...mathematical theorems and formulas. One theorem that is particularly renowned is the Pythagorean Theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of any right triangle. While most people have heard of or even used the Pythagorean Theorem, many know little of the man who proved it. Pythagoras was born in 570 BC in Samos, Greece. His father, Mnesarchus, was a merchant from Tyre who traveled abroad. It is rumored that Pythagoras traveled with his father during his early years and was introduced to several influential teachers, including Thales who was a famous Greek philosopher. Several years and many countries later, Pythagoras found himself in Egypt. It was here that he studied at the temple of Diospolis and was also imprisoned during the Persian invasion. During the time he was imprisoned, Pythagoras began to study the religion called Zoroastrianism (Lauer/Schlager, 2001). It was because of these teachings and ideals that Pythagoras eventually moved to Italy. At age 52, while living in Croton, Italy, Pythagoras established the Pythagorean society. It was through this society and his positions in local government that Pythagoras recruited men and women in order to lead them to the pure life with his spiritual and mathematical teachings. Pythagoras believed that number was limiting and gave shape to all matter and he impressed this upon his followers (Gale, 1998). During his time leading the Pythagoreans, Pythagoras...
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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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...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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...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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...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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...A Treasure Hunt at Castle Rock using Pythagorean Quadratic June Tye-Patterson Math 221: Introduction to Algebra Instructor: Shenita Talton 07-13-2014 A Treasure Hunt at Castle Rock using Pythagorean Quadratic For this week assignment we are given a word problem and the use of the Pythagorean Theorem to solve it. We will be helping Ahmed and Vanessa, who both have a half of a map, find buried treasure in the desert somewhere around a place named Castle Rock. Ahmed map says the treasure is 2x+6 paces from Castle rock, whereas, Vanessa map says in order to find the treasure, go to Castle Rock, walk x paces to the north and then walk 2x+4 paces to the east. In order to discover the location of the treasure, we need to factor down the three quadratic expressions by putting the measurements into the Pythagorean Theorem. The first thing we need to do is to write an equation by inserting the binomials into the Pythagorean Theorem, which also states that every right triangle with legs of length have the relationship of a^2+b^2=c^2 x^2+ (2x+4)^2=(2x+6)^2 The binomials into the Pythagorean Theorem. x^2(2x+4) (2x+4)=(2x+6) (2x+6) The equation squared. x^2 4x+8x+8x+16=4x^2+12x+12x+36 Equation FOILED or distributed. x^2+4x^2=5x^2 First two terms added...
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...Pythagorean Quadratic Diane Todd MAT 221 Introduction to Algebra Instructor Alicia Davis September 29, 2013 Treasure hunts have always been a big deal in our home. Having raised five boys, anything to do with an adventure was exciting. Actually, this past June I planned one of my grandsons birthday parties around the theme of pirates and treasure hunting. I had never considered the math that went behind the maps in which I made up. Needless to say, when I saw the question entitled “buried treasure” in our math book, it brought back numerous memories. 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? Even though Ahmed’s half of the map does not tell him which direction the 2x + 6 paces should go, Ahmed can assume that his and Vanessa’s paces should end up in the same place. If I sketch out this scenario on paper, I see that I have a right triangle with 2x + 6 being the length of the hypotenuse, and 2x + 4 being the legs of the triangle. I now 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 of c, these...
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...Consequently, it is believed that Pythagoras was the first person to establish the concept that (“Pythagoras Biography”), “the sum of the angles of a triangle is equal to two right angles and that for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.” Although the discovery of the Pythagoras theorem had already been somewhat found, Pythagoras was the first to prove it and thus got his name on the theorem. It is still unclear on how Pythagoras managed to figure out the theorem, however, the benefits that the explanation provided were magnificent towards the future because it provided man to be able to finally figure out the missing side of a triangle. Consequently, if a shape is bigger than a triangle, the triangle can be placed inside the bigger shape and be used to give an approximation of the length of the segment one is trying to find. Additionally, this new formula is an extraordinary accomplishment due to the fact that the formula didn’t die out throughout the years, and that it’s being used in the present...
