81. Pythagoras' Theorem Pupils are introduced to pythagoras' theorem with various interactive demonstrations. AbsorbMathematics for GCSE , contents , pythagoras' theorem. http://www.crocodile-clips.com/absorb/AM4/stub/KCA017.html

Mathematics products Mathematics overview Crocodile Mathematics ... contents Pythagoras' Theorem Pythagoras' Theorem This is one of 65 lesson-sized units in Absorb Mathematics for GCSE - a new interactive course for 14-16 mathematics, written by mathematician and multimedia expert Kadie Armstrong, using Crocodile Mathematics simulations and interactive investigations. To celebrate the launch of Curriculum Online, you can access Absorb Mathematics for GCSE live on our website. Click here to find out more. ages 14-16 years old subject Mathematics format Web page format for IE5 and above [Windows] MLE support Microsoft Class Server type Interactive Resource About this unit... Description of resource Pupils are introduced to Pythagoras' theorem with various interactive demonstrations. Examples of its use are offered (in both 2D and 3D problems). The idea of Pythagorean triples is also explored. Curriculum Keywords Angles Pythagoras' theorem Topics covered Demonstrating Pythagoras' theorem Using Pythagoras' theorem Pythagorean triples Pythagoras' theorem in three dimensions Find out more...

82. Pythagoras' Theorem Click Here pythagoras' theorem. pythagoras' theorem allows us to find the lengthof the third side on a right angle triangle if we know the other two lengths. http://www.mathsisfun.com/pythagoras.html

HOME All Pages A - Z Listing Maths Menus Handling Data Miscellaneous Maths Help Discussion Forum Online Form Puzzles Calculators TI Calculators Computer Programs Winlogo Programs Links Add a link Maths links Online Shop Maths Books Contact Us Email Online Form About Mathsisfun Pythagoras' Theorem Pythagoras' Theorem allows us to find the length of the third side on a right angle triangle if we know the other two lengths. Bits to remember It only works on right angled triangles You need to know at least two other lengths. The formal definition is (ready for this) In a right angled triangle the sum of the square of the hypotenuse is equal to the sum of the squares of the other two sides. Algebraically a + b = c c is always the hypotenuse. Therefore 3 Which goes to 9 + 16 = 25 This can be used to find the length of an unknown side a + b = c = c c c = 13 a + b = c + b 81 + b Take 81 from both sides b b = 12 Related Links Right Angled triangles Triangles Pythagorean Triples

83. Homepage Of W. Volk / Pythagoreio Translate this page Hafen zu finden. (Detailinformation zum Denkmal) Weitere Links zuInformationen zu pythagoras und seinem theorem. In autumn 1998 http://www.w-volk.de/samos98.htm

Samos . Diese Stadt ist nach dem bekannten Mathematiker Pythagoras benannt, ein ihm gewidmetes Denkmal ist dort am Hafen zu finden. ( Detailinformation zum Denkmal Weitere Links zu Informationen zu Pythagoras und seinem Theorem In autumn 1998 my wife Inge and me spent our hollidays in Pythagoreio at the southern coast of Samos . This city is named after the great mathematician Pythagoras . A monument located near its harbour is devoted to him. ( Detailed information about the monument in german only) More links to informations about Pythagoras and his theorem Links: Informationen zum Leben und Wirken von Pythagoras sowie auch zu seinem Satz Information on the life as well on the theorem of Pythagoras (german only) Java-basierte Animationen zum Satz von Pythagoras und verwandte Themen (nur auf englisch) Java-based animations on the theorem of Pythagoras and related topics ... statuette of Pythagoras and others at the cathedral of Chartres (France) Pythagoras und kein Ende? " (erschienen im Ernst Klett Schulbuchverlag Rezension In addition the german book of Peter Baptist should be mentioned (see the german text for details). It describes the person Pythagoras and his theorem and showing the relations to other historical persons and informations but also to scientific fields up to the twentieth century (cf. also a review Back to the root Created by W. Volk in November 1998

