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Free Cubic Equations Essays and Papers

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    Cubic Equations

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    Cubic equations were known since ancient times, even from the Babylonians. However they did not know how to solve all cubic equations. There are many mathematicians that attempted to solve this “impossible equation”. Scipione del Ferro in the 16th century, made progress on the cubic by figuring out how to solve a 3rd degree equation that lacks a 2nd degree. He passes the solution onto his student, Fiore, right on his deathbed. In 1535 Niccolò Tartaglia figures out how to solve x3+px2=q and later

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    Solving Cubic Equations Numerically Many cubic equations can be solved algebraically; however, many cannot, which means we have to give approximate answers. Graphs, like the one seen below, cannot be solved algebraically and have to be solved some other way. Here we can see a zoomed in version of the graph which clearly shows the 3 roots that we want to find, the places where the red line cuts the x-axis, but none are exact values, making the equation of the cubic almost impossible to

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    of the Cubic Equation The history of any discipline is full of interesting stories and sidelines; however, the development of the formulas to solve cubic equations must be one of the most exciting within the math world. Whereas the method for quadratic equations has existed since the time of the Babylonians, a general solution for all cubic equations eluded mathematicians until the 1500s. Several individuals contributed different parts of the picture (formulas for various types of cubics) until

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    Srinivasa Ramanujan

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    1898. At the Town High School, Ramanujan did well in all his school subjects and showed himself as a talented student. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series. Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic. It was in the Town High School that Ramanujan came across a mathematics book by G. S. Carr called Synopsis of Elementary Results in Pure Mathematics. Ramanujan used this to teach

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    history of algebra

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    17th century. The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes (“Letters”). Although not very important to the development of algebra, Archimedes (212BC – 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove

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    Math History

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    proved to be the foundation of more high powered mathematical development. Number problems such as that of the Pythagorean triples (a,b,c) with a2+b2 = c2 were studied from at least 1700 BC. Systems of linear equations were studied in the context of solving number problems. Quadratic equations were also studied and these examples led to a type of numerical algebra. Geometric problems relating to similar figures, area and volume were also studied and values obtained for p.The Babylonian basis of mathematics

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    Parabolic Investigation

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    I have used the TI-84 graphic display calculator, the software Geoegebra and Microsoft Excel to do my calculations. I have even investigated the values of D, for polynomials of higher powers and tried to come up with a general solution for all equations. I have been able to do this portfolio from the knowledge learnt from classroom discussions and through various other resources. Question 1 “Consider the parabola y = (x−3)2 + 2 = x2−6x+11 and the lines

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    Gradient Functions

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    4 16x^3 5 4 20x^3 I will plot the graphs of the functions above and I will find their gradient using the formula gradient=increase in y-axis /increase in x-axis. Straight line graphs Straight line graphs are graphs with the equation y=mx+c or y=ax^1,where is stand for the gradient and c is the y- intercept. Gradient calculations 1. y=x graph Gradient of A= increase in y -axis/increase in x-axis = 2/2 =1 Gradient of B= increase in y-axis/increase in x-axis

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    41 61 85 113 Total Squares 5 13 25 41 61 85 113 145 Now so I can find an equation which will tell me how many squares there will be in each sequence, I will find the differences for the black squares first. The 1st difference is constant; I can now make an equation To find the equation I will need bits of information, the equation Is an+b, where a is the difference and b is the 0th term, e.g. the first term here is 4, to find the 0th terms you

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    Triminoes Investigation of Sequences There are different lots of sequences such as Arithmetic progressions, Geometric progressions and other sequences. There are many types of sequences, sequences that increase by a fixed amount between each term are known as arithmetic progressions or arithmetic series. Odd and even numbers both increase by two from one term to the next. The multiples of seven increases by seven, from one term to the next. Arithmetic progressions There are many types

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