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Mathematical Perspective in the Works of M.C. Escher

A resident of Leeuwarden, Holland, and Maurits Cornelis Escher was born in 1898. He became recognized because of his exclusive and captivating mathematical creations in the works of art that explore and demonstrate a broad array of mathematical thoughts. Against the will of his family to turn into an architect, he had the talent for drawing and design, which eventually led him to a career in the graphic arts. His work was not much known till mid 50’s when in 1956 his foremost important exhibition, was published in Time magazine, which attained a universal repute. Mathematicians were one of the leading admirers, who acknowledged his effort as an amazing vision of mathematical ethics in spite of the fact that Escher had no proper mathematics education except till secondary school [Platonic Realm].

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The more his works got matured, the more he got stimulated from the already held mathematical ideas while understanding the geometry of structures and eventually utilized the geometrical principles in his master pieces. He looks enthralled with impossibility of the figures, and produced some intriguing works of art. M.C. Escher possessed exceptional visualization and perceptions. A number of the Escher’s mathematical ideas are not found somewhere else, specifically the interlocking shapes of people, birds and fish and reptiles, which recur on an even surface with no space in between.

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The Mathematical Art

When asked about his style by an interviewer, Escher had replied about his aspiration to fill the space and his desire to fill a restricted level of surface without gaps that stirred much of his work [Biographical Sketches of Mathematical Giants]. His desire was further enhanced when he visited the city of Granada in 1922 where he happened to visit Alhambra palace, which had been built in the fourteenth century as a house for the last of the Moorish courts in Spain. He was fascinated by the designs of the building specifically the walls and floors which were wrapped with complex designs that were simple, yet at the same time were very detailed. The regular divisions of the plane, called “tessellations,” are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. These are the polygons or similar regular shapes, such as the square tiles often used on floors.

Escher, however, was fascinated by every kind of tessellation, regular and asymmetrical, and took special delight in what he called “metamorphoses,” in which the shapes changed and interacted with each other, and sometimes even broke free of the plane itself. This had motivated him to fill a plane with repeated contiguous shapes having no recognizable human or animal form and other simple geometric shapes. Un aware of the mathematical principles behind his work he continued working till until1940 he began his work for depicting standard partition of a flat surface. The work of Escher primarily contained a type of two-dimensional crystallography, which at present has become a science dealing with the formation and structure of crystals and rocks etcetera.

Having read works of other artists i.e. Polya, he used some basic geometric motions to create regular division of a plane including rotation, translation, reflection and glide-reflection. He worked on the development of a total theory for the regular division of a plane with a similar pattern of shapes that were not convex polygons. Ultimately he could reach his theory of “quadrilateral systems” in 1941, which was published, in his book “Regular Division of the Plane with Asymmetric Congruent Polygons.” He also worked on the creation of images that reduce in size until they became considerably minute. To create these prints the geometric principle of similarity is utilized in which the exact same shape but decreased in size is obtained.

It stands proved that of all the regular polygons, only the triangle, square, and hexagon can be used for a tessellation. Escher used these basic patterns in his tessellations; applying what geometers would call reflections, glide reflections, translations, and rotations .He also made these patterns by “deforming ” the fundamental form to depict them into animals, birds, and other figures. Escher’s work also enclosed a diversity of themes all through his life. His initial descriptions, Roman and Italian landscapes and of nature, finally led to expected partition of the plane. Many of his mathematical works were obtained from extraordinary view creating mysterious spatial special effects. Over 150 vibrant and identifiable works confirm the Escher’s originality and curiosity in regular division of the plane. [Maurits Cornelius Escher]


Escher throughout his life saw the beauty in structure and infinity and forced the idea of meaningful lines into the mathematical framework of regular plane division. He liked to challenge the logic of seeing. One can see the mathematical divisions in form of the white birds and regard the black as background. The black and white horses can be seen separately and the black fish can be regarded as the white as background.

Management Issues Term Paper

Management is a very wide topic. It holds numbers of critical issues. Writing on these issues needs deep understanding of all the concepts and processes that are carry out in organizations and business firms. Mostly students of commerce are assigned to write on such topics. In the field of commerce, clear and effective business writing is very important. Some important guidelines are listed here that will surely help you to deploy your work with confidence.

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Before starting you need to build a boundary, i.e. from the pile of management issues, select a single subject to be discussed. It will keep you grounded, focused and on target. Your topic may cover financial issues, economical issues, risk management, crises and security issues etc. Now you know your theme, it will definitely make your writing phase easier.