84. Pythagoras' Theorem pythagoras' theorem. Use the Pythagorgrams widget to undestand what pythagoras'theorem says and why it works. Then try the pencil and paper problems. http://thejuniverse.org/Mathdesign/widgets/Pythagoras/

Pythagoras' Theorem Use the Pythagorgrams widget to undestand what Pythagoras' theorem says and why it works. Then try the pencil and paper problems. Pencil and Paper Problems 1. i) A right-angled triangle has shorter sides of lengths 2 and 5; how long is its hypotenuse? ii) A right-angled triangle has hypotenuse of length 4 and one side of length 2; how long is the other side? iii ) A triangle has two sides of lengths 5 and 6 and area 9. How long is the third side? [There are two possible answers.] 2. How long is the diagonal of a square with sides of length 1? Now, without using Pythagoras' theorem again , how long is the diagonal of a square with sides of length 13579? How long is the diagonal of a square with sides of length s? 3. How long is an altitude of an equilateral triangle with sides of length 2? Without using Pythagoras' theorem again, how long is an altitude of an equilateral triangle with sides of length 24680?

85. NRICH | Secondary Topics | Geometry-Euclidean | Pythagoras Theorem Coordinate + GeometryCoordinate - Geometry-Euclidean + 3D + Angle Properties + Polygons+ Proof + Properties of Shapes - pythagoras theorem + 3D + Application http://www.nrich.maths.org.uk/topic_tree/Geometry-Euclidean/Pythagoras_Theorem/

NRICH Prime NRICH Club ... Get Printable Page March 03 Magazine Site Update News Events Problems Solutions ... Games Archive Problems Solutions Articles Inspirations ... Interactivities Web board Ask NRICH Asked NRICH NRICH Club Register Tough Nuts About Help! ... Where is NRICH? Associated Projects Maths Thesaurus MOTIVATE EuroMaths Millennium Maths ... Project Display maths using fonts images Help Back Issues Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Bernard's Bag(P) - solutions(P) Penta Probs(P) - solutions(P) Let Me Try(P) - solutions(P) Kid's Mag(P) Play Games(P) Staff Room(P) 6 Problems - solutions 15+Challenges - solutions Articles Games LOGOland Editorial News Click on the folders to browse problem topics from the secondary site. You can then go directly to each of the problems. Top Level Algebra Analysis Calculus Combinatorics Complex Numbers Geometry Geometry-Cartesian Geometry-Coordinate Geometry-Coordinate Geometry-Euclidean Angle Properties Circles Polygons Proof Properties of Shapes Pythagoras Theorem Application Enlargements Other shapes Pythagorean triples Ratio and Proportion Similarity Squares Triangles polygons proof transformations Incircles ( July 2001 ) Incircles ( January 2002 ) Graph Theory Groups Investigation Investigations Logic Measures Mechanics Number Pre-calculus Probability Programs Properties of Shapes Pythagoras Sequences Statistics Symmetry Trigonometry Unclassified algebra number

86. NRICH | Secondary Topics | Geometry-Coordinate | Circles | Pythagoras Theorem 3D + Algebra + Analysis + Calculus + Combinatorics + Complex Numbers + Geometry Geometry-Coordinate + 3D - Circles + pythagoras theorem - pythagoras theorem http://www.nrich.maths.org.uk/topic_tree/Geometry-Coordinate/Circles/Pythagoras_

