...The history of Geometry started in Ancient Egypt around 3000 B.C.E. Egyptians used an early stage of geometry when surveying the land, construction of pyramids, and astronomy. And around 2900 B.C.E. they began using their knowledge to construct pyramids with four triangular faces and a square base. It was created because it was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. It was used in Babylonia and in the Indus Valley by the Egyptians, Babylonians, and the people of the Indus Valley but the creators were Pythagoras, Euclid, Archimedes, and Thales. Pythagoras was the first pure mathematician although we know little about his mathematical achievements. He was also, a greek philosopher and created a movement called Pythagoreanism. Euclid is sometimes called Euclid of Alexandria. He is also called the “Father of Geometry” and his elements were one of the most influential works in the history of mathematics, which served as a textbook used for teaching mathematics (especially Geometry) from when it was published till the late 19th century to early 20th century. In the Elements he included the principles of what is now called Euclidean Geometry. Euclidean Geometry is a mathematical system and consists of in a small set of appealing postulates that are accepted as true. In fact, Euclid was able to come up with a great...
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...English Advanced for Business B Name Zhou Yaping Student number 1323440 Assignment Title Report Lecturer’s Name Dr Tony Shannon-Little BA (Hons) English for International Business Communication Wolverhampton: School of Law, Social Sciences and Communication Contents Executive Summary 1 Terms of Reference 2 Analysis 3 Participation 3 Group work 3 Evaluation of Content 4 Animal texting case 4 My language use & development 5 Recommendations 5 Conclusions 6 References 7 Appendices 8 Appendices 1 8 Appendices 2 10 Appendices 3 12 Executive Summary Firstly, the report analysed participation and group work in two parts. It has expressed that how to be participation in a group and theorises or experiences of group works. Following that, it has discussed evaluation of group study and individual development. These reports recommend that in a group work, people should focus on formal language use, cooperation, communication, information and time and task management. Terms of Reference In this report, it has analysed our group work in this module, also evaluate case of animal testing and personal development of language use. Besides, it gave some recommendations for group work and self-development. It is in order to continue development of our skills and learn the theories or task management with animal testing case. Analysis Participation Participation is important if you...
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...LANGUAGE AND GROUP MEMBERSHIP http://skateboardingaustralia.org.au/About-Us/about-us Provide some general discussion on the use of language associated with this hobby/interest. What do you first notice about the language of the website? This website has a mixture of both moderately formal language with little jargon to having more informal language with more jargon, depending on what page of the website you are on. The more informal page of the website is the ‘Goldy Grail’ page which uses informal words like ‘damn’ ‘gammin’’ ‘crap’ ‘go figure’ and ‘dodged a bullet’ and jargon like ‘ally-oops’ ‘squeegied’ ‘full-pipe’ ‘1-foot to the fakies’ ‘lip slides’ ‘nose grinds’ ‘over-vert stalefish in the pipe’ and ‘hosoi-esque aerials’. Other pages in the website like ‘About us’, ‘Learn to skate’ and ‘Hubs’ use more formal language and less jargon. They use words like ‘collective approach’ ‘collaborate’ ‘subculture’ ‘linkage’ ‘chronicle’ and ‘fundamental platform’. Who is the target audience of this website? What assumptions can you make about age, gender, interests, occupation, aspiration and education? What language features help to convey this? The target audience is for anyone who has an interest in skating on a professional or amateur level. It is most likely aimed at people in high school and older because the lexicon that is used is too complex for younger children. I don’t think that this website is aimed at a particular gender but it would lean more towards males because...
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...Generalization: A generalization of this problem as well as its preceding problem (When is Cheryl’s Birthday) would be to connect these questions to the ideas of the birthday paradox, and an even bigger idea of the pigeonhole principle. In math, the pigeonhole principle states that if there are n items to be put into m containers, with the criteria that n > m, then at least one container will hold more than one item. (Herstein, 1964) Another way to explain this principle in a more quantitative way would be to say that for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. (Youtube) This pigeonhole principle can well be applied to what is known as the birthday paradox or birthday problem which is the question that if there are n number of people in a room what is the probability that at least 2 of them will have the same birthday. Using the pigeonhole principle if we do not count leap year then with 366 people in the room there is guaranteed to be a pair of people who share the same birthday as there are 365 possible days to choose from. (Linz, 2006) The paradox also goes on further to explain that even with a group of 70 people there are 99.9% chances of 2 or more people sharing the same birthday and 50% chances with only 23 people, with these conclusions being made with the above assumption that we are going by a 365 day calendar excluding the...