Switch your brain into a frame of mind, keeping the subject matter in mind; visualize all aspects, features and other factors that may have any link with the issue. Now you are all ready to clearly mention the main idea of your writing. You should list all the major points of the issue. Moreover you should also mention the reason to choose that topic. Signify its importance by highlighting the areas it deals with. For example if you have chosen the topic “Planning and scheduling”, you can mention how it can be conducted; in addition you can suggest best ways to run it in a pessimistic manner. Giving solutions to the problems will surely makes your work a masterpiece.

Plain writing style is both, convenient and comprehensible. Try to use short sentences and paragraphs. Rather than impressing, you should focus on expressing your view point. Adding fancy words will make it convoluted. Keep it structured. Put headings and sub heading to make your work presentable and organized.

Management issues usually deals with business and marketing. So it’s your responsibility not to use long conversational style. It will make it dull and boring. Try to keep it effective by avoiding long sentences. It will add energy to your scripts and ultimately your issue will gain reader’s attention.

It is a common practice that we need to focus on management issues so that the upper management could get notified. But the executives, loaded by the burden of work could not found sufficient time to look into the matter. In this way, it’s your responsibility to make it easy for them. You can make it more readable by designing ordered paragraphs; putting subheadings and adding bullets and list. These are excellent ways to grab reader’s attention.

Moreover take care of punctuations, citation, footnotes, revision, time line and finally a stabilized outlook of your management issues term paper. Go through these instructions and get ready to compose an excellent document.

The Horse Dealer’s Daughter

Mabel is dead; as she has not satisfied herself as a woman she is a loveless virgin, more concerned in adoring her dead father than a living man. When her home surroundings are ruined, she decides to destroy herself to join herself to the dead love for her father. Jack, the young doctor, avert her from doing this. He saves her existence by doing an idiotic thing, going into deep water when he can't swim. This proceed of irrational, emotional coercion is precisely what love is to Lawrence.

When a young doctor, Jack Ferguson, saves her. She then supposes that he loves her. Though this thought never take place Jack;s mind, he begins to discover that he really loves her. However, Mabel thinks she is too dreadful to be esteemed, as well as finds that when Jack assert over and over that he needs her and that he loves her, she is further scared regarding that than of Jack not deficient her.

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The cause why she commits suicide is for the reason that she felt reviled at her home. Her father had lately died as well as her brothers were callous to her. The father had left the family in obligation, and the family will almost immediately have to depart their house and shift somewhere else. Mabel has reserved house for her brothers, devoid of assistance of servants, for over ten years. In this time, the business, once affluent, has fall apart into a place. When asked which trail she would follow, she did not respond. I don't think she had something intended. She almost certainly didn't have a good education so there were few alternatives for her.

Possibly she felt besieged with the force to decide what to do, and determined to entrust suicide. Thus, when Jack Ferguson saves her, her optimism in life is transformed and she convinces herself that Jack loves her.

Jack induces himself that he loves Mabel. Conceivably he has never felt love before. He didn't desire to at first, thinking it unethical, as he was a doctor, and she, his patient. No doubt he has exhausted much of his time on study somewhat than girls. When they hold, he feels he can never let go; in anticipation of he smells the unpleasant sluggish smell of that water as of the pond. Both seem to impede and draw away from each other. Mabel had an untamed, hesitant look regarding her; Jack could not understand it. One cause he may have persuaded himself that he esteemed her is for the reason that he did not like that look as well as wanted to impede it.

We can't rationally clarify emotion; it is inbred and right to be governed by our feelings. While we initiate thinking and scrutinizing our acts, we get into difficulty and are despondent. This is precisely what happens to Jack and Mabel after she is saved from obscure. When they believe, they get into difficulty. Jack means a lot in Mabel life but still there many misunderstanding between them which unable them to send life with each other.

This narrative is concerning two people with low sense of worth. They both need love and induce themselves to adore the other. I do not consider this to be genuine love, as it did not last, and one cannot induce them to descend in love with another. Lawrence desires to make the reader sentient at the end of the tale that the couple, Jack and Mabel, may have a hard time ahead if they get married. A male and female union is a great effort and a clash for power of one over the other. Lawrence said the conflicting of abhorrence is not love, but individualism.

History Research Papers

Most students think that history term papers are too boring and when they are assigned to write on history, it makes them more annoyed. Don’t worry; be relaxed as smart students go for smart ideas. Here listed some excellent tips that will turn this bored subject as an interesting one.

