...Pythagorean Theorem The Pythagorean Theorem is used to show the relationship among the three sides of a right triangle. In simple terms the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Since the fourth century AD, Pythagoras has commonly been given credit for creating the Pythagorean Theorem. The theorem dates back to Pythagorean triples found on Megalithic monuments from circa 2500 in Egypt and northern Europe incorporating right triangles with integer sides. The Middle Kingdom Egyptian papyrus Berlin 6619, written between 2000 and 1786 BC, includes a problem whose solution was a Pythagorean triple. Even though the theorem had been previously utilized by the Babylonians and Indians and no evidence shows that Pythagoras worked on or proved this theorem, he and his students are credited for constructing the first proof. Pythagoras was born between 580 and 572 BC on the island Samos of the coast of Greece. As a young man Pythagoras was advised to head to Memphis in Egypt to study with priests who were renowned for their wisdom. It may have been in Egypt that Pythagoras learned geometric principles that fueled the theorem named after him. Pythagoras later migrated to Croton, Calabria, Italy and established a secret religious cult very similar to the earlier Orphic cult. Toward the end of his life, Pythagoras fled Croton because of a plot against him and his followers, Pythagoreans, by a noble of Croton named...
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...Term Paper On Role of the Pythagoras in the field of mathematics Business Mathematics code Submitted By Team Harmony 1. Faisal Enayet (B1506003) 2. HafijulHasan (B1506007) 3. Plato Khisa (B1506035) 4. FarhanajAnchal (B1506075) 5. K.HusFariha (B1506120) 6. SumaiyaMeher(B1506155) Submitted To Lecturer AKTER KAMAL Business Mathematics Bangladesh University of Professionals Submission on Date: 02/05/2016 BBA 2015; SEC- C LETTER OF TRANSMITTAL 02 may 2016 Akter Kamal Lecturer Faculty of Business Studies Bangladesh University of Professionals Subject: Submission of term paper on “The role of Pythagoras in the field of mathematics” Respected Sir, We the students of BBA, section C, we are very glad to submit you the term paper on the topic of “The role of Pythagoras in the field of mathematics” that you asked us to submit, which is a part of our course requirement. For the purpose of completing the term paper we did a simple research on the provided topic. We have completed our research and assessment on our term paper topic according to your specification and regulation. We have tried our best to gather information according to the requirements and our ability. There may be a few mistakes, because we are still beginner in this line of work but we hope that in future this term paper will remind us not to make the same mistakes again and so this will become a great learning in experience. At last, we would like to thank to you...
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...Random numbers in C++ and The Pythagorean Theorem Literature Review Name Course Date Literature Review The increase in technological advancements has seen a similar increase in the number of computer programs which are designed to command a computer to carry out a given specified task. The number of languages that are available which are used in this creation and design include Java Script, C++, Java and Sage. It is worth noting that while these are the most notable ones, the number of languages in computer programming design might be higher. However, computer programmers argue that the rest of the languages, despite being of equal capabilities, have not met the required usage to warrant widespread literature review. Hiscotta is particularly critical of this in 10 programming languages you should learn in 2014 by asserting that The field of computer programming is particularly important with regards to the increasing use and adoption of the internet use. This has seen the field carve out a distinct field of study which is purely dedicated to the understanding of how the programs work. The first step in the design of the computer programs is the basic understanding of the dynamics that are involved in the working of computers. This forms the initial step which will eventually be accompanied by software writing involving random numbers with the sole undertaking of coming up with a particular outcome. Of critical importance is the adherence to source code representation...
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...Born during 570 BC on an island shaped as a peninsula called Samos, Pythagoras, the most well-known philosopher/ mathematician now in days, grew up with a wealthy family which provided him with an education. While growing, Pythagoras had many tutors and sophists that lead him to the path in which he took of math. At the age of 18, Pythagoras meets and got influenced extraordinary by a master of math and astronomy called Thales. Since back then, all the variety of science and math that we now have, were very limited due to the lack of scientific discovery. The main section of study before was philosophy, and years after, a cluster of subject’s appeared with the root word “logos” meaning the study of something that requires logic. Furthermore,...
