Triangulated Polygons Essay -- Mathematics

From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe. There are many applications to mathematics such as triangulating polygons. Triangulation is a surveying technique in which a region is divided into a series of triangular elements based on a line of known length so that accurate measurements of distances and directions may be made by the application of trigonometry. (Company, 2009) Since its discovery, triangulation has lent the world many beneficial advantages. Polygons exist as multi-sided shapes. These shapes can be subdivided into many non-overlapping triangles. These triangles connect corners to corners, creating diagonals that section it off. These sections are called convex hulls. The many uses of algorithms allow anyone to calculate these triangular hulls. The mathematics behind triangulating polygons was originated in Alexandria by the man, Euclides. Euclides was a Greek mathematician who was highly revered as the â€Å"Father of Geometry.† Euclides possessed a mysterious personal life, because his life was not documented and often confused with others. He taught many children mathematics during the reign of Ptolemy. His father and grandfather were thought to be Greek, but this is not certain considering the confusion between him... ...'s Formula. Retrieved from ENRICH: http://nrich.maths.org/1384 Company, H. M. (2009). Triangulation. Retrieved from TheFreeDictionary by Farlex: http://www.thefreedictionary.com/triangulation csunplugged. (2010, October 30). Santa's Dirty Socks (Divide and Conquer Algorithms). Retrieved from Youtube: http://www.youtube.com/watch?v=wVPCT1VjySA lecture, P. T. (1993). Triangulations and Arrangements. McGill University. Math Open Reference. (2009). Euclid. Retrieved from Math Open Reference: http://www.mathopenref.com/euclid.html Suksak, P. S. (2010, November 30). Catalan Numbers Presentation 2. Retrieved from Slide Share: http://www.slideshare.net/PaiSukanyaSuksak/catalan-number-presentation2 Teter, M. (2000, March 15). Sonar a way of seeing sound. Retrieved from Cornell Center for Material Research: http://www.ccmr.cornell.edu/education/ask/index.html?quid=260 Triangulated Polygons Essay -- Mathematics From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe. There are many applications to mathematics such as triangulating polygons. Triangulation is a surveying technique in which a region is divided into a series of triangular elements based on a line of known length so that accurate measurements of distances and directions may be made by the application of trigonometry. (Company, 2009) Since its discovery, triangulation has lent the world many beneficial advantages. Polygons exist as multi-sided shapes. These shapes can be subdivided into many non-overlapping triangles. These triangles connect corners to corners, creating diagonals that section it off. These sections are called convex hulls. The many uses of algorithms allow anyone to calculate these triangular hulls. The mathematics behind triangulating polygons was originated in Alexandria by the man, Euclides. Euclides was a Greek mathematician who was highly revered as the â€Å"Father of Geometry.† Euclides possessed a mysterious personal life, because his life was not documented and often confused with others. He taught many children mathematics during the reign of Ptolemy. His father and grandfather were thought to be Greek, but this is not certain considering the confusion between him... ...'s Formula. Retrieved from ENRICH: http://nrich.maths.org/1384 Company, H. M. (2009). Triangulation. Retrieved from TheFreeDictionary by Farlex: http://www.thefreedictionary.com/triangulation csunplugged. (2010, October 30). Santa's Dirty Socks (Divide and Conquer Algorithms). Retrieved from Youtube: http://www.youtube.com/watch?v=wVPCT1VjySA lecture, P. T. (1993). Triangulations and Arrangements. McGill University. Math Open Reference. (2009). Euclid. Retrieved from Math Open Reference: http://www.mathopenref.com/euclid.html Suksak, P. S. (2010, November 30). Catalan Numbers Presentation 2. Retrieved from Slide Share: http://www.slideshare.net/PaiSukanyaSuksak/catalan-number-presentation2 Teter, M. (2000, March 15). Sonar a way of seeing sound. Retrieved from Cornell Center for Material Research: http://www.ccmr.cornell.edu/education/ask/index.html?quid=260

Nutritional Analysis Paper

WELLNESS-FOCUS NUTRITION Diet Analysis Paper Being an insulin dependent diabetic with Celiacs Disease has played the main role in dictating my eating patterns for the last six years. I walk a fine line of balancing blood glucose levels with diet and exercise. Many of the foods I eat are simply because I have to follow a gluten free diet to manage my Celiacs Disease. With all of the emerging publicity of gluten free diets people assume that eating gluten free is a healthy, weight friendly, approach to eating.I find that a naturally occurring gluten free diet lives up to many of those expectations, however when certain foods are replaced with a formulated gluten free version it then becomes a different story. When gluten free adaptations of grains in breads, pastas, cereals, etc. are added into my diet I find myself eating a much higher amount of carbohydrates