81. Pythagoras’ Theorem « What’s New Sep 14, 2007 My favorite proof of the Pythagorean theorem is given by this picture. . I once gave a talk about Pythagoras s theorem and before it I http://terrytao.wordpress.com/2007/09/14/pythagoras-theorem/

Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing ... Subscribe to feed 14 September, 2007 in expository math.HO non-technical area ... Terence Tao My colleague Ricardo Pérez-Marco showed me a very cute proof of In the above diagram, a, b, c are the lengths BC, CA, and AB of the right-angled triangle ACB, while x and y are the areas of the right-angled triangles ADC and CDB respectively. Thus the whole triangle ACB has area x+y. Now observe that the right-angled triangles ADC, CDB, and ACB are all similar (because of all the common angles), and thus their areas are proportional to the square of their respective hypotenuses. In other words, (x,y,x+y) is proportional to is equivalent to the assertion that the matrices and have the same determinant. But it is easy to see geometrically that the linear transformations associated to these matrices differ by a rotation, and the claim follows. Homework: why are the above two proofs essentially the same proof? Share this: Print Email Possibly related posts: (automatically generated) Infinite fields, finite fields, and the Ax-Grothendieck theorem

82. Pythagoras' Theorem | Teachers TV Jan 19, 2010 In this programme from Maths 4 Real series 1, Ben is sporting combats as he prepares to plunge down an aerial ropeway for the sake of http://www.teachers.tv/videos/pythagoras-theorem

Skip to main content Accessibility Register for email updates or Login SEARCH all SUBJECTS Subjects - English ... CPD Quickly access content relevant to you. Log in below or Register now. Email address Password Remember me Bookmark this page Follow Teachers TV Pythagoras' Theorem We have detected that you are accessing this website from outside the United Kingdom. Unfortunately, rights have not been granted for international streaming and downloading of this programme. Duration: 15 mins No Subtitles Published: 20 June 2006 Licence information for Pythagoras' Theorem Part of the series Maths 4 Real Summary In this programme from Maths 4 Real series 1, Ben is sporting combats as he prepares to plunge down an aerial ropeway for the sake of investigating Pythagoras' famous theorem. Katie looks in detail at the special relationship between the sides of a triangle that Pythagoras expressed in his theorem. Save to my viewing log to your viewing log close[x] Viewing log notes (What's this) Start making your notes now or come back later Initial notes: (Why is this video of interest? What points have you identified that you will implement? How will you put what you have learned into practice?)

83. Pythagorean Theorem Apr 23, 2009 The theorem has been known in many cultures, by many names, for many years. Pythagoras, for whom the theorem is named, lived in ancient http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html

+ Text Only Site + Non-Flash Version + Contact Glenn To better understand certain problems involving aircraft and propulsion it is necessary to use some mathematical ideas from trigonometry the study of triangles. Let us begin with some definitions and terminology which we will use on this slide. We start with a right triangle . A right triangle is a three sided figure with one angle equal to 90 degrees. A 90 degree angle is called a right angle and that is where the right triangle gets its name. We define the side of the triangle opposite from the right angle to be the hypotenuse, h . It is the longest side of the three sides of the right triangle. The word "hypotenuse" comes from two Greek words meaning "to stretch", since this is the longest side. We are going to label the other two sides a and b . The Pythagorean Theorem is a statement relating the lengths of the sides of any right triangle. The theorem states that: For any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

84. Pythagorean Theorem - Simple English Wikipedia, The Free Encyclopedia The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the http://simple.wikipedia.org/wiki/Pythagorean_theorem

Pythagorean theorem From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , the Pythagorean theorem or Pythagoras' theorem is a statement about the sides of a right triangle One of the angles of a right triangle is always equal to 90 degrees . This angle is the right angle . The two sides next to the right angle are called the legs and the other side is called the hypotenuse . The hypotenuse is the side opposite to the right angle, and it is always the longest side. The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the Greek mathematician Pythagoras If the lengths of the legs are a and b , and the length of the hypotenuse is c , then, a b c There are many different proofs of this theorem. They fall into four categories: Those based on linear relations: the algebraic proofs. Those based upon comparison of areas: the geometric proofs. Those based upon the vector operation.

