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43. Theorem Of Pythagoras 2.10 Special Quadratic Equations. Theorem of Pythagoras. from Basic Algebra One Step at a Time 2002. p. 193 200. Dr. Robert J. Rapalje http://www2.seminolestate.edu/rrapalje/Tech-Prep-Math/Theorem of Pythagoras/Theo

Special Quadratic Equations Theorem of Pythagoras from Basic Algebra: One Step at a Time p. 193 - 200 Dr. Robert J. Rapalje Seminole State College of Florida Sanford, FL 32773 ANSWERS TO ALL EXERCISES ARE INCLUDED AT THE END OF THIS PAGE To see selected solutions in Living C O L O R click here! Before introducing the Theorem of Pythagoras, we begin with some perfect square equations. Perfect square equations (see the first example and the exercises that follow) can be solved by taking the square root of both sides of the equation. This is called the square root property of equations. When you use this property, you must include a "±" (that is, "+" or "-") in order to obtain both solutions of the equation. EXAMPLE 1. Solve the equation x Solution: The solution is essentially to answer the question, "What number can be squared (multiplied times itself!) in order to get 16. There are actually two answers: x = 4 and also x = -4. This answer may be also written as x = ± 4. EXAMPLE 2. Solve the equation x

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45. Pondering An Artist's Perplexing Tribute To The Pythagorean Theorem That's why the title of the work is Meditation on the Theorem of Pythagoras and not simply Theorem of Pythagoras, Bochner noted, and also why art is not an illustration of http://www.maa.org/mathtourist/mathtourist_02_02_09.html

The Mathematical Tourist By Ivars Peterson February 2, 2009 Pondering an Artist's Perplexing Tribute to the Pythagorean Theorem The cover illustration of the January 2009 issue of The College Mathematics Journal Mel Bochner titled Meditation on the Theorem of Pythagoras The artwork references the idea of relating the lengths of the sides of a 3-4-5 right triangle to the areas of the squares on those sides. To create the piece, Bochner used chalk and hazelnuts placed directly on the floor, materials that would have been familiar to Pythagoras. The construction represented his response to a visit to a temple in Metapontum, the city where Pythagoras purportedly died. For some, the artwork represents a mathematical bungle. A contributor to the blog, for example, wrote recently: "If the intent was to illustrate a right triangle, then the arrangement of hazelnuts is off." 360 is the unofficial blog of the Nazareth College math department in Rochester, N.Y., and features contributors from the college, local rival St. John Fisher College, and elsewhere. "To my eye," the commenter continued, "the hazelnut grids look exactly like pins on a Geoboard, or lattice points in the plane. And given that perspective on this image, we see a 2-3-4 triangle, an obtuse triangle, and squares of area 4, 9, and 16." So, from that viewpoint, the mathematics isn't correct.

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48. Pythagorean Theorem Dec 2, 1998 When asked what the Pythagorean Theorem is, students will often state that a2+b2 =c2 where a, b, and c are sides of a right triangle. http://www.ms.uky.edu/~lee/ma502/pythag/pythag.htm

The Pythagorean Theorem Introduction There are an uncountable number of topics that students are expected to cover each year in school. For example, they are expected to learn about right triangles, similar triangles, and polygons. We expect them to learn about angles, lines, and graphs. One of the topics that almost every high school geometry student learns about is the Pythagorean Theorem. When asked what the Pythagorean Theorem is, students will often state that a +b =c where a, b, and c are sides of a right triangle. However, students often don't know why this is true. Most have never proved it. On the pages that follow, there is history, several proofs, and ways for high school students to use the proof in real life situations. To understand the following information, a general knowledge of geometry and algebra should be sufficient. The proofs are not difficult and with some thought it is clear that the Pythagorean theorem works and is important. I. The Pythagorean Theorem To begin, the Pythagorean theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides. (Gardner, 152) One will find the converse of this statement to also be true. The Pythagorean theorem was a mathematical fact that the Babylonians knew and used. However 1000 years later, between the years of 580-500 BC, Pythagoras of Samos was the first to prove the theorem. It is possible that someone proved the theorem before Pythagoras, but no proof has been found. Because of this, Pythagoras is given credit for the first proof. (MacTutor History of Mathematics Archive)