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...Enviro Voraxial® Technology 821 NW 57th Place, Fort Lauderdale, FL 33309 Phone 954.958.9968; Fax: 954.958.8057; E-mail: info@evtn.com Website: www.evtn.com Case Study Voraxial Oil Spill Recovery System A System Designed for Service on Open Waters ® Summary: April 2010 This Case Study summarizes the design and function of the Voraxial® Oil Spill Recovery System. The Voraxial® Oil Spill Recovery System is designed to recover the free floating oil from surface waters and industrial facility wastewater ponds. The oil is separated by a Voraxial Separator into a clean water stream and a concentrated oil steam. The water is returned to the water source, or discharged, and the recovered oil stream is collected in a storage tank. The Voraxial Separator has high collection/separation efficiency for the free oil in spills. The Voraxial Separator has demonstrated separation efficiencies in the 95% to 100% range for this oil condition. In addition to high collection/separation efficiency, there are many other benefits provided by the Voraxial Separator. These benefits include: operation at low pressure, high flow rates, low energy requirements, an open low shear non-clogging impeller, treatment of a wide range of flows, high “G” force, and a compact unit with small footprint. In order to protect The System Equipment against ingress of water on open waters all electrical equipment is designed to meet IP66 standards. IP66 standards require complete protection against strong jets of water...
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...1) First hole is played by the golfer Assuming the golfer plays Kth hole. Since he played the kth hole he must also play the k+1th (given) =>Therefore the golfer will play all the holes 2) a) P(1) is the statement 1^3 = ((1(1 + 1)/2)^2 b) Both sides of eqn evaluate to 1. c) Induction hypothesis is P(k) for positive integer k the statement 1^3+ 2^3+· · ·+k^3 = (k(k+ 1)/2)^2 d) Lets assume P(k) holds, we have to show that P(k + 1) is true, we have to derive equation 1^3+2^3+· · ·+k^3+(k+1)^3 = ((k + 1)(k + 2)/2)^2 e) Add (k + 1) ^3 to LHS and RHS of equation in induction hypothesis. Showing that LHS in d) is equal to (k(k + 1)/2) ^2 + (k + 1) ^3. We find this equals ((k + 1)(k + 2)/2)^2. Therefore LHS = RHS f) We did the basis step and the inductive step. Principle of mathematical induction now proves that P(n) is true for all positive integers n. 3) 4) Base Case(s): Notice that we can form 18 cents of postage using 6 3-cent stamps. We can form 19 cents of postage using 1 10-cent stamp and 3 3-cent stamps. We can form 20 cents of postage using2 10-cent stamps. Induction Step: Assume we form any postage i with 18 ≤ i ≤ n, with n ≥ 20.Consider forming n + 1 cents of postage. By strong induction hypothesis, since n ≥ 20, n − 2 ≥ 18, we then have n − 2 cents of postage. Adding single three cent stamp then gives n + 1 cents of postage. Hence proved 5) The assumption in the inductive step is that there always is minimum 1 3-cent stamp or minimum 2 4-cent stamps. Proof is also flawed since...
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...Mirror Realism Matt Leonard Let’s suppose that spacetime substantivalism is true. In other words, space- time regions exist independently of the objects that occupy them. They shouldn’t be thought of as mere ‘things’ or ‘events’ which happen to stand in spatiotemporal relations.1 Even with such an assumption, there is a lot to disagree about. And so, for the moment, let’s make a few more assumptions: let’s suppose that (1) material objects exist independently of spacetime re- gions (i.e., material objects are not identical to spacetime regions) and (2) material objects are exactly located at certain spacetime regions. Given this setup, it seems right to say that material objects and spacetime regions pos- sess mereological and topological properties, and enter into mereological and topological relations. Now consider the following question about the relation- ship between spacetime and material objects: are material objects a perfect mirror of their spacetime regions? We might ask: if two objects share some mereotopological relation (for instance, if one is a part of the other, or if one is connected to the other), does it follow that the regions of space at which the objects are located, share the same relation? Similarly, if two regions of space are related in some mereotopological way, are the objects located at those regions, related in the same way? If an object x is a proper part of some other object y, does it follow that the location, lx, of the former object is a proper...