85. Pythagorean Triangles And Triples Pythagoras Theorem applied to triangles with wholenumber sides such as the 3-4- 5 triangle. Here are online calculators, generators and finders with methods http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html

Right-angled triangles with whole number sides have fascinated both professional mathematicians and number enthusiasts since well before 300 BC when Pythagoras wrote about his famous "theorem". The oldest mathematical document in the world, a little slab of clay that would fit in your hand, is a list of such triangles. So what is so fascinating about them? This page starts from scratch and has lots of facts and figures with several online calculators to help with your own investigations. What's on this page indicates a link to an interactive Calculator on this page links to the Puzzles and Problems for that section. Right-angled Triangles and Pythagoras' Theorem Pythagoras and Pythagoras' Theorem Some visual proofs of Pythagoras' Theorem The ... Links and References for Further Reading Right-angled Triangles and Pythagoras' Theorem Pythagoras and Pythagoras' Theorem Pythagoras was a mathematician born in Greece in about 570 BC. He was interested in mathematics, science and philosophy. He is known to most people because of the Pythagoras Theorem a h b If the longest side (called the hypotenuse) is h and the other two sides (next to the right angle) are called a and b , then: a + b = h Pythagoras' Theorem or

86. Pythagoras Theorem, MathsFirst, Institute Of Fundamental Sciences, Massey Univer Oct 20, 2006 Pythagoras Theorem. A right triangle is a triangle that has one angle equal to 90 º If the missing side is a, then by pythagoras theorem http://mathsfirst.massey.ac.nz/Algebra/PythagorasTheorem/Pythagoras.htm

Home College of Sciences Institute of Fundamental Sciences Maths First ... Pythagoras Theorem Pythagoras Theorem A right triangle The side opposite the right angle in a right triangle is called the hypotenuse . The hypotenuses of the right triangles above are shown in red. In any right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides. That is, in the above triangle: a b c Click here to see a proof Example 1 Find the length of the missing side: The hypotenuse (side opposite the right angle) is the missing side. If this side is c , then by pythagoras theorem c c Example 2 Find the length of the missing side: The hypotenuse is the side of length 10. If the missing side is a , then by pythagoras theorem a Rearrange to solve for a a a Example 3 Find the length of the missing side: The hypotenuse is the side of length 29. If the missing side is b , then by pythagoras theorem b Rearrange to solve for b b b Example 4 Consider the right triangle below with sides a and b and hypotenuse c a c b Exercise 1 Now try some yourself. Consider the right triangle below with sides

87. Pythagoras And The Pythagoreans Feb 6, 1997 Did Pythagoras or the Pythagorean s actually prove the Pythagoras Theorem? Probably not. Although a proof is simple to give, the Pythagorean http://www.math.tamu.edu/~dallen/history/pythag/pythag.html

Next: About this document Pythagoras and the Pythagoreans Historically, Pythagoras means much more that the familiar theorem about right triangles. The philosophy of Pythagoras and his school has impacted the very fiber of mathematics and physics, even the western tradition of liberal education no matter what the discipline. Pythagorean philosophy was the prime source of inspiration for Plato and Aristotle; the influence of these philosophers is without question and is immeasurable. Pythagoras and the Pythagoreans Little is known of his life. Pythagoras (fl 580-500, BC) was born in Samos on the western coast of what is now Turkey. He was reportedly the son of a substantial citizen, Mnesarchos. There he lived for many years under the rule of the tyrant Polycrates, who had a tendency to switch alliances in times of conflict which were frequent. He met Thales, likely as a young man, who recommended he travel to Egypt. It seems certain that he gained much of his knowledge from the Egyptians, as had Thales before him. Probably because of continual conflicts and strife in Samos, Pythagoras settled in Croton, on the eastern coast of Italy, a place of relative peace and safety.

88. How To Prove Pythagoras Theorem: A Simple Proof Of The Pythagorean Equation by M Bell 2009 http://www.suite101.com/content/how-to-prove-pythagoras-theorem-a115640

89. The History Of The Pythagorean Theorem The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.?500 B.C.?), who was perhaps the first to offer a proof of http://ualr.edu/lasmoller/pythag.html

Did you know . . .? The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.?-500 B.C.?), who was perhaps the first to offer a proof of the theorem. But people had noticed the special relationship between the sides of a right triangle long before Pythagoras. The Pythagorean theorem states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypoteneuse, or, in mathematical terms, for the triangle shown at right, a + b = c . Integers that satisfy the conditions a + b = c are called "Pythagorean triples." (Illustration source: http://www.cs.ucla.edu/~klinger/dorene/Gif/math1pic1.gif Ancient clay tablets from Babylonia indicate that the Babylonians in the second millennium B.C., 1000 years before Pythagoras, had rules for generating Pythagorean triples , understood the relationship between the sides of a right triangle, and, in solving for the hypoteneuse of an isosceles right triangle, came up with an approximation of accurate to five decimal places. [They needed to do so because the lengths would represent some multiple of the formula: 1

90. Pythagoras's Crazy Theorem Game - Play Fun Trivia Quiz How much do you know about the theorem of Pythagoras? This quiz will involve questions about the theorem, determining side lengths, and will also have http://www.funtrivia.com/playquiz/quiz2049161776b68.html