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50. Pythagorean Theorem Lesson By MATHguide In this section, you will learn 1) Pythagoras equation, 2) how The Theorem of Pythagoras can be derived, 3) how to use The Pythagorean Theorem to find the http://www.mathguide.com/lessons/Pythagoras.html

Pythagorean Theorem Home Lessons Search Introduction In this section, you will learn 1) Pythagoras' equation , 2) how The Theorem of Pythagoras can be derived , 3) how to use The Pythagorean Theorem to find the length of a hypotenuse given two sides, and 4) how to use The Pythagorean Theorem to find a leg given the hypotenuse and the other leg. You will also be invited to try our quizmasters at the end of each lesson. The Equation The Pythagorean Theorem is a mathematical relationship between the sides of a right triangle. A right triangle is any triangle that has one right internal angle. Pythagoras stated, if the length of the legs (smallest side) are squared and their sum is found, the sum will be equal to the square of the hypotenuse (longest side). Algebraically speaking, the relationship looks like... The Pythagorean Theorem The legs are traditionally marked with an 'a' and a 'b,' while the hypotenuse is marked with a 'c.' If that is the case, then the formula is a + b = c . The next section will explain how the equation can be derived. Deriving the Relationship The derivation of the algebraic relationship is also not very complicated, as far as most derivations go.

51. BBC - Standard Grade Bitesize Maths II - Theorem Of Pythagoras (Converse) Maths II. Standard Grade Bitesize is the easy to use revision website from BBC Scotland. http://www.bbc.co.uk/scotland/learning/bitesize/standard/maths_ii/measure/conver

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Support the Monkey! Tell All your Friends and Teachers Let Colleges Recruit You Sell Your Books For Cash! Find Free College Money! ... New Title Request Win a $1000 or more Scholarship to college! Please Take our User Survey 6.2 The Theorem of Pythagoras Figure 6.3 D ABC is a right triangle. l (AB) = c l (BC) = a l (CA) = b CD is perpendicular to AB such that D ABC ~ D CBD or l (BC) l (AB) l (CD) a = c x = cx D ABC ~ D ACD or l (AC) l (AB) l (AD) b = c Therefore, from (1) and (2) a + b = cx + cy = c ( x + y ) = c c = c a + b = c The square of the hypotenuse is equal to the sum of the squares of the legs. Converse of Pythagoras Theorem : In a triangle if the square of the longest side is equal to the sum of the squares of the remaining two sides then the longest side is the hypotenuse and the angle opposite to it, is a right angle. Figure 6.4 Given that in D ABC l (AC) l (AB) l (BC) To prove that D ABC is a right triangle or that m ABC = 90 Construct a D PQR such that l (QR) = l (BC)

54. NOVA Online | The Proof | Pythagorean Puzzle | Theorem Demonstrate the Pythagorean Theorem. Think of each side of a right triangle as also being How can I use the Pythagorean theorem to solve real problems? http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html

Demonstrate the Pythagorean Theorem Think of each side of a right triangle as also being a side of a square that's attached to the triangle. The area of a square is any side multiplied by itself. (For example, a x a a On the diagram below, show that a b c , by moving the two small squares to cover the area of the big square. How can I use the Pythagorean theorem to solve real problems? Andrew Wiles Math's Hidden Woman Pythagorean Puzzle ... WGBH Support provided by

55. Math Forum - Mathematics Teacher Bibliography: Right Triangles, Pythagorean Theo Mathematics Teacher Geometry Bibliography Right Triangles and the Theorem of Pythagoras. Hubert Ludwig, Ball State University Back to Geometry Bibliography Contents http://mathforum.org/mathed/mtbib/right.triangles.html

Mathematics Teacher Geometry Bibliography: Right Triangles and the Theorem of Pythagoras Hubert Ludwig, Ball State University Back to Geometry Bibliography: Contents 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ Home The Math Library Quick Reference ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies

