Solution 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 the full solution was reached; these men included Scipione dal Ferro, Nicolo Tartaglia, Girolamo Cardan, and Lodovico Ferrari. Dal Ferro was the Chair of the Arithmetic and Geometry department at the college in Bologna, Italy, for around thirty years. Around 1515 he discovered the way to solve cubics of the form x3 + mx = n. Dal Ferro was extremely hesitant to share his work with anyone until 1526 when he was about to die and demonstrated his process to a student, Antonio Fior. In fact, no writings of Dal Ferro …show more content…
Tartaglia wished to debate with Cardan publicly to heighten his own standing in the mathematical world and have the chance to get even. Cardan, well accomplished in several areas of mathematics, knew he would gain nothing by this and scarcely saw the need to reply to the attacks of the lowly math teacher. Cardan’s student Ferrari did take up the fight, trading letters back and forth with Tartaglia for some time, asking for a debate. Tartaglia finally agreed after receiving the offer of a new post in Brescia and wishing to improve his chances of obtaining the lectureship. Although Tartaglia had debated more regularly, Ferrari understood both cubics and quartics better and was having more success. Tartaglia left the contest early, effectively conceding to Ferrari and later even losing the payment for his
In the beginning of the course, we discussed “NGD”. The two areas of “NGD” that we focused on were number and geometry. Number is discrete, finite, time, or sound. Geometry is continuous, infinite, space, or vision. Bronowski mentioned how “it’s said that science will dehumanize people and turn them into numbers” (374). This tragically became true during the Holocaust where people were no longer considered human beings, but rather numbers. We discussed various mathematical topics concerning numbers like the well-ordering pair. In the well-ordering pair, ever subset has a least member. There are also figurative numbers, squared numbers, and even Pythagorean triples.
Michael Guillen, the author of Five Equations that Changed the World, choose five famous mathematician to describe. Each of these mathematicians came up with a significant formula that deals with Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. The book is divided into five sections, one for each of the mathematicians. Each section then has five parts, the prologue, the Veni, the Vidi, the Vici, and the epilogue. The Veni talks about the scientists as a person and their personal life. The Vidi talks about the history of the subject that the scientist talks about. The Vici talks about how the mathematician came up with their most famous formula.
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 Cardano begs Tartalia for the methods. Cardano finally publishes the methods of solving the cubic and quartic equations.
Pierre de Fermat Pierre de Fermat was born in the year 1601 in Beaumont-de-Lomages, France. Mr. Fermat's education began in 1631. He was home schooled. Mr. Fermat was a single man through his life. Pierre de Fermat, like many mathematicians of the early 17th century, found solutions to the four major problems that created a form of math called calculus. Before Sir Isaac Newton was even born, Fermat found a method for finding the tangent to a curve. He tried different ways in math to improve the system. This was his occupation. Mr. Fermat was a good scholar, and amused himself by restoring the work of Apollonius on plane loci. Mr. Fermat published only a few papers in his lifetime and gave no systematic exposition of his methods. He had a habit of scribbling notes in the margins of books or in letters rather than publishing them. He was modest because he thought if he published his theorems the people would not believe them. He did not seem to have the intention to publish his papers. It is probable that he revised his notes as the occasion required. His published works represent the final form of his research, and therefore cannot be dated earlier than 1660. Mr. Pierre de Fermat discovered many things in his lifetime. Some things that he did include: -If p is a prime and a is a prime to p then ap-1-1 is divisible by p, that is, ap-1-1=0 (mod p). The proof of this, first given by Euler, was known quite well. A more general theorem is that a0-(n)-1=0 (mod n), where a is prime...
Tubbs, Robert. What is a Number? Mathematical Concepts and Their Origins. Baltimore, Md: The Johns Hopkins
Bernard Bolzano (1781-1848), presently a logician and mathematician of international repute, worked from 1805-1819 as a theological professor at the Prague University. This post he received immediately after he ended his mathematics and theology studies. In this period he had already published his first scientific study Betrachtungen über einige Gegenstände der Elementargeometrie (A reflection on some elementary geometry questions), which was his final dissertation study. In the study Lebensbeschreibung des Dr. B. Bolzano (Biography of Dr. B. Bolzano), he remembers, that it was not easy to dec...
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 the theories of mathematics (“Archimedes”).
The Bernoulli family had eight significant and important mathematicians, starting with Jacob Bernoulli, born in 1654. Though there was a great deal of hatred and jealousy between the Bernuollis, they made many remarkable contributions in mathematics and science and helped progress mathematics to become what it is today. For example, Daniel discovered a way to measure blood pressure that was used for 170 years, which advanced the medical field. Daniel’s way of measuring pressure is still used today to measure the air speed of a plane. Without the Bernoulli family’s contributions and advancements to calculus, probability, and other areas of mathematics and science, mathematics would not be where it is now.
Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic.
Melville, Duncan J, Tokens: the origin of mathematics, St Lawrence University IT Retrieved January 19th 2014, from St Lawrence University: http://it.stlawu.edu/~dmelvill/mesomath/tokens.html
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
In conclusion, it is clear that while their ancient civilization perished long ago, the contributions that the Egyptians made to mathematics have lived on. The Egyptians were practical in their approach to mathematics, and developed arithmetic and geometry in response to transactions they carried out in business and agriculture on a daily basis. Therefore, as a civilization that created hieroglyphs, the decimal system, and hieratic writing and numerals, the contributions of the Egyptians to the study of mathematics cannot and should not be overlooked.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world. A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest richness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.