Fun Trivia Quizzes Games People ... Log In Currently players online. Play, Compete, and Win for FREE! Click here to Get Started! Pythagoras's Crazy Theorem Created by XxHarryxX Fun Trivia Quizzes Theorems "How much do you know about the theorem of Pythagoras? This quiz will involve questions about the theorem, determining side lengths, and will also have questions about Pythagorean Triples. All non-integral solutions will be in radical form." 15 Points Per Correct Answer - No time limit What is the formula for the Pythagorean Theorem? (^2 means squared) a + b = c^2 a^2 + b^2 = c^2 (a + b)^2 a^2 + b^2 = c What is the only type of triangle the Pythagorean Theorem can be used on without being given any other measurements besides the sides (no height given)? Answer: (Two Words, Second Word is "Triangle") If you have a right triangle with shorter side lengths a = 3 and b = 4; what will the hypotenuse, c, equal? none of these If you have a right triangle with short side length a = 5 and hypotenuse length c = 13, what is the value of side length b? none of these If you have a right triangle with side length b = 15 and hypotenuse length c = 17, what is the value of side length a?

91. Pythagoras' Theorems The Pythagoreans were the first to prove that the Pythagorean Theorem was correct, even though Pythagoras learned it from the Babylonians in his travels. http://library.thinkquest.org/4116/History/theorems_pyth.htm

Pythagoreans noticed that strings produce different notes when they vibrate. If the ratios of the length of two strings are whole numbers, the notes make different pitches. They also knew that any triangle with side ratios of 3:4:5 was a right triangle. The Pythagoreans were the first to prove that the Pythagorean Theorem was correct, even though Pythagoras learned it from the Babylonians in his travels. During the 6th century BC, a square with a side of n was shown as the area of a square with a side of n. The Pythagorean Theorem stated that in a right triangle, the square of side a added to the square of side b will be equal to the square of side c (the hypotenuse). Irrational Numbers Irrational numbers are numbers with decimals that do not terminate, or repeat. The most widely known irrational number is p (pi). Pi can be calculated to billions of digits that go on forever. The number pi is related to curves, ellipses (ovals) and circles.

92. The Pythagoras Theorem The Pythagoras theorem was invented by Pythagoras. Pythagoras (ca. 582 ca 497 B.C.) was a Greek philosopher and mathematician. http://www.slideshare.net/gtekriwal/the-pythagoras-theorem

93. The Pythagorean Theorem The Pythagorean Theorem is one of the oldest, most wellknown, and widely used mathematical relationship in history. It has been a fundamental part of math http://www.worsleyschool.net/science/files/pythagoras/pythagoreantheorem.html

94. Pythagorean Theorem@Everything2.com The Pythagorean Theorem the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the http://everything2.com/title/Pythagorean Theorem

Near Matches Ignore Exact Everything Pythagorean Theorem cooled by bozon idea by dutchess Thu Apr 14 2005 at 1:49:56 Try saying this out loud. It's not only fun, it's also a concise definition. And accurate. The Pythagorean Theorem: the sum of the square s of the length s of the leg s of a right triangle is equal to the square of the length of the hypotenuse This definition amuses me. I teach Pre-Algebra and Algebra ; for the sake of integrating discipline s, I have my students count the preposition al phrases therein. I like it! C! thing by Noether Tue Jul 25 2000 at 16:43:08 Pythagoras 's theorem says that for a right angled triangle with sides of length a,b,c (with c the length of the hypotenuse ) we have c =a +b Here is one proof (of many). Start with a square of side length a+b , call it square 1. Put a square of side length c in the middle of square 1, call it square 2. Now rotate square 2 so that each vertex of the square 2 meets one of the edges of square 1. At this point our original right angled triangle occurs in each of the four corners of square 1. So the area of square 1 is the area of square 2 + the 4 x the area of our original triangle. That is square 1 has area

95. Pythagorean Theorem Proof And Applications File Format PDF/Adobe Acrobat Quick View http://blossoms.mit.edu/video/pythagorean/pythagorean-overview.pdf

96. Pythagorean Theorem Proof Below is an animated proof of the Pythagorean Theorem. Starting with a right triangle and squares on each side, the middle size square is cut into congruent http://www.usna.edu/MathDept/mdm/pyth.html

Animated Proof of the Pythagorean Theorem Below is an animated proof of the Pythagorean Theorem. Starting with a right triangle and squares on each side, the middle size square is cut into congruent quadrilaterals (the cuts through the center and parallel to the sides of the biggest square). Then the quadrilaterals are hinged and rotated and shifted to the big square. Finally the smallest square is translated to cover the remaining middle part of the biggest square. A perfect fit! Thus the sum of the squares on the smaller two sides equals the square on the biggest side. Afterward, the small square is translated back and the four quadrilaterals are directly translated back to their original position. The process is repeated forever. To USNA homepage To Math homepage To Meyerson homepage

97. Relations And Sizes - Right Triangle Facts - First Glance A Greek mathematician named Pythagoras developed a formula, called the Pythagorean Theorem, for finding the lengths of the sides of any right triangle. http://www.math.com/school/subject3/lessons/S3U3L4GL.html

Page 5     81-97 of 97    Back | 1  | 2  | 3  | 4  | 5