...Tessellations: Mathematical Art San Juanita Cramer Southern New Hampshire University The Heart of Mathematics Professor Anca Parrish Abstract This paper discusses the historical background of tessellations, the mathematics of tessellations, and the applications of tessellations in the real world. Tessellations are found everywhere. M.C. Escher is the father of tessellations and his style and examples are discussed as well as the Islamic tessellations. There is an overview of the mathematics that is involved in tessellations and the polygons that can be tessellated and those that can’t. Finally, tessellations are used in real world applications. Examples are given of tessellated buildings and tessellations found in nature. Tessellations: Mathematical Art What is a term used for the tiling a surface without gaps or overlaps? The term is Tessellation. The Math Forum states that “ a tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps” (“What is a Tessellation?”, n.d) Early cultures used tessellations to cover the floors and ceilings of buildings, many of its artistic elements can be found in many early cultures (Hoopes-Myers, 2010). Tessellations are also found in the nature. A perfect example of nature’s tessellation is the honeycomb of the honeybee; there are no gaps or overlaps in its hexagonal shapes. In Ireland, a volcanic episode created tessellations in the landscape of The Giant’s Causeway (“Giant’s...
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...Europa Green/Roman Mosaics during the Third Century A.D. were one of the most common attributes of private homes and communal buildings during the rein of the Greek/Roman Empire. Nonetheless, mosaics are not just aesthetic works of fine art but merely are an indispensable memoir of substantial myths, stories, and legends of the past, whether it may be depicting a heroic scene of one of the greatest battles of time to a royal celebration of some sort. The intricate details and time put into creating such a piece of work reveal so much about the Greek/Roman culture. They revere and honour all the hardship they went through and then develop these fascinating life changing events into works of art, which, we now read about in books or view in museums. One specific work of art, which, portrays so much is The Abduction of Europa mosaic, now placed in the National Museum of Beirut. Nevertheless, most Greek/Roman mosaics were used and created to strengthen and support the Greek/Roman social structure and their societal reputation in the empire. They were not only created for societal purposes, but also to keep consequential evocations alive throughout history. The mosaics of the Greek/Roman culture have been said to be influenced vastly from Hellenistic art - some of the most common subject matters artists liked to capture and portray were scenes of the sea and Greek myths, such as Gods and Goddesses and the encounters they endured. This explains clearly, the mosaic we encountered in...
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...was developed in the Eastern Roman Empire between 330AD and 1453AD. It was the first ever Christian empire its capital was Constantinople, now known as Istanbul. This period produced remarkable works in history, fine poetry, much religious prose, and the visual arts flourished too. The term, however, refers more to a style associated with Byzantium than to its area. Byzantine art was a religious art, the orthodox subjects were chosen according to traditional themes and theological meanings. Christianity had an immense influence on Byzantine art. Most of the artists remained anonymous working as servants of the court or belonged to religious orders. Panel painting, frescoes, Ivory carvings, Byzantine crosses, illuminations, metal work and mosaic decoration attest to their skill. Byzantine art was intended as religious lessons, they were presented clearly and simply in order to be easily learned. The Byzantine era lasted for an immense time period so it is difficult to make concrete generalizations about this diverse period. Byzantine art can clearly be seen in direct relation to foreign ideas and radically different styles, both architectural and artistic. Byzantine artist continued that which his predecessor had taught him, demonstrating the style of a particular region or school. This uniform made it challenging for artists to demonstrate their individual flair however emerging individual personalities started to seep into their work. This style is simplified, flowing and symbolic...
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...start a new life in a safer environment. The first waves were welcoming by the American society; however, the following waves were rejected even by their own community. The Jewish people had to adapt to the American culture as many immigrants whose cultural background differs from that of the receiving country. However, they managed to maintain their cultural traits that differentiate themselves from other religions and cultures. To every city they went to, they got in contact to resident Jews and together built their communities, schools, synagogues, and more projects. There are organizations across the United States that date from beginnings of the nineteenth century, which principal objective is to help and guide coming Jews Immigrants. Their work is...
