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
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
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
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
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
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
more complex, such as with cubic and quadratic functions, mathematicians call upon more convoluted methods of finding roots. For many functions, there exist formulas which allow us to find roots. The most common such formula is, perhaps, the quadratic formula. When functions reach a degree of five and higher, a convenient, root-finding formula ceases to exist. Newton’s method is a tool used to find the roots of nearly any equation. Unlike the cubic and quadratic equations, Newton’s method – more accurately
set of Triminoe cards and the largest number used on the cards. PLANNING These are some of the formulas I will be using in order to complete the tasks: f (n) =an+b (Linear equation) f (n) =an2+bn+c (Quadratic equation) f (n) =an3+bn2+cn+d (Cubic equation) f (n) =an4+bn3+cn2+dn+e (Quartic equation) METHOD 1. First I am going to the number 0 and find out how much different possibilities I can make with the one number, this is obviously one. 2. I will then try two numbers
The quartic equation is used by geometry teachers around the world and in computer graphics. This formula originated in Italy in the 1500’s. It was rare for someone to find a solution and achieve fame in doing so. The chances of that happening were slim to none due to the lack of education during this period. A mathematician named Lodovico Ferrari beat those odds and created a formula that still has applications today. Italy in the 1500’s was a different place than what people know now. They had
results I know. Pattern Number Number of Squares 1st Difference 2nd Difference 1 1 4 4 2 5 8 3 13 4 12 4 25 The 2nd difference is constant; therefore the equations will be quadratic. The general formula for a quadratic equation is an2 + bn +c. The coefficient of n2 is half that of the second difference Therefore so far my formula is: 2n2 + [extra bit] I will now attempt to find the extra bit for this formula. Pattern Number
the ground. Fracking has become a highly successful process for increasing natural gas reserves in the United States. This process also lowers the United States dependence on foreign gas and oil and it accounts for an estimated forty two trillion cubic meters of natural gas, which is said to be enough to keep the United States in motion for sixty five years. As good as the fracking system sounds, there is always the down sides like the fact that the chemicals used to obtain the gas are extremely
Bernoulli’s Equation. The Bernoulli equation states that, [IMAGE] but only when · point 1 and 2 lie on a streamline, · the fluid has a constant density, · the flow is steady · there is no friction. Although these restrictions sound severe, the Bernoulli equation is very useful, partly because it is very simple to use and partly because it can give great insight into the balance between pressure, velocity and elevation. Bernoulli's equation is the explanation
can calculate the side lengths minus the cut out squares using the following equation. Volume = Length - (2 * Cut Out) * Width - (2 * Cut Out) * Height Using a square, both the length & the width are equal. I am using a length/width of 10cm. I am going to call the cut out "x." Therefore the equation can be changed to: Volume = 10 - (2x) * 10 - (2x) * x If I were using a cut out of length 1cm, the equation for this would be as follows: Volume = 10 - (2 * 1) * 10 - *(2 * 1) * 1
Missing figures/equations My goal in writing this paper is two fold. Goal one is to try and understand how a stationary magnet exerts force by means of a magnetic field (even across a complete vacuum). Frequently, electromagnetic fields are compared to the gravitational field. Goal two is to explore the similarities between the two types of fields to see if comparison throws any light on the mechanism of magnetic field generation. The term action-at-a-distance is often used to describe forces
creative and find ways to keep pushing the student onward as well as upward. In order to devise the ultimate plan for educating students, a teacher must acknowledge that the “students” are what teaching is all about. The most important factor in the equation is unequivocally the STUDENT! All humans are different in some sort or fashion. But the fact still exists that we all have only this place to function in. So help by putting forth an effort to make it a better place for us all. I’m a firm believer
imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature
to find 3 equations, that would give me an answer, if I had certain information. The first was to find one that if you knew that there were four pegs on the boundary, and none on the interior, you could get the area. The second was if you knew that there were 4 pegs on the boundary, and you knew how many were on the interior, you could get the area. And last, if you had the number on the interior, and the number on the boundary, you could get the area. Process The first two equations, were a preparation
involved means that the potential energy is greater therefore the kinetic/moving energy will also be greater. Variables: Force to pull the band back. This will be between 3 and 11 Newton’s. Equations: Distance = Speed Time Speed = Time Distance Time = Distance Speed I also have Equations for EPE in my research. Method: 1) Attach an elastic band to the hook on the end of a Newton metre and stretch the band until the Newton metre reads three Newton’s 2) Then Release the
things in a restaurant could not happen without math such as paying for your meal. Math is used to add up the total cost of a person’s bill as well as adding in the sales tax. More advanced math is used in the restaurant business as well. Using equations to determine what your business can afford to buy as well as the difference in the cost of the product and the profit it turns over is all determined by math. Jobs you might not even think require math do, such as portioning products or prepping
straight line relationship, expressed as Y = α + βX + e. Here, Y is the dependent variable, and X is the independent variable. α is the intercept of the regression line, and β is the slope of the regression line. e is the random disturbance term. The equation Y = α + βX (ignoring the disturbance term “e”) gives the average relationship between the values of Y and X. For example, if Y is the cost of goods sold and X is the sales, and α = 2 and β = 0.75, and if the sales are 100, i.e., X = 100, the cost