This website uses cookies to ensure you have the best experience. Learn more

Peter Dirichlet Essay

958 words - 4 pages

Peter G.L. Dirichlet was born in the time period of Napoleon’s great attempt at world domination, Thomas Jefferson’s inauguration, and the birth of Webster’s dictionary. Ultimately this period of time is known as the 1800s, and Peter G.L. Dirichlet was born in 1805. Dirichlet was not born into great wealth, (nor are many others, in this day and age either) his father was a postmaster in Germany where Dirichlet and his family lived. Though they didn’t have much spare change, it was recorded that Dirichlet would use any collected money to purchase math books. Dirichlet was said to be a model pupil, attentive in class and predominantly fascinated by history and mathematics. His parents ...view middle of the document...

The theorem had claimed that in order for “n > 2 there are no non-zero integers x, y, z such that xn + yn = zn.” (Connor) Mathematicians, Euler and Fermat had already proved n=3 and n=4, while Dirichlet worked to find n=5. To which he eventually did. However, this is not his most famous feat.
His most notable work is known as the Dirichlet Principle, also known as the Pigeonhole Principle. Dirichlet was studying the variance of possibilities in the amount of which a number could have. His example was of a Pigeonhole. There could be nine holes for each pigeon to go inside, however, if there were twenty pigeons, and only nine holes; then it must be assumed that there are multiple pigeons in some of the holes. Dirichlet used this principle to prove a result about approximating irrational numbers by rationals. His principle states:
“If one puts n+1 pigeons into n pigeonholes, then at least one pigeonhole will contain at least two pigeons.
More generally, if one puts kn+1 pigeons into n pigeonholes, then at least one pigeonhole will contain at least k+1 pigeons.”(Neale)
Dirichlet basically developed a sequence in which individuals could estimate similarities in situations. An example of one through the use of the Pigeonhole Principle would be: “For every 27 word sequence in the US constitution, at least two words will start will the same letter.” (Haslam. 16) Because there are only twenty six letters in the alphabet, and each of the twenty seven words must start with one of the twenty six letters, it can be assumed by the Pigeonhole Principle that at least two words must start with the same letter.
Dirichlet’s discovery of the Pigeonhole Principle aided today’s work in estimating the amount of expected errors, collisions, or malfunctions in machinery. This strategy is mainly noted in computer software, as well as large company facilities in which...

Find Another Essay On Peter Dirichlet

phase diagram Essay

4456 words - 18 pages Introduction: Chemical equilibrium is a crucial topic in Chemistry. To represent and model equilibrium, the thermodynamic concept of Free energy is usually used. For a multi-component system the Gibbs free energy is a function of Pressure, Temperature and quantity (mass, moles) of each component. If one of these parameters is changed, a state change to a more energetically favorable state will occur. This state has the lowest free energy

Revolutionary Work of Art Essay

1890 words - 8 pages Walter Benjamin emphasizes in his essay, “The Work of Art in the Age of its Technological Reproducibility” that technology used to make an artwork has changed the way it was received, and its “aura”. Aura represents the originality and authenticity of a work of art that has not been reproduced. The Sistine Chapel in the Vatican is an example of a work that has been and truly a beacon of art. It has brought a benefit and enlightenment to the art

Enlightenment Thought in New Zealand Schools

1594 words - 6 pages In this essay I will be looking at how the political and intellectual ideas of the enlightenment have shaped New Zealand Education. I will also be discussing the perennial tension of local control versus central control of education, and how this has been affected by the political and intellectual ideas of the enlightenment. The enlightenment was an intellectual movement, which beginnings of were marked by the Glorious Revolution in Britain

Psychological Egoism Theory

2240 words - 9 pages The theory of psychological egoism is indeed plausible. The meaning of plausible in the context of this paper refers to the validity or the conceivability of the theory in question, to explain the nature and motivation of human behavior (Hinman, 2007). Human actions are motivated by the satisfaction obtained after completing a task that they are involved in. For example, Mother Teresa was satisfied by her benevolent actions and

How Celtic Folkore has Influenced My Family

1587 words - 6 pages Every family has a unique background that influences the way they live and interact with other people. My parents, who emigrated from Ireland to the States with my three brothers in 1989, brought over their own Celtic folklore and traditions that have helped shaped the way our family operates and lives. One aspect of folklore that has helped shape my family dynamic is the Celtic cross—both its background and what role it has played in our lives