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...ether. Typically rich in color, Byzantine artists often used deep gold, blues and greens. The use of gold expressed the glory and richness of the faith. Bright colors helped make figures in paintings and mosaics identifiable from a distance. In secular art, those colors helped to distinguish the ranks of the subjects being depicted. For many Byzantine pieces, those colors have withstood centuries of exposure and remain vibrant today. http://archaeology-travel.com/photo-album/byzantine-mosaics-in-the-art-institute-of-chicago/ Mosaic traditions in the Middle East begin in late Antiquity, and one of the largest and best preserved Roman mosaics is the now well-travelled Lod Mosaic found not that long ago in Israel. From the fifth century on, from Syria to Egypt mosaics were used to decorate both religious and secular, public buildings. The tradition comes to an end in the eighth century, after the fall of the Umayyad dynasty in 750: churches fell into disrepair and were later destroyed. The only surviving examples are those that have been found in archaeological excavations. Some of which have found their way into various museum collections around the World. https://www.agapetile.com/products/techniques.php?technique_page=ind&technique_num=4 – Source D Mosaic is the art of creating images by assembling small pieces of glass, stone, gemstone, ceramic or seashell. Different colors are used to create the...
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.....3 1. Create a Tile Images List.......................................................................................................4 2. Set the parameters of the Mosaic..........................................................................................6 3. Select the Main Image...........................................................................................................7 4. Create the Mosaic..................................................................................................................7 User Interface Language .........................................................................................................9 Different Program versions ......................................................................................................9 Load/Save Settings...................................................................................................................9 Main Image to reproduce as a Mosaic.....................................................................................9 Size Parameters.......................................................................................................................9 Mosaic Size ............................................................................................................................10 Mosaic Resolution...................................................................................................................10 Tile Size................................
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...Dr. Lane Study Guide for Exam #1 Feb 2014 In brief, Exam #1 will cover two broad areas: (1) Everything we have covered in class on the Pentateuch. (2) The nature of covenants, and which OT covenant is which, so far. Here are the handouts the exam will cover: #12.2 Genesis 1–4, Creation & the Fall The exam will not ask about the different views of creation, but the other material is testable. #14 Essential Passages in the Pentateuch #16 Basic Nature of OT Covenants & ANE Treaties #17 Thirteen Propositions Re: . . . Covenants #19.1 Conclusions from the Pentateuch Be able to identify each of the five books we've covered, by way of main events (esp., the covenants), the main characters, and where the books fit into the redemptive-historical context of the Pentateuch. Know which sort of covenant is which (esp. H/O #16), and esp.(!) what are the specific covenants we have seen so far in the OT. What are their features, whom are they with, etc. A few must-know chapters & verses: (These are not the only ones; these are the must-know chapters). Gen 12, 15, 17 & 22 Exod 19, 20 & 24 Exod 34:6 Lev 26:12 Lev 26 Deut 7 Otherwise, be able to identify the chapters in boxes . Other items / ideas we have stressed: Israel's religion and cosmology and cosmogeny (vs.( that of pagan religions. Be able to answer...
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...Few memories as a failure on a major project from half a decade ago still vividly remains in memories. As a Research Assistant to Tim, it was my first paid job. Tim, an Engineer, worked in silos and had driver social style to his heart beat. He only communicated the expectations without delving in the details that he had in his mind. Even though the Office space was a closed knit space for 16 students, Tim seldom hung out with people to build personal relationships. He only interacted with others when there was a need. His lack of explanation on why the project was needed had left me wondering regarding purpose and design aspects of the new programming project. I struggled on how to effectively design the project and often sought help from other people, who recommended me that the project needed investment in new programming platform as old platform was incapable of achieving the project objectives. After making almost no progress on the project and wasting time in attempts to make old platform workable, I received a vehement email from Tim, stating that XYZ Inc. was deciding to scale back on funding, as no progress reports were submitted. I was shocked to learn that I was even expected to submit progress reports at the end of quarter on the undertaken project in which I had neither any clue nor communication. As an amiable person, I was too quick to reach an agreement with Tim on project deliverables. I had thought that I would be receiving friendly advice and guidance from...