Now the start up tip, when you have to write on history term paper or research paper, you have to do research on it. It means you have to learn and examine about the available past records. You can use both the primary and secondary sources to get a broader appreciation of the topic.

The article how to write on history research paper topics tells you tips to write in such a way that you will actively get engage in this subject. Your personal involvement in the area will let you to produce greater understanding of the literature.

While writing on history papers, demonstrate it using evidences. Your scripts should let both you and your reader to understand the subject deeply. Along with providing general understanding of the matter, you should also produce a logical argument. While writing on any subject will surely assist you to express your view points and ultimately help you in clarifying the confusion.

As you know that history always reveals a subjective perspective, you can easily found a lot of material on history, having variety of interpretations. Different historians often project different pictures on the same issue. So writing on history gives you an excellent platform to render your opinion about the issue.

The article how to write history papers tells you that after gathering all evidences don’t mix them. Prioritize them according to its significance. A good writing should depict organized and structured synthesis of quality material.

As a student, you should well aware of the writing style and basic component of article, namely introduction, body and conclusion. It should be on your tips that your introduction should be impressive, supporting paragraphs should hold integrity and conclusion should be the extract of your entire research work.

Moreover, smart students always take care of sequential manner, punctuations, citation, simple language, footnotes, revision, time line and finally a stabilized outlook in their term paper. Now you can start writing on any history term papers and research papers with all your zeal and zest

Homeland Security Topics

The U.S Department of Homeland Security was established after the 9/11 attacks to counter terrorist activities against the United States. Homeland security is officially defined by the National Strategy for Homeland Security as "a concerted national effort to prevent terrorist attacks within the United States, reduce America's vulnerability to terrorism, and minimize the damage and recover from attacks that do occur".

Homeland security topics may include discussion on the various departments that come under the Department of Homeland Security , such as the United States National Guard, the Federal Emergency Management Agency, the United States Coast Guard, U.S. Customs and Border Protection, U.S. Immigration and Customs Enforcement, United States Citizenship and Immigration Services, the United States Secret Service, the Transportation Security Administration, and Civil Air Patrol.

Or, they could include discussions on the current homeland security topics that are of concern to the Department of Homeland Security. These topics could range from whole-body scanners to 100 percent air cargo screening to social Web sites to communication interoperability to the consequences of climate change. Whichever homeland security topics you chose to write on, there are a few pointers that you could try to cover in your term paper.

1. When and why the Department of Homeland Security was formed?
2. What are the various departments or sections that come under its control?
3. The range and dynamics of the homeland security topics.
4. The cross border activities of the departments; basically focusing on its purpose and usefulness.
5. Which department has best achieved its goals and what factors led to their accomplishments?
6. How these departments have helped improve the overall effectiveness of the organization.
7. The difficulties and challenges in its operations.
8. The research and developments in emerging technology to aid in homeland security.
9. Critically assess each department’s role and how they have come to help achieve the overall objectives of the organization.
10. Analyze and evaluate the strategies and responsibilities of each department, and research on any short-comings and deficiencies in implementing them.
11. You could help your nation by becoming a part of homeland security, by reviewing the defects in the system and coming up with a remedial plan of to help make US safer from threats.

After you have chosen the homeland security topics you can begin researching and collecting relevant and reliable information through various sources such as official websites, newspapers, publications, journals, or you could even setup an interview with a government employee.

Due to the sensitive and critical nature of the homeland security topics and you should provide references and seek permission before adding it in your term paper.

Finance as a Concentration

A concentration in Finance strengthens the key concepts and tools of finance, demonstrates how to relate them to speedily varying problems and use them by way of modern technology and information sources. A concentration in Finance offers a strong foundation, an understanding of global issues, and skill in financial engineering.

The Finance concentrations organize students for complex work in areas linked to financial management. Whereas openly appropriate to those working in the finance industry, this concentration is as well important to those accountable for financial decision making in any business. Electives obtainable comprise advanced work in advanced financial management, financial markets and instruments, and international finance.

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Through the Finance Concentration, students attain acquaintance in how firms make financial decisions as well as how these decisions influence individual organizations and society as an intact. Moreover, it helps to learn how firms obtain and assign funds, how financial markets function, and the function these markets participate in economic welfare. The study of finance embraces the exploit of models to expand investigative approaches to troubles. Students are qualified to take positions in financial institutions like profitable and speculation banks, in finance departments of main corporations, or with consulting firms.