NRICH Prime NRICH Club ... Get Printable Page March 03 Magazine Site Update News Events Problems Solutions ... Games Archive Problems Solutions Articles Inspirations ... Interactivities Web board Ask NRICH Asked NRICH NRICH Club Register Tough Nuts About Help! ... Where is NRICH? Associated Projects Maths Thesaurus MOTIVATE EuroMaths Millennium Maths ... Project Display maths using fonts images Help Back Issues Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Bernard's Bag(P) - solutions(P) Penta Probs(P) - solutions(P) Let Me Try(P) - solutions(P) Kid's Mag(P) Play Games(P) Staff Room(P) 6 Problems - solutions 15+Challenges - solutions Articles Games LOGOland Editorial News Click on the folders to browse problem topics from the secondary site. You can then go directly to each of the problems. Top Level Algebra Analysis Calculus Combinatorics Complex Numbers Geometry Geometry-Cartesian Geometry-Coordinate Circles Pythagoras Theorem Pythagoras Theorem Square Pair Circles ( July 2002 ) Square Pair Circles ( August 2002 ) Graphs Properties of Shapes Straight Lines Transformations Vectors Geometry-Coordinate Geometry-Euclidean Graph Theory Groups Investigation Investigations Logic Measures Mechanics Number Pre-calculus Probability Programs Properties of Shapes Pythagoras Sequences Statistics Symmetry Trigonometry Unclassified algebra number

87. Solving Problems Using Pythagoras' Theorem pythagoras' theorem. There are several proofs of pythagoras' theorem one ofwhich can be found elsewhere on this site. What is pythagoras' theorem? http://mathz.com/pythagoras.html

Pythagoras' Theorem There are several proofs of Pythagoras' Theorem one of which can be found elsewhere on this site. Here we will look at how to use the theorem to solve problems. Before using Pythagoras' Theorem you must be comfortable rounding numbers and using powers and roots What is Pythagoras' Theorem? Pythagoras, a Greek mathematician, discovered a peculiar property of right angled triangles, namely that if you add together the lengths of the shorter sides squared you will get the length of the longest side squared. So, in this triangle: If we add together the lengths of the shorter sides squared we get: If we square the length of the longest side we also get 25. (5 = 25). The longest side of a right angled triangle is also called the hypotenuse. The theorem works for any right angled triangle, not just the one with the above dimensions, so it is common to state the theorem using the letters a b , and c to represent whatever the lengths of the sides are. c is the length of the longest side (the hypotenuse) and a and b represent the lengths of the shorter two sides.

88. PYTHAGORAS THEOREM pythagoras theorem. pythagoras theorem will only work if you havea right angled triangle. a 2 + b 2 = h 2. The side opposite the http://www.i-t-teacher.freeserve.co.uk/revision/pythag.html

PYTHAGORAS THEOREM Pythagoras Theorem will only work if you have a right angled triangle. a + b = h The side opposite the right angle is always the LONGEST side a. Finding "Unknown" on LEFT b. Finding "Unknown" on RIGHT

89. Pythagoras Theorem pythagoras' theorem. Ironically it is the theorem bearing pythagoras'own name which was the downfall of much that he believed in.) http://www.langara.bc.ca/mathstats/resource/onWeb/precalculus/pythagoras.htm

Langara College - Department of Mathematics and Statistics Internet Resources for Mathematics Students Pythagoras' Theorem This is with good reason the most famous theorem in all of Mathematics! It is the key to understanding how angles and distances are related, and it allows us to find the distances between distant points in space, as well as showing us the existence of lengths which cannot be related by whole number ratios. (An example of such an "irrational" length occurs if we take a and b of length 1 in the picture, for then c squared is 2 and this is not possible for any ratio of whole numbers. This was very upsetting to Pythagoras and his followers as their philosophy idealized such ratios. Ironically it is the theorem bearing Pythagoras' own name which was the downfall of much that he believed in.) There are many ways of proving this important theorem and no-one's education can be said to be complete without understanding at least one. Here are some links to proofs of the theorem that you can find on the Web: This award winning presentation of an animated proof of Pythagoras' Theorem by UBC's Jim Morrey was an early example of the use of JAVA to help with the understanding of mathematical ideas.