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...and answer document, uploaded to D2L dropbox. You will have to find an IT professional to interview on your own. Description of this assignment 1. Each student needs to find a candidate for a Post-implementation Review (PIR) report describing an information systems development project. 2. Where can you find an information technology professional to interview? You will have to find an IT professional to interview on your own. 3. If you work for a business or government organization, you should consider interviewing the IT/MIS director for your organization. If you work P/T or F/T in any reasonably sized organization, it is likely that there are some IT workers around (like help desk staff, programmers, analysts, network technicians or even IT managers). It can even be a friend, relative or acquaintance you know who works in such a job. 4. The following is a list of themes that you could address in the interview: Please do not write this paper in question and answer format. Use the questions below to help guide the interview. ▪ What type of job does he/she do? For whom? ▪ What projects is he/she currently working on for the organization? ▪ What projects has he/she recently completed? ▪ What IT applications has the firm recently implemented? ▪ Were the most recently applications developed in-house, were they outsourced development or were they application software packages that were customized and purchased? ...
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...Kempen | C402/C405 | Extend Diploma Mechanical Engineering EDENGM22A/B | Peter Kempen | C402/C405 | | GCSE English | Katherine Davey | G4 | GCSE English | Katherine Davey | G4 | | AS English Literature | Francesca Thomas | A58 | | | | | Archaeology: Unit 1 | Caroline Wilcox | B254 | Archaeology: Unit 2 | Caroline Wilcox | B254 | | Vocational Business assignment completion | Kemi Osoba | A49 | Vocational Business assignment completion | Bekoe Newman | A49 | | Vocational Sport and Travel Tourism assignment completion | Danny Chilvers | A50 | Vocational Sport and Travel Tourism assignment completion | Danny Chilvers | A50 | | AS /A2 GraphicsExtend Diploma Year 2 Final Major Project | Mark Pearson | Art Rooms | AS /A2 GraphicsExtend Diploma Year 2 Final Major Project | Mark Pearson | Art Rooms | Spring Term Revision Schedule 2013-14 Week 1 | Tuesday 8th April | | Morning session 10.00-12.00 | Afternoon Session 1.00-3.00 | | Subject/course | Teacher | Room | Subject/course | Teacher | Room | | A2 Business (China Research Theme) | Nessa | A25 | AS Business | Nessa | A25 | | A2 Economics | Charles | G5 | AS Economics | Charles | | | AS Business | Sarah (11.00-12.30) | A39 | A2 Business (Higher level exam technique) | Sarah | A39 | | AS Law | Amina | A26 | | | | | Vocational Business assignment completion | Kemi Osoba | A49 | Vocational Business assignment completion | Bekoe Newman | A49...
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...For ""Anticipated Project Size"" use your internal metrics as guidance. For example, if you use lines of code, then mentally assign ball park values to Small, Medium and Large as part of determining whether to give this criteria a high or low score. Follow a similar process ""Anticipated Duration"". Since project duration depends on project complexity, mentally categorize earlier projects as short, average or long duration to help put the current project in context. 2. After assigning a score for each criteria, view the Feasibility Study Suitability Indicator to discover the best method to use for determining project viability. 3. Omitted criteria will give an inaccurate result, so ensure all criteria are scored before checking the indicator." Criteria "Score (1=high, 3=low)" Guidelines Business Risk "1 = Significant, high-risk projects 2 = Low-to-modertate risk projects 3 = Small, low risk projects" Technology Risk "1 = Significant, high risk technological risks 2 = Low-to-moderate technological risks 3 = Small, low technological risks" Anticipated Project Size "1 = Large 2 = Medium sized 3 = Small" Anticipated Project Duration "1 = Long 2 = Medium duration 3 = Short" Project Dependencies "1 = Substantial and intricate project dependencies 2 = Minimal or manageable project dependencies 3 = No project dependencies" ...
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...(EPIEC) . From there he gained a lot of working experience and knowledge which made him to success in his business later . Business Motivation and starting One of the motivating factors was his father’s dream of his establishment in the society and another factor was after the independence of Bangladesh Aminul Islam realized that a new country has been born, therefore, a lot of construction will be needed for the development of the country and that is when he came up with the idea of Project Builders Limited. He proposed the idea to three other recent BUET graduates and they agreed to start with this new business. After the death of one of the partner and other two sold their share currently Aminul Islam is the only Managing Director and Chairman of Project Builders Limited. Vision The vision of Project Builders limited is to make quality constructions and make a strong infrastructure development of the country. Mission Construction of important structure and projects and to become the number one construction builder in Bangladesh. Initial Finance The company was initially started with four partners along...