Career opportunities in finance can be originate in all sector of society. The potential comprise: corporate finance positions such as treasurer, controller, credit manager, cash manager and benefits officer etc.

Sociology Research Topics, Sociology Topics

Sociology is a cross-disciplinary field that studies society. It uses empirical observation, social and scientific experimentation and critical analysis to explore human social activity. To write on a sociology research topics one must study and understand the sociological theories from an objective and scientific point of view and develop their own personal opinion, analysis, observations and critique to the findings.

Sociology is a very rich field often overlapping with other disciplines. Therefore selecting sociology research topics can be a testing decision and careful consideration needs to be given to your own understanding of the topic you select. You should give particular importance to your ability to research and expand on the topic, especially your ability to view the topic objectively or without bias.

Here are some of the points you need to consider when writing on sociology research topics, illuminating the cross-disciplinary makeup of the subject.

Since sociology is a very broad discipline and numerous researches are an on-going process in this field, therefore it is best if you check to see if someone else is working on the same sociology research topics or another researcher has already covered it. Normally research topics in sociology are in the form of questions and the essay you write on it is basically an answer to that question. In that answer you may explain the concepts and theories governing the topic; give analysis from your own research and experimentation of the topic and critically evaluate the reliability and validity of the topic and findings. A few examples of sociology research topics are as follows:

• Prostitution – should it be made legal?
• Religion and Terrorism – the connection?
• Public Funding for Abortion – a right for the mother?
• Marriage between the same sexes – should be made legal or not?

Select a topic that really interests you and make certain that you have an extensive understanding about its theories and perspectives. Since the subject of sociology is concerned with human behavior and social interactions, choosing a theme for your research paper is relatively easier than other disciplines. There are three sociological theoretical perspectives; Conflict, Functional and Symbolic Interactive perspectives; and may dictate your analysis in light of your chosen topic.

After carefully selecting sociology research topics you need to focus on conducting research to draft your essay. As sociology is bounded with social phenomenon, you can find loads of research materials on it, such as facts, text books, newspapers, journals and articles, charts, graphs, questionnaires and other statistical data. In addition to this you can collect study materials from historical records, experimental outcomes, sociological studies etc.

Last but not the least you should give your own analysis or view point on the sociology research topics you have chosen and take care of minor details such as sequential flow, persuasive tone and references and citations.

Leadership Statement College Paper

Knowing the way, going the way and showing the way convey a set of conditions that can unleash tremendous potential for the leader and also for its followers. Although organizations tend to prefer a ‘status quo’ rather than a change, but in fact it is change that creates, or in the context of high performing organizations maintains, excellence. Almost every organization face such challenges from time to time. Since moments of change also encounter the leadership, therefore, leaders should sought after and embrace change rather than avoiding it.

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It is important to recognize the skills or techniques pertaining to leadership. As Jeffrey Glanz (2002), says in his definition of a leader, “we tend to place more importance on the practical performance to the exclusion of the characteristics that may be more important” (p. 12). An educated leader may understand how to establish a budget, set priorities, and carry out a strategic plan. But this individual might, for example, exhibit unethical behaviors or demonstrate lack of empathy for others. The question we need to ask is, “What kind of leader do we want for a particular position?”

These are challenging times for leaders. The day-to-day pace has increased and everything seems to be changing. School leaders think in terms of pre and post “Columbine”. Leadership practices are evaluated differently after the incident of “September 11”. Today’s world is simply different and requires leaders that can adapt to these changes. Good leaders are those who understand the importance of the practical performance. They also realize that with so much going on it helps to take a step back periodically and focus on the foundation of effective leadership.

Traditionally, most leadership studies are dealing with what is called “leadership paradigms,” with each generating a group of theories. House & Aditya (1997) outline the two major research paradigms as:
Leadership Traits: Examining the differences between leaders and followers while using physical, psychological and mental characteristics or abilities; Leader Behavior: Studying the way “leaders” behave, either under controlled laboratory settings or as described by others in the field.

The universal traits possessed by the leaders are intelligence, assertiveness in social situations, self-confidence, high levels of energy, and knowledge aimed more towards task achievement rather than self-reflection or theory. This needs to be placed in a social context to work. According to House & Aditya (1997): “Leadership is embedded in a social context, and the idea of social intelligence implies that differences in cognitive abilities between leaders and non-leaders go beyond conventional IQ measures” (p. 509).