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...make a point to emphasize contributions from both Western and non-Western civilizations. This learning module teaches students about the history of the Pythagorean theorem, along with proofs and applications. Feel free to use your own motivational ideas and tailor it to your students! This lesson is geared toward high school Geometry student that have completed a year of Algebra. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups, I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers. Calculators are optional. This lesson addresses the national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning, specifically: • • • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Use visualization, spatial reasoning, and geometric modeling to solve problems Understand and apply basic and advanced properties of the concepts of geometry; Use the Pythagorean theorem...
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...Pythagorean Quadratic Melissa Hernandez MAT221: Introduction to Algebra Instructor Srabasti Dutta August 4, 2014 Pythagorean Quadratic Ever since I can remember when I was a little girl full of curiosity, I enjoyed the thought of finding a buried treasure and thus set out on treasure hunts with my sisters. Depending on how big your imagination is, you can take yourself to exotic locations, around town, or in your very own backyard. Finding buried treasures is a fun activity to do on your own or in a group. In this activity, we will be finding a buried treasure near Castle Rock with Ahmed and Vanessa. The assignment reads; 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? (Dugopolski, 2012, p. 371) In this problem, we will use the Pythagorean Theorem which says that when a triangle has a right angle of 90 degrees, and squares are made on each of the three sides, then the biggest square has the exact same area as the other two squares put together. The Pythagorean Theorem can be written as: a^2 + b^2 = c^2 with “c” being the longest side or otherwise called the hypotenuse of the triangle, and “a” and “b” are the...
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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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...Pythagorean Quadratic Treasure Hunters Pythagorean Quadratic Treasure Hunters Introduction to Algebra Treasure Hunters Ahmed and Vanessa both have possession of one half of a complete treasure map. Ahmed’s map shows the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa’s map shows the treasure buried at x paces to the north and 2x + 4 paces to the east. When the two combine information, the location of the buried treasure is going to be a lot easier to find and they can share in the booty loot that they discover. Castle Rock is the lowest left point of the hypotenuse and at the bottom of the left leg and the treasure is at the furthest right point of the right leg. To factor the equation we start with the following, X2+(2x + 4)2 = (2x+6)2 Using the Pythagorean Theorem, a2+2ab+b2 i get a compound X2 +(4x216x+16)=4x2+24x+36 equation. It is then necessary to simplify using the quadratic 5x2+16x+16=4x2+24x+36 equation ax2-bx+c=0 so that I can factor. (x2+2)(x-10)=0 everything is set to zero for the zero factor X = 10 solve for x Plugging the x value for a, b, and c to the legs or the hypotenuse and what this does is it gives me the equation of how many paces it is to the treasure A= 10 B=2(10)+4 = 20+4 = 24 C=2x+6 = 2(10)+6 = 26 In conclusion, castle rock is located at the bottom left of a right hand triangle, and the treasure is 26 paces northeast of Castle...
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...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 issue is because of the high level of secrecy among the Pythagorean society, many people are still not convince or sure whether the entire theorem related to Pythagoras were originally his work. Despite the uncertainty, many people still believes that the mathematical knowledge of him and his followers have make him a very important figure in the history...
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...Running Head: PYTHAGOREAN QUADRATIC Running head should use a shortened version of the title if the title is long! All capital letters for the title and the words Running and Head should be capitalized as well. 1 Pythagorean Quadratic (full title; centered horizontally & vertically) First Name Last Name MAT 221 Dr. xxxxxxxxxxx xxxxxxxxx Date PYTHAGOREAN QUADRATIC 2 Pythagorean Quadratic Be sure to have a centered title on page 1 of your papers!! [The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following paragraph is not an introduction to the paper but rather the beginning of the assignment.] Here is a treasure hunting problem very similar to the one in the textbook (Dugopolski, 2012). This problem involves using the Pythagorean Theorem to find distance between several points. Spanky has half of a treasure map, which indicates treasure is buried 2x + 9 paces from Leaning Rock. Buckwheat has the other half of the treasure map, which says that to find the treasure one must walk x paces to the north from Leaning Rock and then 2x + 6 paces east. Spanky and Buckwheat found that with both bits of information they can solve for x and save themselves a lot of digging. How many paces is x? Even though Spanky’s...
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