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...profile report Mr Andy Lin 2016 Questionnaire 星星星 星星星 Report Type Enhanced Report Style Informal Textual Content Standard Report: Classic Category IMBA20160410 Gender Male Report Printed 11 四四 四四 11 行行行行行行 Candidate Analysed on behalf of 實實實實實實實 Prepared by DISC 2016 Phrase-based External Internal Summary Shifts PRIVATE AND CONFIDENTIAL Any purely behavioural tool should never be used to make a recruitment or redeployment decision unsupported by other techniques. I S C D I S C D I S C D Discus Licence 0044-14-05-15172341 / 0033-08-11-00012572, licensed to ?Copyright 1995-2016 Axiom Internet Group Ltd. R Discus is a registered trademark of Axiom Internet Group Ltd. (4.0.822) I S C 實實實實實實實 D 1 . Discus personality profile report for Mr Andy Lin DISC Profile Series Internal D External I S C D I Summary S C D I Shifts S C D I S C Internal Profile The Internal Profile reflects the candidate's true motivations and desires. This is the type of behaviour that often appears outside a working environment, or when an individual is placed under pressure. Internal Factors Dominance 37% Influence 44% Steadiness 56% Compliance 90% External Profile The External Profile describes the candidate's perception of the type of behaviour they should ideally project...
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...Wall-E created this movie with a universal message of what will happen to our society over time if we do not stop relying on technology. Thousands of years have passed that we have lived with technology, and it has worked in our benefit in many circumstances. However, it has become an addiction, distraction and a nuisance to our society. Society craves the latest technology, and we want more. I will admit I can’t last without my cell phone. Unlike the past however, humans are buried in technology in which we depend on. Cavemen many years ago survived without technology; why is it now that we have become so reliant on it? Just as the passengers on the Axiom in Wall-E, we are controlled and driven by technology. But, what will society do if technology takes a turn for the worse and goes against us? In the film the robots on the Axiom turned against the passengers to assist Wall-E and Eve in saving the Earth. One-day robots could ultimately turn on society and we will be left with nothing to do. Technology is assisting society in becoming helpless and unable to fend for ourselves. Technology has also created a large impact on communication. When my parents were growing up they were close with all of their neighbors and they talked on a daily basis. The technology we have now didn’t exist back then, and because of this I barely know my neighbors. We are friendly and wave but that’s about it. Technology has caused us to have...
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...It is a common fact of life that with every new day, individuals are infused with a number of uncertainties; some small and miniscule, such as meeting a student next to you in a classroom, while others life-changing and pivotal, including switching careers or becoming a parent. As each new unpredictable day arises, uncertainty fills the air, constantly swarming one’s emotions and daily interactions. While factors of uncertainty revolve around routinely aspects, Charles Berger and Richard Calabrese (1975) narrowed their focus and devised a theory specifically on uncertainty and interpersonal communication. By studying how human communication is used to gain knowledge and create understanding, Berger and Calabrese unveiled the first generation to reducing uncertainty in interpersonal communication (Griffin, 2011). Known as the Uncertainty Reduction Theory (Berger, 1975), its original form focused on how strangers communicate, noting that the “beginnings of personal relationships are usually fraught with uncertainties” (Griffin, 2011, 130). By means of intensive research and ultimately, complete comprehension, it is evident that the Uncertainty Reduction Theory helps scholars correlate uncertainty with interpersonal communication, thus advancing to significant predictions on how people behave when they are uncertain. Before diving into its specific components, it is important to acknowledge the foundation and premise of the Uncertainty Reduction Theory in order to fully grasp...
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...What is a proof? Yes- there is a big leap when we prove something from everyday axioms. But do they not assume the title of axioms once proved? If they were axioms, what is the need to prove it? Does it not reflect the inability of a person to actually see the ‘obvious’ when he is searching for proofs? Let me be clear that I enjoy a well written and elegant proof and am immensely discontent when I am unable to prove a seemingly obvious statement. But is not the fact that my intuition suggests that the statement has to be true reason enough? You may argue that a proof leaves nothing to chance and gives you a guarantee that the statement has to be true. But when you dissect a proof right down to its base axiom, there you will have to rely on an assumption- that our intuition deems valid. I am not here to argue on the basis of the correctness in our underlying assumption of the base axiom. Proofs are merely a way to deduce results from a given premise. And the premise here is the truth of the axiom. I am uncomfortable about the fact that people are willing to accept the intuition behind the base axiom but not the intuition behind the results that follow. True, in most cases it is easier to be aware of the former- and the latter may be hard to see as obvious. A case in point would be Fermat’s last theorem. Andrew Wiles did come up with an absolutely marvellous proof of the theorem- something that puzzled the greatest minds for three and a half centuries. But in those three and...
