Knotting Special!
Knotting Special! The investigation of knots began as a response to Lord Kelvin's belief that atoms were knots in the aether, and that chemical properties of the atoms were related to the type of knot. In 1877, P.G. Tait began an attempt at enumerating the knots, and it took him (and work by C.N. Little) 23 years to enumerate the knots up to ten crossings. (Livingston, 1993, p1-2) The focus then, is to create a list of all the knots, and to include each knot only once. A knot may appear to be completely different to another, but in fact may be the same knot, deformed by several twists and turns of the rope forming the knot. In this project, we focus on some of the earlier attempts to distinguish knots, from the trivial looped string (the unknot), and from other knots that may appear to be the same, but may not in fact be. The project passes through the following areas: Reidermeister Moves - the rules for deforming knots Knot Colouring - A basic attempt at distinguishing knots Labelling mod p - A more elaborate 'colouring' procedure Alexander Polynomials - The first polynomial used to distinguish knots Joining of knots - what happens to their Alexander Polynomials Kauffman's construction of the Jones Polynomial However, Lord Kelvin was mistaken about atoms being knots (although physicists now have something called Super-string theory, which may evoke memories of
admin in business
Introduction This coursework is for Unit 20, which is also called Administrative Operations (or Admin Ops) for the Business AVCE course. In this coursework, I have to show I' am capable of showing a variety of administrative skills for a project of my own choice. I have chosen to base my project on the Old Bailey. In order to carry out my administrative skills, I had to carry out an activity such as, setting up and participating in an away day trip to an organisation for at least six people, in which I' am the key administrator. I also have to show knowledge and understanding of the roles of administrators in organisations. In this coursework I' am required to work in a group of people that have specific roles in the group and plan and organize (or administer) our own event for AVCE Business Studies Year 2, unit 20 - Admin Ops. Our event has to be well planned and multi-layered, as this will allow each individual in the group to act out their role. My group is built up of 6 people. They are, Rachel, Chris, Sophie, Asif, Ashraf and me. We have all worked together in Unit 1 (Business At Work) and have all obtained experience of producing information. Examples are in, Unit 3, 4 and 10 (Marketing, HR and Customer Service). We all set each other positions or roles in the group in order to get our event started up. Below are my group's roles/positions. * Rachel - Boss *
Suffocating.
Suffocating 2027 March 7th It scares me more with each day that comes, walking down the streets with people coughing all around me. It just keeps getting worse and doesn't stop. I don't think life could ever return to the way it used to be. As I walk down the street, raindrops start to fall on the ground and with each fall a load of dust lifts up making people cough even harder. I pick up my pace but so does the rain and soon I find it hard to see the way home. As I run down the street I can hear all around me that unforgettable sound. That's what kills people now, not cancer like back in the day. It's a good thing I know my way around even with my eyes shut, which is practically how I am now. I might as well be blindfolded. I keep on running I don't want to stop, because I can't stand the idea of being as I'll as them. Finally there's my house and as I walk in I can breathe again. Ah, the sweet taste of fresh air. You can't get that anywhere else; this is the best thing around. The inside of my house is infested with plants and all sorts of different flowers, that's why I'm still living at 40. Most of other people don't get this far in their life and that is why I am so thankful for these plants, they give me life. My whole house is like a rainforest, not many people get to find out this. I live alone and everyone I know has died a long time ago. Apart from the very
It is so hot, that is the thought that has been running through my head all night, now it is 6:30am and my alarm is ringing...