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...knowledge to serve my best to the organization as well as my professional growth. Academics Relevant Courses: • Completed six weeks course and training in JAVA from SLR Infotech Pvt. Ltd, CHANDIGARH. • Pursuing 6 Months course and training in JAVA from DUCAT,NOIDA. • Completed six weeks course in C++ From ICT, KAITHAL B. Tech Projects: S.No Name Of the Project Description Team Members Roles and Responsibilities 1. CHANDIGARH TOURISM (B.Tech Summer Training Project) It was a software project based on core JAVA. It includes all the places to visit , map of chandigarh , hotel room booking , slides . Backend was based on MS-ACCESS . 2 Coding of Some pages, database manipulation & connectivity and preparing Crystal Reports. 2. DELHI TOURISM (B.Tech Minor Project ) It was a software project based on core JAVA. It includes all the places to visit , map of delhi , hotel room booking , slides . Backend was based on MS-ACCESS . 2 Coding of Some pages, database manipulation & connectivity and preparing Crystal Reports. 3. CRIME FILE MANAGEMENT (B.Tech Major Project ) It was a website describing various departments in crime department. It includes 3 modules WRITER , INSPECTOR , ADMIN. Writer writes complaints , Inspector investigates by watching the record using id’s and admin has all the controls. Platform used was ECLIPSE and backend was ORACLE database. 2 Overall designing of pages & coding of Admin Panel. Extra...
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...The following case represents a realistic situation facing construction firm that has just won a competitive contract. The realistic conditions complicating the project are described in detail, as are the alternatives offered by the staff for dealing with these complexities. Case The Sharon Construction Corporation The Sharon Construction Corporation has been awarded a contract for the construction of a 20,000-seat stadium. The construction must start by February 15 and be completed within one year. A penalty clause of $15,000 per week of delay beyond February 15 of next year is written into the contract. Jim Brown, the president of the company, called a planning meeting. In the meeting he expressed great satisfaction at obtaining the contract and revealed that the company could net as much as $300,000 on the project. He was confident that the project could be completed on time with an allowance made for the usual delays anticipated in such a large project. Bonnie Green, the director of personnel, agreed that in a normal year only slight delays might develop due to a shortage of labor. However, she reminded the president that for such a large project, the company would have to use unionized employees and that the construction industry labor agreements were to expire on November 30. Past experience indicated a fifty-fifty chance of a strike. Jim Brown agreed that a strike might cause a problem. Unfortunately, there was no way to change the contract. He inquired about...
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...FOR PROJECT A Cash Flows DCF (13%) PV 350,000 0.8850 309,750 350,000 0.7831 274,085 350,000 0.6931 242,585 826,420 NPV = 826,420 – 735,000 NPV = 91,420 FOR PROJECT B Cash Flows DCF (13%) PV 300,000 0.8850 265,500 300,000 0.7831 234,930 300,000 0.6931 207,930 708,360 NPV = 708,360 – 690,000 NPV = 18,360 FOR PROJECT C Cash Flows DCF (13%) PV 200,000 0.8850 177,000 200,000 0.7831 156,620 200,000 0.6931 138,620 472,240 NPV = 472,240 – 600,000 NPV = (127,760) Assuming the cost of capital increase to 15%, the new NPV will be as follows FOR PROJECT A Cash Flows DCF (15%) PV 350,000 0.8696 304,360 350,000 0.7561 264,635 350,000 0.6575 230,125 799,120 NPV = 799,120 – 735,000 NPV = 64,120 FOR PROJECT B Cash Flows DCF (15%) PV 300,000 0.8696 260,880 300,000 0.7561 226,830 300,000 0.6575 197,250 684,960 NPV = 684,960 – 690,000 NPV = (5,040) FOR PROJECT C Cash Flows DCF (15%) PV 200,000 0.8696 173,920 200,000 0.7561 151,220 200,000 0.6575 131,500 456,640 NPV = 456,640 – 600,000 NPV = (143,360) At this point it is necessary for one to determine the sensitivity of the change in NPV of the three projects due to the increase in cost of capital. SUMMARY OF NPVS’ CALCULATIONS PROJECT | NPV @ 13% | NPV @ 15% | % CHANGE IN NPV | A | 91,420 | 64,120 | * 29.86% | B | 18,360 | (5,040) | * 127.45% | C | (127,760) | (143,360) | * 12.2% | From the table above it is clear that all three projects had...
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