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...All the people aboard the axiom however seem to be living a secluded life, they never interact with anybody face to face, or walk anywhere, and they are constantly eating fast food. They live such a secluded life that when they are introduced to a new colour for their suits, as to which it says “try blue, it’s the new red” and they all happily change into it. None of the people aboard the axiom really start to pay attention until Wall-E arrives; he accidentally knocks someone off of their chair and then introduces himself to them, giving them their first face to face interaction. He later does it again when he switches off a woman’s screen on her chair, and again introduces himself to her. Pixar make a point of showing that is Wall-E that is the one who shows both us the audience and the people aboard the axiom, what it is to be human, through his love for Eve and his sacrifice for her mission. He’s the one who opens the captain’s eyes with regards to earth and saving...
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...geometries can help one determine our physical space rather than inferring because of past experiences, or in this instance postulates of geometry. Euclidean geometry studies planes and solid figures based on a number of axioms and theories. This is explained using flat spaces, hence the usage of paper, and dry erase boards in classrooms, and other flat planes to illustrate these geometrical standards. Some of Euclid’s concepts are 1. The shortest distances between two points is a straight line. 2. The sum of all angles in a triangle equals one hundred eighty degrees. 3. Perpendicular lines are associated with forming right angles. 4. All right angles are equal 5. Circles can be constructed when the point for the center and a distance of the radius is given. But Euclid is mostly recognized for the parallel postulate. This states that through a point not on a line, there is no more than one line parallel through the line. (Roberts, 2012) These geometries went unchallenged for decades until other forms of geometry was introduced in the early nineteen hundreds, because Euclid’s geometry could not be applied to explain all physical spaces, this gave rise to non- Euclidean geometry. Non Euclidean geometry are in correspondence with axioms when metric geometry or the parallel postulate is replaced, in other words non Euclidean geometry negates Euclid’s parallel postulate. Some popular non Euclidean geometry is hyperbolic or the saddle which states If L...
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...PROBLEMS WITHOUT A CALCULATOR! Formula rearrangement refers to isolating a letter term other than the one already isolated in the formula. Solving formulas in the manner often shortens our work when doing repeated formula evaluations. After we solve the formula for the desired variable, we rewrite the formula with the variable on the left side for convenience and for use in electronic spreadsheets. Problem 1: Solve the "mark up" formula M = S - C for S. To solve the equation above, we will use the Addition Axiom to isolate the variable S by "moving" all terms associated with S by addition away from the variable. The variable associated with S by addition is C. Therefore, we must add C to both sides of the equation. M+C=S-C+C and M + C = S Finally, we rewrite the formula with S on the left S=M+C Problem 2: Solve the interest formula I = PRT for R. It stands for Interest = Principal Time. Rate To solve the equation above, we will use the Multiplication Axiom to isolate the variable R by "moving" all terms associated with R by addition away from the variable. The variables associated by multiplication with R are P T or PT. Therefore, we will multiply both sides of the equation by its reciprocal **, which is . ** Interchanging the numerator and denominator of a fraction results in a fraction that is called the reciprocal of the original fraction. When a number is multiplied by its reciprocal, the product equals 1. Carrying out the multiplications...
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...sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one. The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of rigorous deductive reasoning.[1] Contents [hide] 1 History 2 Description 3 Axiom of induction 4 Example 5 Variants 5.1 Starting at some other number 5.2 Building on n = 2 5.2.1 Example: product rule for the derivative 5.2.2 Example: Pólya's proof that there is no "horse of a different color" 5.3 Induction on more than one counter 5.4 Infinite descent 6 Complete induction 6.1 Transfinite induction 7 Proof of mathematical induction 8 See also 9 Notes 10 References [edit]History In 370 BC, Plato's Parmenides may have contained an early example of an implicit inductive proof.[2] The earliest implicit traces of mathematical induction can be found in Euclid's [3] proof that the number of primes is infinite and in Bhaskara's "cyclic method".[4] An opposite iterated technique, counting down rather than up, is...
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