It is so hot, that is the thought that has been running through my head all night, now it is 6:30am and my alarm is ringing... I rolled out of the king size bed in the middle of the master bedroom in a house I had recently purchased, the house more less completely covered with marble, was still ridiculously hot with out air-conditioning in very humid South Florida, no matter for this will all be taken care of by the decorator by the time I return to this part of the world, and I wont have to deal with this irritating nonsense. I told Tommy to be ready to leave at 7:15am, so that gave me time to have a shower and get ready, usually I would not of hurried of to get dressed before smoking my usual morning cigarette, but due to being awake most of the night I has already smoked enough in bed. After my shower I put on a black suit and shoes, a red tie, and a pair of Armani sunglasses. And went down to the kitchen. At the bottom of the stairs sat my luggage, two black leather suitcases and my briefcase. Tommy met me in the kitchen; he made me a cup of coffee, and put my bags in the limo. I met him in the car a few minutes later. It was about an hours drive to the airport in which time I slept. When we arrived at the airport it was a short wait in the First Class line to check in. Tommy and I then proceeded to the First Class lounge, where we sat for about 40 minutes before boarding
Duke of Edinburugh's Silver award - Expedition Log Book.
Purposes For The Expedition I had several purposes for this expedition. My first was to improve on my map and navigation skills as, although I did know how to navigate, I had never really put it into practice because I had always been in groups with a definite map reader however, this time, we did not and so I wanted to get involved with navigation. My second purpose was to get to know Laura better. I have spent a large amount of time with Mia, Erin and Frankie before however, I had never really spoken to Laura before and I think one of the best things about D of E is getting to know people you didn't know before. By the end of the expedition I knew a lot more about Laura and the others. My third purpose was to improve at walking long distances as I find this very difficult because I am very unfit! Having done a gold practice before, I was hoping that I wouldn't find this too much of a challenge but I still found it quite tough at some points, like when walking up Phen-y-Ghent! I was very pleased that I could keep up with the group as in the past I haven't been able to so, during the course of my practices I must have improved! My final purpose was research for the project I am doing which is 'Tourism in The Yorkshire Dales.' I chose this project because I am interested in the way that tourism can affect an area like this and what places like the Yorkshire Dales have
Algebra Coursework (payphone problem).
Algebra Coursework (payphone problem) Introduction A pay phone will take only 10p, 20p, 50p, and £1 coins. A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. To make a call costing 50p, she could put in the coins in any order; 20p, 20p, 10p or 10p, 20p, 20p or 10p, 10p, 20p, 10p There are more ways of making 50p with only 10p and 20p coins. . The woman is going to make a phone call costing any multiple of 10p. I am going to investigate the number of different ways she could put the 10p and 20p coins into the payphone. A man also wants to use the pay phone. He has plenty of 10p and 50p coins. He has no other coins. He wishes to make a telephone call costing any multiple of 10p. 2. I am going to investigate the number of different ways he has of entering the 10p and 50p coins into the telephone. 3. I will then investigate the more general cases leading into special cases. There can be made 8 different combinations using only 10p and 20p coins to make a call costing 50p. These are; . 10,10,10,10,10,10 2. 10,10,10,20 3. 20,10,10,10 4. 10,20,10,10 5. 10,10,20,10 6. 10,20,20 7. 20,10,20 8. 20,20,10 . The woman is going to make a phone call costing any multiple of 10p. Investigate the number of different ways she could put the 10p and 20p coins into the pay phone. Multiple of 10p Combinations
The woman is going to make a phone call costing any multiple of 10p. I am going to investigate the number of different ways she could put the 10p and 20p coins into the payphone.
Introduction A pay phone will take only 10p, 20p, 50p, and £1 coins. A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. To make a call costing 50p, she could put in the coins in any order; 20p, 20p, 10p or 10p, 20p, 20p or 10p, 10p, 20p, 10p There are more ways of making 50p with only 10p and 20p coins. . The woman is going to make a phone call costing any multiple of 10p. I am going to investigate the number of different ways she could put the 10p and 20p coins into the payphone. A man also wants to use the pay phone. He has plenty of 10p and 50p coins. He has no other coins. He wishes to make a telephone call costing any multiple of 10p. 2. I am going to investigate the number of different ways he has of entering the 10p and 50p coins into the telephone. 3. I will then investigate the more general cases leading into special cases. There can be made 8 different combinations using only 10p and 20p coins to make a call costing 50p. These are; . 10,10,10,10,10,10 2. 10,10,10,20 3. 20,10,10,10 4. 10,20,10,10 5. 10,10,20,10 6. 10,20,20 7. 20,10,20 8. 20,20,10 . The woman is going to make a phone call costing any multiple of 10p. Investigate the number of different ways she could put the 10p and 20p coins into the pay phone. Multiple of 10p Combinations for 10p, 20p Total no of combinations
The Dice Game - Probabilities.