Julia Margaret Cameron

1406 words - 6 pages At a time when women were looked upon as being homemakers, wives, mothers and such the late 1850's presented a change in pace for one woman in specific. Photography was discovered in 1826 and soon after the phenomenon of photography was being experimented with and in turn brought new and different ways of photo taking not only as documenting real time, but also conceptualizing a scene in which an image would be taken. Julia Margaret Cameron will

Evaluation of School Improvement

1403 words - 6 pages The evaluation process should be progressive to incorporate overall planning, implement changes, which contribute to success. In order to focus on school climate and norms, the evaluation design must include the students, instructions, and outcomes to improve communication and building-level concerns to be address in this response. School Climate and Social Norms The school principal, other staff leaders, and personnel set the tone and the

Case Study: The Benefits of Animal Testing

1757 words - 7 pages Nine year old Amy has already had a rough start in life. She was born with an abnormal heart that hinders her everyday activities. Amy is unable to keep up with kids her own age because she often tires out easily. As a consequence, she has very little friends and is often alone. Amy is forced to take different medications everyday just to survive. Amy’s life consists of medicine, doctors, and constant hospital visits. However, Amy is due for a

Myth and Magic: Realism in "One Hundred Years of Solitude"

1531 words - 6 pages “He enjoyed his grandmother's unique way of telling stories. No matter how fantastic or improbable her statements, she always delivered them as if they were the irrefutable truth” (Wikipedia, 2011). Experiences are particular instances of one personally encountering or undergoing something and in these moments of time life changes for the best or the worst and memories are formed. These recollections such as riding your first bicycle, going to

Adiponectin: a Novel Indicator of Malnutrition and Inflammation in Hemodialysis Patients

2384 words - 10 pages Objective Protein-Energy malnutrition (PEM) and inflammation are common and overlapping conditions in hemodialysis patients which are associated with increased risk of morbidity and mortality. Adiponectin is an adipocytokine which is exclusively produced by adipose tissue. Few studies in hemodialysis patients have demonstrated that serum levels of adiponectin were significantly higher in malnourished patients compared to well-nourished ones. The

The Congo Free State: A Legacy of Apathy, Exploitation and Brutality

2298 words - 9 pages Between 1885 and 1908, Belgium’s Leopold II ruled Congo, a region in central Africa, as his personal colony, exploiting the resources and inhabitants for his own gain. Leopold allowed and encouraged Europeans and other Westerners to enter Congo and set up companies whose primary purpose was to gather rubber, which was abundant but difficult to get to in the Congo, using the Congolese as the laborers for the Europeans. Rubber gathering in Congo

Similar Essays

Contributions Of Isaac Newton Essay

1251 words - 5 pages dealt with derivatives, integrals, and binomials. However, Newton’s calculus and today’s calculus differs in that there were numerous mathematicians who lived after Newton who invented more calculus, expanded on calculus, or applied calculus to other things. These men were Euler, Fourier, Johann Carl Friedrich Gauss, Johann Peter Gustav Lejeune Dirichlet, and Bernhard Riemenn. Euler invented the symbols e and π. In addition, Euler dealt with the

The History Of Math Essay

4801 words - 19 pages German mathematicians Georg Cantor and Karl T. W. Weierstrass. A further important problem, which arose out of the problem-first stated in the 18th century-of describing the motion of a vibrating string, was that of defining what is meant by function. Euler, Lagrange, and the French mathematician Jean Baptiste Fourier all contributed to the solution, but it was the German mathematician Peter G. L. Dirichlet who proposed the definition in terms of

Mathematics Ara Essay

4768 words - 19 pages mathematician Jean Baptiste Fourier all contributed to the solution, but it was the German mathematician Peter G. L. Dirichlet who proposed the definition in terms of a correspondence between elements of the domain and the range. This is the definition that is found in texts today.In addition to firming the foundations of analysis, as the techniques of the calculus were by then called, mathematicians of the 19th century made great advances in the

When The Bubble Burst Essay

1539 words - 6 pages By the time I arrived state side from my second tour in the Middle East the housing bubble had already burst. I noticed a drastic change in the way that many of my friends and family were living. Several of my friends that worked in real estate had sold their boats and seconds houses. My own stock portfolio had lost a third of its value. My sister and her husband had defaulted on their home mortgage leaving them scrambling for a place to live. I