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...Mat 105 Midterm Pythagoras One of the ways to really learn about the history of mathematics and its contribution to the living standard of people is by looking into the lives and work history of some of the greatest people who either directly or indirectly has play an important role in the history of mathematics. One of those people is Pythagoras. Pythagoras (circa 572-circa 495 BC) was born at Samos. He then moved to croton in Southern Italy mainly to escape persecution. While in Croton he founded a group of followers who today are referred to many people as Pythagoreans and these groups of people are sometimes regarded by many as a religious society, cult, or a social movement. Pythagoras has contributed immensely to many important aspects such as Philosophy, Mathematics, Mystic, and Science but today he is best known by many people around the world for a theorem named after him known as the Pythagoras theorem. This is a theorem in geometry that states that in a right angle triangle, the area of the square on the hypotenuse is equals to the sum of the areas of the squares of the other two sides and this can be mathematically represented as follow: A2 + B2 = C2 According to a website known as the math open references, among the key things Pythagoras believes in is as follow: “All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understand through mathematics.” However, one major...
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...The technique of generalization, which is about developing general principles with broad applications, rather than rules with specific use. The theorem developed by Pythagoras was true not only for the 3:4:5 triangle, but it was a principle applicable to any other right triangle, regardless of its dimensions. Furthermore, the theorem showed that a triangle is a right triangle if, and only if, the square of the longest side matches the sum of the squares of the remaining two sides: the right angle lay where the two shorter sides met. 3. The art of deductive reasoning. This is about having a set of initial general statements or premises and reaching conclusions by working out its logical implications. 4. Mathematics in the sense of demonstrative deductive arguments. By combining deductive reasoning and generalization, mathematics was no longer seen as a static set of rules but rather as a dynamic system capable of complex development. 5. We owe to Pythagoras, or maybe to his followers, these important Greek innovations in the field of...
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...Pythagoras theorem Abstract Pythagoras theorem gives a relationship of the three sides of right angled triangles. It is extended to draw relationship among the interior angles of such right-angles triangles to form what is known as trigonometrical ratios. The theorem has vast application in science and mathematical phenomena. It is also used in the derivation of other theorems. This paper attempts to uniquely explain the theorem by experiment. Calculations and measurements will be done to arrive at stated proofs. I addition, theoretical values (value obtained through calculation) and practical ones are compared to establish the degree of error so allowed. Introduction Pythagoras theorem is mathematically expressed as So that c is the square root of the first two terms The sides as labeled are: a is the adjacent, b the opposite and c the hypotenuse. Therefore, the square of the hypotenuse is equal to the sum of the squares of the opposite and the adjacent. The adjacent can be called the base and the opposite the height of the triangle. These two sides are often referred to as the legs of the triangle and the hypotenuse as the longest side of the triangle. Relationships of the interior angles This is basically the trigonometrical ratios. Included angle is the angle enveloped by any two sides in the triangle. We use capital letters to denote the angles so that A is the angle included by band c. Similarly the rest will be B and C. stated otherwise, c corresponds...
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...History of Geometry Geometry was thoroughly organized in about 300 BC, when the Greek mathematician Euclid gathered what was known at the time, added original work of his own, and arranged 465 propositions into 13 books, called 'Elements'. The books covered not only plane and solid geometry but also much of what is now known as algebra, trigonometry, and advanced arithmetic. Through the ages, the propositions have been rearranged, and many of the proofs are different, but the basic idea presented in the 'Elements' has not changed. In the work facts are not just cataloged but are developed in a fashionable way. Even in 300 BC, geometry was recognized to be not just for mathematicians. Anyone can benefit from the basic learning of geometry, which is how to follow lines of reasoning, how to say precisely what is intended, and especially how to prove basic concepts by following these lines of reasoning. Taking a course in geometry is beneficial for all students, who will find that learning to reason and prove convincingly is necessary for every profession. It is true that not everyone must prove things, but everyone is exposed to proof. Politicians, advertisers, and many other people try to offer convincing arguments. Anyone who cannot tell a good proof from a bad one may easily be persuaded in the wrong direction. Geometry provides a simplified universe, where points and lines obey believable rules and where conclusions are easily verified. By first studying how to reason in...