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Don't forget to FOLLOW US on Twitter - Become our fan and follow us on Facebook x Home About Subscribe via: RSS EMAIL Art Featured ... Cool GIF Animations of Pythagoras Theorem Posted on 23 May 2010 Everybody of us have contact with Pythagoras Theorem. Some of us hate it, someone love it (like me); but nobody can stay First one gif is made by me, with lot of help of my professor Predrag Janicic. We did it using GCLC (tool for visualizing and teaching geometry, and for producing mathematical illustrations). First we made gclc file, then we create gif of this gclc. At link shown up you can download gclc f ile ting if you using GCL C). Rest of posts is: One good joke about Pythagoras, and (in my opinion) best gif animations of Pythagoras Theorem that I found. At the bottom of post I put incredible Pythagoras monument at Samos. I hope you will enjoy as I did. picture source picture source picture source picture source ... picture source Check out these awesome galleries! Loading... 3 Comments For This Post Stu says: August 18th, 2010 at 10:22 am

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58. Pythagoras' Haven The following window shows a geometrical proof of Pythagoras Theorem. The three buttons, NEXT, BACK, RESTART, allow you to go through the steps of the http://www.math.ubc.ca/~morey/java/pyth/

The following window shows a geometrical proof of Pythagoras' Theorem. The three buttons, NEXT, BACK, RESTART, allow you to go through the steps of the proof. As well, if you would like to repeat the action of the diagram simply click on the image. (The text can be retyped by clicking on the text box). Good luck understanding the proof. This will hopefully turn into a place for geometric proofs of the Pythagorean Theorem the square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides. Take a look at the poorly documented program and its helpers Banner and fillTriangle this hacked from the hotjava people my home page

59. Bochner’s Meditation On The Theorem Of Pythagoras « 360 The January 2009 issue of The College Mathematics Journal has a Pythagorean theme. While the articles consist of the usual mix of varied mathematical topics, most of the http://threesixty360.wordpress.com/2009/01/28/bochners-meditation-on-the-theorem

12 tables, 24 chairs, and plenty of chalk Simple Addition: Apparently not so simple Meditation on the Theorem of Pythagoras By TwoPi The January 2009 issue of The College Mathematics Journal has a Pythagorean theme.  While the articles consist of the usual mix of varied mathematical topics, most of the smaller sidebar inserts contain quotes from books or articles about Pythagoras, and the issue concludes with reviews of recent books by Eli Maor and by Christoph Riedweg on the Pythagorean Theorem and the life of Pythagoras, respectively. I love the simplicity:  illustrating the fundamental ideas of relating the lengths of the sides of a triangle to the areas of the squares on those sides using readily available materials. I do have one nit to pick, though.  If the intent was to illustrate a right triangle, then the arrangement of hazelnuts is off.  To my eye, the hazelnut grids look exactly like pins on a Geoboard, or lattice points in the plane.  And given that perspective on this image, we see a 2-3-4 triangle, an obtuse triangle, and squares of area 4, 9, and 16. I suspect that what was intended was something akin to the following: Here we can view the diameter of each hazelnut as being our unit of length, so that the circular area taken up by each hazelnut suggests the unit of area (the circumscribing square) .

60. Pythagoras' Theorem The beauty of Pythagoras Theorem is its simplicity. But even so, there are many applications of this theorem, which seems to have been known by ancient http://www.mathsisgoodforyou.com/conjecturestheorems/pythagoras.htm

Pythagoras' Theorem home courses topics theorems ... timeline The beauty of Pythagoras' Theorem is its simplicity. But even so, there are many applications of this theorem, which seems to have been known by ancient Babylonians Pythagoras' Theorem states that the sum of squares on two smaller sides of the right angled triangle are equal to the square on hypotenuse: You can try to prove this theorem when you do Pythagoras' Theorem worksheet . Otherwise see some other web pages which have interactive proofs on the left-hand side. See about Pythagoras himself here. See some nice interactive proofs of Pythagoras' Theorem by clicking on the links below: Proof which will remind you of areas of triangles. Proof which works well with our worksheet. Learn about other ancient Greeks contributions to mathematics. Thales lived before Pythagoras . Can you tell when? artefacts numerals concepts people ... babylonians Search WWW Search www.mathsisgoodforyou.com Acknowledgements Contact Mission Statement Tell a friend about this site

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