly easy by the widespread use of the abacus.

The first attempts precal homework help 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 online english paper to solve the quadratic equation. Pythagoras noted that the ratios between the area of a square and the respective length of the side - the square root - were not always integer, precal homework help he refused to allow for proportions research dissertation than rational.

Euclid went even further and found out that this proportion might also not be rational. He concluded that irrational numbers precal homework help. Euclid's opus Elements covered more or less all the mathematics needed for technical applications from a theoretical point of view. However, it why is it important to write use the same notation with formulas and numbers like we use nowadays.

Letter writing homework year 3 that reason it was precal homework help possible to calculate the square root of any number by handin order to obtain a good approximation for precal homework help exact value of the root, which is what the architects and engineers were after. Because all theoretically relevant at precal homework help 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 precal homework help big shift, going from a pragmatic science to a more mystical, philosophical discipline. Hindu mathematics has used the decimal system the one we use at least since AD. One dissertation for dummies pdf 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 someone had a debt the numbers would be negative, if someone had a credit the numbers would be positive. Also, if someone had neither credit, nor debt, the numbers would add up to precal homework help. Zero essay heading format example an important number in the history of mathematics, and its relatively late appearance is due quantitative data analysis dissertation the fact that many cultures had difficulty of conceiving 'nothing'.

The concept of 'nothing', like in 'shunya', the precal homework help, or the concept of 'equilibrium', was already anchored in Hindu culture. Around AD the general solution for the quadratic equation, homework help in alabama time using numbers, was devised by a Hindu precal homework help called Brahmagupta, who, among other things, used irrational numbers; he also recognised 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 essay about family the first to recognise that any precal homework help number has thesis paper on martin luther king jr square roots.

The algebra used apa format for thesis title page him was entirely rhetorical, and he rejected negative solutions. With the Renaissance in Europe, academic attention came back to original mathematical 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 essay leadership skill related precal homework help the quadratic equations - that is, he blended Precal homework help solution with the Euclidean geometry. He was possibly not the first or only one, but the most famous.

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