and calories from starch. Many of the gluten free versions of whole grains are very dense in carbohydrates.The reason behind th e heightened calories and carbohydrates is because it usually takes multiple types of gluten free flours mixed together to substitute for one non gluten free all purpose flour. I anticipate my carbohydrate intake will be on the elevated side in the initial three day data, but I am consciously mindful to try to avoid too many gluten free replacements and instead opt for foods that are naturally gluten free. Other influences on my food choices would include my on the go lifestyle and my Diabetes. I have been a type one insulin dependent diabetic for twenty seven years.Over the last three decades the guidelines for a diabetics diet and target blood glucose range have changed drastically. Target blood glucose levels for â€Å"good† blood sugar control was 180 when I was first diagnosed. At the age of 12 I remember 150 being the upper limit. Now, at the age of 29, 120 is considered the highest â€Å"good† limit. These numbers hold relevance to me because they are how I dete rmine my insulin intake and diet adjustments. I have to count my carbohydrates in order to determine how much humalog to distribute. For every ten carbohydrates I consume I require one unit of insulin.These numbers all influence my food and beverage intake. My schedule is also a deciding factor of my diet. I begin my day at five a. m. every day and am headed to the gym by five thirty every morning. From there I head to school, where I am a full time student, until approximately 4 p. m. . I then drive to my job teaching competitive dance teams in Oxford until 9 p. m. . I get home, in Rochester, around 9:30 p. m. and begin my homework. My weekends are filled with competitions many times, which leaves me with very little time to grocery shop and prepare my meals in advance.I try the best I can to prepare my foods at home, but occasionally do resort to microwavable gluten free foods or salads from drive through windows. My expectations for my initial seven day data are that my levels wi ll show higher carbohydrates, but an adequate amount of vitamins and minerals. I do not anticipate my fat intake to be too high because I generally gravitate towards healthy fats. Fiber is definitely well incorporated in my diet through the variety of fruits, vegetables and skin on potatoes I eat. My vitamin D levels via food consumption may be low, but I am not concerned with it because I have been on a Dr. rescribed supplement for six years due to my Celiacs Disease. Based on the data collected in the first seven days of data recording , two of my initial hypothesis are correct. I have an elevated level of grains intake , which is shown on the my plate chart, and an extremely low level of vitamin D. During my second phase of dieting I will definitely be cautious of my starch intake in an attempt to lower it below the 112% of the recommended daily intake. A few things I am surprised to discover are that my vegetable intake and dairy intake are much lower than my recommended daily i ntake .I am also disappointed to find out that my dietary fiber, potassium and vitamin E levels are much lower than expected. Vitamins E and C work to stabilize free radicals and repair injury to the cell membrane and tissues. Thankfully I am consuming three times the amount of vitamin C recommended, however my vitamin E level is at a mere 17% of what it should be. Free radical damage could become quite significant if I continue to be so deficient in vitamin E. Good sources of vitamin E to incorporate into my diet are nuts, more spinach, peanut butter and avocado.Potassium is an essential electrolyte that affects the body’s fluid balances, nerve transmissions and muscle contractions. During dance I have noticed that lately, while pointing my toes, I have been experiencing foot cramping more times than not. The low levels of potassium I am consuming may be playing a role in that. Adding more fruits and vegetables to my diet is going to increase my vegetable intake as well as i ncrease my potassium and fiber levels. Fiber is important in aiding the digestive tract and supporting regular bowel movements. Soluble fiber is known to lower both blood cholesterol and glucose levels.Additionally to fruits and vegetables, adding more legumes to my diet is a great way to get more fiber. Upon completion of the second phase of data entry I had definitely made some effective changes. I increased my vegetable intake from 68% to 209% by adding vegetables in as snacks and incorporating them into as many meals as possible. The most notable effects of eating more vegetables are that my fiber level increased from a 50% to a 96% and my vitamin E from a 24% to a 35%. My folate levels went from a 48% to a 77% and my vitamin A levels went from a 82% to a 230%, both can be attributed to the consumption of more fruits and vegetables.I increased all of my B vitamins except for Thiamin, which respectively stayed the same. By adding more dairy through milk, cheese and yogurt I incre ased my calcium from a 70% to a 116%. My bones will surely thank me for that. Sodium increased from a 87% to a 128%. Ironically I increased my carbohydrate intake from a 55% to a 72%, yet reduced my grain intake from a 68% to a 52%. Adding a larger variety of fruits, dairy and vegetables to my diet was the key to lowering my grain intake while raising my carbohydrate intake.The grain intake on the my plate report is quite a fluctuation between the first and second phases, but I believe with continued monitoring and experimenting with interchanging foods that that can be balanced out. Another notable change is that I cut my fats by nearly half by eating more vegetables and low fat dairy items. I did increase my fruit intake slightly from a 74% to a 83%, but I think that overall I do consume an adequate amount of fruit regularly. My recommended daily caloric intake is 1,858. 