90. Pythagoras' Theorem Friberg, a leading authority on Babylonian mathematics, presented convincing evidencethat the old Babolonians were aware of the pythagoras theorem around 1800 http://www.math.ntnu.no/~hanche/pythagoras/

Behold! The above picture is my favourite proof of Pythagoras' theorem. Filling in the details is left as an exercise to the reader. A detailed version of the proof, for those who do not feel up to the challenge, appears in Alan M. Selby 's Appetizers and Lessons for Math and Reason (although he only uses the righthand picture with algebra, not geometry, to prove the required identity). Is this the oldest proof? This proof is sometimes referred to as the Chinese square proof , or just the Chinese proof . It is supposed to have appeared in the Chou pei suan ching (ca. 1100 B.C.E.), according to Ralph H. Abraham [see ``Dead links'' below,] who attributes this information to the book by Frank J. Swetz and T. I. Kao, Was Pythagoras Chinese? . See also Development of Mathematics in Ancient China According to David E. Joyce 's A brief outline of the history of Chinese mathematics , however, the earliest known proof of Pythagoras is given by Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.) I have been told that this proof, with the exclamation `Behold!', is due to the Indian mathematician Bhaskara II (approx. 1114-1185). A web page at the

91. Perseus Update In Progress turned this rose into a briar. Unfortunately, nobody knows how pythagoras originally proved the theorem, but here are three ways. http://www.perseus.tufts.edu/GreekScience/Students/Tim/Pythag'sTheorem.html

The Perseus Digital Library is Being Updated Notice The main Perseus web site (at Tufts) is unavailable from 5:00 to 6:00, US Eastern time, in order to rebuild its databases with new or changed meta-data. We apologize for this inconvenience.

92. Pythagoras's Theorem In Moving Pictures, By Henry Bottomley A visual demonstration of pythagoras's theorem. Copyright Henry BottomleyJuly 1998. pythagoras's theorem. a visual demonstration http://www.btinternet.com/~se16/hgb/pyth.htm

Pythagoras's theorem a visual demonstration that for a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, by Henry Bottomley The four blue triangles remain in the picture, so the red and yellow areas are constant, so the area of the biggest red square (on the hypotenuse) is equal to the sum of the other two red squares (on the other two sides). A proof of the theorem based on the second diagram: the area of the big square is (a+b)^2 , but it is also c^2 + 4.1/2.a.b so a^2 + 2.a.b + b^2 = c^2 + 2.a.b , so a^2 + b^2 = c^2 return to top Henry Bottomley's home page Seven formulae for the area of a triangle An optical illusion ... Oliver Byrne's 19th century graphical translation of Euclid's proposition I.47

93. XOREYTES PRODUCTIONS Three Quarters Pythagoras' Theorem pythagoras' theorem. 1997. Choreographer Jeremy Nelson. Rhythm inits full range. Pythagorean Theory consists of indirect references http://www.dancers.gr/pyth.en.html

94. Pythagorean Theorem It is possible that someone proved the theorem before pythagoras, but no proof hasbeen found. Because of this, pythagoras is given credit for the first proof. 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)

95. Cinderella: Pythagoras' Theorem Gallery pythagoras' theorem. Please enable Java and reload the pagefor an interactive construction (with Cinderella). pythagoras http://www.cinderella.de/en/demo/gallery/pythagoras.html

Cinderella HOME INFO DEMO SUPPORT RESEARCH COMMUNITY The Interactive Geometry Software Gallery Browser Download Gallery: Pythagoras' theorem Please enable Java and reload the page for an interactive construction (with Cinderella). Pythagoras' Theorem tells us that the area of the square over the hypotenuse c of a right angled triangle is the same as the sum of the aread of the squares over a and b. Here you can see why: Take four copies of the triangle and arrange them as shown in the middle square. The remaining area is a²+b². Rearrange them as shown in the right square: The remaining area is c². That's all! You can pick the top point of the triangle and move it, or you can move points A and B to verify that the theorem is still true for different right angled triangles.