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...three forces on a diagram with a pair of x and y axes. Find the angle of each force with the x-axis. This angle is called the reference angle, and is the one used to calculate sines and cosines. Next compute the x- and y-components of the three forces, placing like components in columns. Place plus or minus signs on the various quantities according to whether an x-component is to the right or left of the origin, or whether a y-component is up or down relative to the origin. Add the columns with regard to sign (subtracting the minus quantities), and place the correct sign on each sum. The resulting quantities are the x- and y-components of the resultant. Since they are forces at right angles to each other, they are combined by the Pythagorean Theorem. The angle of the resultant is found by the fact that the ratio of the y-component to the x-component is the tangent of the angle of the resultant with the x-axis. Make a new drawing showing the two components of the resultant along the x- and...
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...Philosophy 390M Thinking About Thinking What does it mean to think? This question may have a lot of different answers depending on who you ask You may get as simple of explanation as picturing a cat in your head. Or you could Google it and come up with the definition of “think” which is directing one’s attention toward something or to have a particular opinion idea or belief about someone or something. People in the science field may try to say that thinking is brain activity. Someone may have a answer completely different from any of these, but are these examples really thinking? I believe that true thinking is something far more than the simple idea of a cat or someone’s opinion of something. Before we can figure out what it means to think we have to look at what it is not. First of all, thinking is not remembering which is easily confused on a daily basis. When try to remember something we say that we are trying to think, but we are not. We are trying to recall something to our memory such as a past experience or the name of person you met last week You are not trying to think of that persons name because they already have one, you are simply trying to put a face and name together. Which brings me to my next point, thinking is not puzzle solving. Putting something together as simple as a four year olds puzzle or as complex as a car motor require the same amount of thinking, none. Each piece of the puzzle has only one way in which it will work. We may figure out how they fit...
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...Running head: Pythagorean Quadratic Pythagorean Quadratic Sharlee M. Walker MAT 221 Instructor Xiaolong Yao December 2, 2013 Pythagorean Quadratic Ahmed’s half of the map doesn’t indicate which direction the 2x + 6 paces should go, we can assume that his and Vanessa’s paces should end up in the same place. I did this out on scratch piece of paper and I saw that it forms a right triangle with 2x + 6 being the length of the hypotenuse, and x and 2x + 4 being the legs of the triangle. Now I know how I can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, these lengths have the formula of a2 + b2 = c2. Let a = x, and b = 2x + 4, so that c = 2x + 6. Then, by putting these measurements into the Theorem equation we have x2 + (2x + 4)2 = (2x + 6)2. The binomials into the Pythagorean Thermo x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36 are the binomials squared. Then 4x2 on both sides of the equation which can be (-4x2 -4x2) subtracted out first leaving the equation to be x2 + 16x + 16 = 24x + 36. Next we should subtract 16x from both sides of equation, which then leaves us with: x2 +16 = 8x + 36. The next step would then be to subtract 36 from both sides to get a result of. x2 -20= 8x. Finally we need to subtract 8x from both sides to get x2 – 8x...