As for Leader Behavior Paradigm, the aim was to pinpoint what makes a leader through the person’s visible actions. This research led to the discovery of two major types of behavior—task-oriented and person-oriented. However, as the research could not come up with agreed-upon universal leadership behaviors, a set of “contingency” theories was created (Fiedler, 1971; House & Mitchell, 1974; Hersey & Blanchard, 1982). Several more modern leadership theories have arisen in the last decade including:

Leader Member Exchange Theory (Graen & Uhl-Bien, 1995): The type of leader-follower relationship can provide more predictive results of how an organization is doing compared to traits or behavior studies;
Implicit Leadership Theory (Lord & Maher, 1991): Along with all the other leadership qualities and behaviors, what makes a leader, is the fact others perceive the person as a leader;

Neocharismatic Theory (House et al, 1996): This is actually a group of theories, stretching back into the 1970s, which attempt to explain how leaders can get their followers to achieve highly-positive results in the face of overwhelming odds.

Proof Reading

Writing is truly an art or for that matter any interface that requires communicating is a world in itself as it requires military precision to understand the purpose of your communication and above all the requirements of your audience and relaying the message you are trying to convey in the right vein and tone.

When one starts with something one is bound to commit mistakes but it should be realized that mistakes are just part of the creation process. Correction of small nuances in a report or essay is at times so vital that one infinitive or two can make the whole difference in the interpretation of the subject matter presented. One can correct the matter only after it has been completed first and all the ideas have been put into paper. This can be achieved by in careful, in-depth and inquisitive proof reading. The article/report should then be given a first reading by an independent reader to take an overview and grasp the essence of the essay, i.e.; the audience understands what is being communicated to them.

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Once that is over, the next phase is to check for grammatical structuring and the general usage of the language so that the writer effectively communicates his thoughts. This is a painstaking process which may take sometime and several re-readings and corrections. If it is not urgent, one may take a day or two and go through the matter from beginning till end until one is completely satisfied. The thing to look out for is that the sentence written must make sense to the reader and it should be as much as possible in a user friendly mode so that it makes for an interesting reading. If your reader loses interest then that will be your biggest shortcoming. Once through this, the presentation of the report must be checked and formatted in a way to look most presentable when handed over to someone for reading.

Finally, one must give a last reading to the material from the viewpoint of his audience to better understand the objective which he sets out to achieve.

Protection for Children on the Internet

The era in which we are living today is known as the era of internet. The web revolution has provided the mankind with the powerful tools, huge collections of services and varieties of resources. With the emergence of these trends, the entire world has wrapped into a global village. It has provided fast communication, easy access to information, ebusiness, entertainment and other range of services. But the darker side of the picture is really very challenging one.

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The fast and easy access to the open and unlock internet world is targeting people of every age, particularly children. Parents for the sake of their kid's enjoyment allow them to spend several hours in front of their computers. That unawareness and lack of concern from the parents side, engaged them in the mess of nasty and malicious stuff. Wary websites with explicit images, suspicious chat rooms having disgusting talks, spam emails by culprits containing blatant portraits.

All these horrifying consequences need to be investigated and resolved. The first and foremost step is the parents concern and control. Trusting the child is another issue, but keeping eye on them is truly very important. There are control logs that help in tracking and monitoring their internet activities. Particular software programs are also present for parents that can be launched to watch the snapshots of all those activities their kids have performed.

Protection for children from internet needs continuous supervision from parent’s side. In this age of World Wide Web, chat rooms are a source of fun and entertainment for kids. Mostly children join different chat rooms to find new friends online. It is the parent’s duty to provide guidelines to make their chatting safe and secure. They should tell them not to reveal their identities, their name, address, educational institutes, phone numbers and other personal information. Moreover also direct them to prevent meetings and companies of strangers.

File sharing is so appealing for the young children. But it’s a risky and dicey act. Parents should ban sharing and downloading of photos, music and videos as the possibility of containing objectionable data is very high.

Providing limited internet access is also a suitable idea in order to protect children from internet. Parents can use robust filtering utilities to gain more control over the web. These services provide proper observation on overall activities. It forbids explosion to doubtful websites, blocks streaming content and file sharing, filters improper emails and chats, and checks access to new groups and communities.

Protecting the child from internet is no doubt a tough and difficult task. But the convenience and protection provided by standalone parental control products have given release and comforts to the parents to a great extent. On the other hand it also provides knowledge and awareness of the horrific surrounding your child is moving in.