96. Pythagoras' Theorem pythagoras' theorem. man; However, the Pythagoreans are usually creditedwith the first proof of this theorem. pythagoras' theorem http://students.bath.ac.uk/ns1thab/Theorem.html

Pythagoras' Theorem The Pythagoreans new, as did the Egyptians before them, that a triangle whose sides were 3:4:5 was a right angled triangle. The Pythagorean Theorem which states that "The square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides" may have infact been known in Babylonia, where Pythagoras traveled as a young man; However, the Pythagoreans are usually credited with the first proof of this theorem. Pythagoras' Theorem The theorem is of fundamental importance in Euclidean Geometry where it serves as a basis for the definition of distance between 2 points. The theorem is of fundamental importance in the Eulidean Geometry where it serves as a basis for the definition of distance between 2 points. The Theorem is reversible which means that a triangle whose sides satisfy a + b = c is right-angled. (Click on the image below for 'The Oldest Known Proof Of Pythagoras') Back to Pythagoras Home

97. NOVA Online | The Proof | Pythagorean Puzzle | Theorem Proof menu (see bottom of page for text links), Demonstrate the Pythagoreantheorem. 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

98. Pythagoras' Haven - In Deutsch Translate this page Der Lehrsatz des pythagoras a 2 + b 2 = c 2 wird bewiesen. Die Schalter NEXT, BACKund RESET erlauben einen Gang durch den Beweis. Der Satz des pythagoras. http://didaktik.physik.uni-wuerzburg.de/~pkrahmer/java/pythago/pythago.html

Der Lehrsatz des Pythagoras a + b = c wird bewiesen. Die Schalter NEXT, BACK und RESET erlauben einen Gang durch den Beweis. Zum JAVA Applet: Original Applet von Jim Morey (morey@math.ubc.ca) (deutscher Text von mm-physik). Der S atz des P ythagoras mm-physik

99. Pythagorean History Legend has it that upon completion of his famous theorem, Pythagorassacrificed 100 oxen. Although he is credited with the discovery http://www.geom.umn.edu/~demo5337/Group3/hist.html

A Brief History of the Pythagorean Theorem Just Who Was This Pythagoras, Anyway? Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities. Eudoxus developed a way to deal with these unutterable numbers. The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. This relationship has been known since the days of the ancient Babylonians and Egyptians, although it may not have been stated as explicitly as above. A portion of a 4000 year old Babylonian tablet (c. 1900 B.C.E.), now known as Plimpton 322 , (in the collection of Columbia University, New York), lists columns of numbers showing what we now call Pythagorean Triplessets of numbers that satisfy the equation a^2 + b^2 = c^2 Hands On Activity It is known that the Egyptians used a knotted rope as an aid to constructing right angles in their buildings. The rope had 12 evenly spaced knots, which could be formed into a 3-4-5 right triangle, thus giving an angle of exactly 90 degrees. Can you make a rope like this? Now use your knotted rope to check some right angles in your room at school or at home.

100. Pythagorean Theorem: Proof Proof of the Pythagorean theorem. There are many ways to prove the Pythagoreantheorem. A particularly simple one is to use the scaling http://www.emsl.pnl.gov:2080/docs/mathexpl/ptprove.html

Proof of the Pythagorean Theorem There are many ways to prove the Pythagorean Theorem. A particularly simple one is to use the scaling relationship for areas of similar figures. Consider any right triangle ABC. Choose point D on the hypotenuse AB, such that line CD is perpendicular to AB. Then the large right triangle ABC is split into two smaller right triangles ADC and BDC. All three triangles have equal angles and are therefore similar , so their areas are related by the scaling formula: for some number "s" that is the same for all three triangles. Scroll down to see the rest of the proof.) The two small triangles exactly cover the large triangle, so the large area must equal the sum of the two smaller areas. Since "c", "a", and "b" are the corresponding sides, we can write the equation: But then simple algebra tells us that we can divide both sides of the equation by the number "s" to eliminate that symbol (even though we never know what its value is!). This leaves us with the Pythagorean Theorem: So, the Pythagorean Theorem is true just because of a simple scaling law:

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