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...Buried Treasure Allen Raikes MAT 221 DR. Steven Flanders Ahmed and Vanessa has a treasure that needs to be located. It’s up to me and to help find it, I will do that by using the Pythagorean quadratic. On page 371 we learned that the Ahmed has a half of the map and Vanessa has the other half. Ahmed half in say the treasure is buried in the desert 2x+6 paces from Castle Rock and Vanessa half says that when she gets to Castle Rock to walk x paces to the north, and then walk 2x+4 paces to the east. So with all the information I have I need to find x. the Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, which have of a relationship of a2+b2=c2. In this problem I will let a=x, and b= 2x+4, and c=2x+6. So know it time to put the measurements into the Theorem equation; 1) X2+ (2x+4)2=(2x+6)2 this is the Pythagorean Theorem 2) X2+4x2+16x+16 = 4x2+ 24x+36 are the binomials squared 3) 4x2 & 4x2 on both sides can be subtracted out. 4) X2+16x+16 = 24x +36 subtract 16x from both sides 5) X2+16 = 8x+36 now subtract 36 from both sides 6) X2-20 = 8x 7) X2-8x-20=0 this is the quadratic equation to solve by factoring using the zero factor. 8) (x-)(x+) Since the coefficient of x2 is 1 we have to start with pair of () is the 20 in negative there will be one + and one – in the binomials. 9) -2, 10: -10,2: -5,4; -4, -5 10) Looks I’m going to use -10 and 2 is...
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...Assignment 5 1 Assignment 5 DeJuan Stanley MAT 221 Prof Timothy Kilgore June 2, 2014 MAT 221 Week 5 Assignment Buried treasure. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x? The key to solving this equation is to use the Pythagorean Theorem which has a right angle in the equation with a & b equaling side c. Based on the example we know that we will have to use the formula A^2 + B^2 = C^2. What we know is that Ahmed’s half of the map is 2x + 6 = treasure, which would be how far he would need to walk, (A^2). Vanessa’s map needs to show her how to get to the North of Castle Rock, which is 2x + 4, (C^2). We are trying to solve for X (side B). Vanessa is forming a 90 degree angle from point B and walk (2x + 4) until she made it to C. The formula we would use to solve for X is the following: (2x + 6)^2 = x^2 + (2x + 4)^2 4x^2 + 24x + 36 = x^2 +4x^2 + 16x + 16 The next step would be to combine like terms, multiplying, adding, and subtracting. 24x + 36 = x^2 + 16x + 16 -24x -24x 36 = x^2 – 8x + 16 -36 -36 Now we have a quadratic...
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...x 10-27 kg, moves along the positive y-axis with a speed of 6.0 x 106 m/s. Another particle of mass 8.4 x 10-27 kg, moves along the positive x-axis with a speed of 4.0 x 106 m/s. Determine the third particle’s speed and direction of motion. (Assume that mass is conserved) Write down what you know mnucl = 17 x 10-27 kg m1 = 5.0 x 10-27 kg m2 = 8.4 x 10-27 kg m3 = mnucl – (m1 + m2) = 17 x 10-27 kg – (5.0 x 10-27 kg + 8.4 x 10-27 kg) = 3.6 x 10-27 kg vnuci = 0 m/s v1 = 6.0 x 106 m/s @ y-axis v2 = 4.0 x 106 m/s @ x-axis v3 = ? Draw a vector diagram of the momentum Solve for the momentum of the third particle and then find its velocity Right angled triangle so use Pythagorean Theorem P12 + P22 = P32 therefore: ( (P12 + P22) = P3 ( ((m1v1)2 + (m2v2)2) = P3 ( ((5.0 x 10 –27 kg)(6.0x106m/s))2 + (8.4 x 10-27kg)(4.0 x 106 m/s))2 = P3 ((2.0 x 10-39 kg2m2/s2) = 4.50 x 10-20 kgm/s = P3 v3 = P3 / m3 = 4.50 x 10-20 kgm/s / 3.6 x 10-27 kg = 12.5 x 106 m/s Use...
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...equations, radicals, roots, plane geometry, and verbal problems. | Course Objectives: | Upon successful completion of this course, the student should be able to: * perform basic functions with rational numbers, including integers; * simplify expressions containing exponents; * use the order of operations agreement; * read and interpret various graph formats; * calculate mean, median, and mode of data sets; * determine the probability of an event; * work with metric units; * evaluate and simplify variable expressions; * solve basic algebraic equations; * define and describe geometric concepts, including angles and plane figures; * calculate perimeter, area and volume of geometric figures and solids; * use the Pythagorean Theorem to solve for the unknown side of a right triangle; * interpret the rectangular coordinate system and graph basic linear equations and functions; * complete daily tasks in a timely manner; and * work...
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