11, however I fell short in both phases. I am comfortable at a 1200 calorie diet.I was full every day and could not eat any more without becoming uncomfortably full. Overall this diet analysis was very informative to what changes I can make in my life for a more balanced diet that is high in nutrients, vitamins and minerals. It was eye opening what positive changes adding more variety to my diet can actually make. My stress levels do fluctuate daily, however one stress factor that remains constant and I would rate at a 4 is my frustration with my lack of losing weight while giving a solid 100% effort over the last three months. I did not have any higher than usual stressful days.Mondays are always a higher stress day, simply because I have a more hectic schedule. I teach the largest number of children ages 7-18 dance on Mondays and having that many children for three hours does wear on my patience. I teach a total of 52 children that are split into three separate classes on Mondays. My schedule on Mondays, Tuesdays and Wednesdays has me up at 5a. m. , out the door at 5:45am and not returning home until 9 at night. I go directly from the gym to school to work on Monday, Tuesday and Wednesdays. That being said, I would rate my stress levels on Monday a 6, Tuesday a 5 and Wednesday a 4.Planning and packing meals, change of clothes, choreography, homework and medical supplies ahead of time makes a tremendous difference in how smoothly those three days run. My diabetes is a contributor to my daily stress factor. I maintain some sort of stress on a daily basis that is based around my blood sugar levels, balancing them and the effect a high or low has on my body both physically and mentally. Every single day, regardless of other influences or happenings, my stress is maintained at a level 2 strictly because of my health management.With my activity level being so high and my schedule being so demanding, I know that averaging four hours of sleep a night is not healthy or ideal. I will try to aim for seven hours of sleep a night in order to give my body the chance to rest and re cuperate that it needs. My ability to focus and process information at an optimal level should also improve with more sound sleep. Stress levels may not diminish, but they will more than likely lower for me with improved sleeping patterns. I feel confident in being able to recognize unhealthy patterns and rectify them the best I can while moving towards a healthier future.

Nike ( Nyse Nke ) - 1851 Words

Nike (NYSE:NKE) Company Description Nike specializes in research, development, manufacturing, and distribution of various products within the apparel footwear and accessories market. Founded in 1965 and headquartered in Beaverton, Oregon, the company operates in three core segments: footwear, apparel, and other equipment. The apparel and equipment product segments offer a variety of products from shirts, pants, protective gear and many other sporting goods. Within the footwear segment, Nike has been a global leader in technology and style innovation. The company currently has over 44,000 employees and operates globally. Investment Thesis At this time, Nike presents an interesting investment opportunity. With the consistent longevity of dividend increases coupled with the attractive ROE ratio in comparison to competitors, Nike appears to be a great investment but that may not be the whole story. With an intrinsic value calculated from the discounted cash flow model of $87.84, Nike stock currently seems overpriced. While Nike has a strong history of consistent revenues and profits, which it is poised to continue in the future, and is a global power in its industry, Nike’s recent acquisition of Converse is driving up stock price. In the eyes of Graham this would be an unattractive investment. However, if the gap between stock price and intrinsic vale were to close, I believe this company to be a solid long-term investment in the eyes of Buffett.Show MoreRelatedCapital Structure1215 Words   |  5 PagesInformation My company choice is Nike Inc. (Nike), a multinational sports footwear, equipment and apparel manufacturing company based in Oregon, United States. This puts Nike in the apparel industry. In 2010, Forbes rated Nike as the top sports business with a total value of $10.7 billion. The most effective marketing strategy Nike employ is the sponsorship agreements they have with numerous top athletes in a variety of sports. Operating Risks of Nike When Nike was initially started out, theRead MoreCase Study : Ford