The Dice Game Three players A, B, C play a game with a single dice. The rules of the game are: Player A ALWAYS goes first. A rolls the dice. If the dice lands showing a 1 then A wins the game. If A does not throw a 1 then B has a turn. B rolls the dice. If the dice lands showing a 2 or a 3 then B wins the game. If B does not throw a 2 or 3, then C has a turn. C rolls the dice. If the dice lands showing a 4 or a 5 or a 6 then C wins the game. If C does not throw a 4 or a 5 or a 6 then A starts again. The procedure continues until there is a winner. INVESTIGATE ANY OR ALL OF . The probabilities of each A, B, or C winning the game. 2. Who will be the most likely winner? 3. The most likely length of the game in terms of the number of rolls of the dice to produce a winner. I've decided to investigate question 1 out of the three. Player A has to throw a 1 to win the game. This means that in terms of probability, the probability that A will win is going to be (1/6). The probability that A will loose is (5/6) because: - (1/6) = (5/6) Player B has to throw a 2 or a 3 to win the game. This means that the probability that B will win would be (2/6), because: (1/6) + (1/6) = (2/6) The probability that B will loose would be (4/6) because that is the remainder of 1: - (2/6) = (4/6) Player C has to throw a 4 or a 5 or a 6 to win the game. This means that the
The Framework Knitting Museum: An Accurate Reflection of History or Not?
The Framework Knitting Museum: An Accurate Reflection of History or Not? The Framework Knitter and the Bag Hosier lived different lifestyles and worked in different conditions, however, there also were similarities between them; and I am going to compare and give reasons for both in this part of my essay. Firstly, I will compare and look at the similarities in lifestyle; afterwards I will move on to overlooking work conditions. The framework knitter received very poor pay, and you can see this by the cleanliness and overall state of his home; his dishes were black and his knives and forks also, the dishes contained many cracks and looked unfit to eat off. He ate upon a rickety old wooden table and sat on old wooden chairs. However, the bag hosier had expensive, high quality china, and there were surfaces in the living room that could be used to eat on, it was easy to tell that the reason for these differences was the difference in wages. When cooking both would use the fireplace to heat their pots and pans, as there were no electric ways of cooking. The bag hosier's cottage contained a scullery, which would be their "kitchen", it was used to clean pots and pans and ready foods for dinner, everything in there would be done by hand. In the Framework Knitter's cottage he would have had to clean his pots by hand, but didn't have good equipment in with which to do so because he
Commentary on One or More Events at the Olympic Games Based on Primary Evidence
The Olympic Games Commentary on One or More Events at the Olympic Games Based on Primary Evidence Myron: Good morning and welcome to day two of the Olympic Games in Olympia held in the honour of Zeus. I'm Myron and with me is Phayllos. Greetings to all the listeners who have joined us at these very hot and exciting Games. I do believe that this has probably been one of the hottest days in this lunar month, so far. If this is the first time you have tuned into us, then you missed the swearing-in ceremony for competitors and judges before the altar and statue of Zeus. You missed public sacrifices in the Altis, orations by well-known philosophers and recital by poets and historians and this is just to name but a few. Remember this prestigious event is only held every four years so don't miss this one or you'll be sorry for the next four years! You've joined me for the chariot racing, which has not started just yet so Phayllos will tell us about the legendary origin of the chariot races. Phayllos: Thank you Myron, hello and welcome to all the listeners who have joined us today. I am Phayllos and before I tell you the origin of the chariot racing, I just have to thank my hero, Herakles who is the founder of the Games. These Olympic Games are to celebrate one of his twelve labours which was the cleaning of King Augeas' stables, which he successfully completed. I