Corporation, And Nike Corporation Essay859 Words   |  4 Pagesselected for this project were Microsoft Corporation, Ford Corporation, and Nike Corporation. Their company symbol which is exhibited by the National Association of Securities Dealers Automated Quotations (NASD) and New York Stock Exchange (NYSE) for Microsoft is MSFT, for Ford is (F) and Nike is NKE. Financial Results of Investment The companies that I selected for this project were Microsoft Corporation, Ford Corporation, and Nike Corporation. Their company symbol which is exhibited by the National AssociationRead MoreNike, Clothing, Fashion Accessory, Foot Wear, Sports Equipment824 Words   |  4 PagesIntroduction Company Name: Nike, Inc. Industry: Clothing, Fashion Accessory, Foot Wear, Sports Equipment Internet address: www.nike.com Primary SIC code: 3021 - Rubber and Plastics Footwear Primary NAICS Code: 316210 - Footwear Manufacturing Major Products and Services: 1. Nikes major products are; athletic shoes and apparel for soccer, basketball, tennis, football, Running, golf, the Jordan brand, Men’s Training, Women’s Training, Action Sports. 2. Equipment: Nike produces sporting equipmentRead MoreNike vs Adidas1039 Words   |  5 PagesNike, Inc. (IPA: / naÉ ªki/) (NYSE: NKE) is a major publicly traded sportswear and equipment supplier based in the United States. The company is headquartered in Beaverton, near the Portland metropolitan area of Oregon. It is the world s leading supplier of athletic shoes and apparel and a major manufacturer of sports equipment with revenue in excess of $18.6 billion USD in its fiscal year 2008 (ending May 31, 2008). As of 2008, it employed more than 30,000 people worldwide. Nike and Precision CastpartsRead MoreFinancial Report Nike2833 Words   |  12 PagesA financial study showing how the company Nike is performing in the market Financial Report: Nike and its competitors Nike Nike is a $280 billion industry that is highly competitive in the mature market. Some of their main competitors are companies such as Adidas and Puma, which we will analyze in this report to compare and contrast their financial position in the market. As of now, the following graph shows the market share for Nike and our competitors: They are in the industryRead MoreNikes Financial Analysis4313 Words   |  18 PagesDividends 7 Recent stock performance. 8-9 SWOT Analysis 10-12 Final Thoughts 13-14 References 15 Appendixes 16 Abstract The purpose of this paper is to provide investors with comprehensive information on Nike, its financial health and activities, its strength and weaknesses, and whether Nike creates value to its shareholders. This paper will analyze Nikes capital structure, scope of international operations, recent stock performance, and dividend policy. Examine how Nikes international operationsRead MoreNike Marketing Strategy5981 Words   |  24 PagesProfessor Gregory F StiberBy: Brizaida Ribalta, Jessica Halsey and Shereen Hijazi | Nike, Inc. | Marketing Plan Project | Nova Southeastern University H. Wayne Huizenga School of Business amp; Entrepreneurship    Assignment for Course: | MKTP 5005 – Introductory Marketing   Ã‚   | Submitted to: | Gregory F Stiber | Submitted by: | Brizaida Ribalta, Jessica Halsey, Shereen Hijazi. | | | | | | | | | Date of Submission: August 30th, 2012 Title of Assignment: Term ProjectRead MoreNike Inc. : Financial And Profitability1822 Words   |  8 Pagesestablished by Bill Bowerman Philip Knight, became Nike, Inc. on May 30,1972. Nike, Inc. established the Nike swoosh logo and the â€Å"Just Do It† trademark. Nike. Inc., is one of the largest publicly traded sportswear, athletic shoes apparel company with revenues of $19 billion in 2010 (3). NIKE, Inc. headquartered is located in Beaverton, Oregon. NIKE, Inc. sells merchandises through distributors, licensees, and subsidiaries in 120 countries globally. NIKE, Inc. has experienced generous amount of financialRead MoreNike Inc. : Financial And Profitability2053 Words   |  9 Pagesestablished by Bill Bowerman Philip Knight, became Nike, Inc. on May 30,1972. Nike, Inc. established the Nike swoosh logo and the â€Å"Just Do It† trademark. Nike. Inc., is one of the largest publicly traded sportswear, athletic shoes apparel company with revenues of $19 billion i n 2010 (3). NIKE, Inc. headquartered is located in Beaverton, Oregon. NIKE, Inc. sells merchandises through distributors, licensees, and subsidiaries in 120 countries globally. NIKE, Inc. has experienced generous amount of financialRead MoreEssay about Nike, Inc vs. Toys R Us1476 Words   |  6 Pages NIKE, INC VS TOYS R U Page LIST OF ILLUSTRATIONS†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.2 INTRODUCTION†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.4 nbsp;nbsp;nbsp;nbsp;nbsp;Procedures†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..4 nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp; COMPANIES.........†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦...4 COMAPARISONS†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦7 GROWTH†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..9 CONCLUSION AND RECOMMENDATIONS†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..11 REFERENCES†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..12