Mathematics@work - Beauty, Purity Truth! A database of mathematics links.Category Science Math Directories math archives, pascals triangle image generator. mathgate, the fibonacci association. theprime pages, sacred geometry. prime numbers factoring, solar geometry. http://www.geniusatwork.co.uk/mathematics.htm
Extractions: mathematics n. the abstract science of number, quantity, and space studied in its own right. isaac newton institute for mathematical science fibonacci numbers and the golden section unsolved mathematics problems fibonacci numbers and the pascal triangle ... elements@work [ mathematics@work ] biblical prophecy@work bhoys@work playright@work mind games@work ... freebies@work
Re: N-Dimentional Polytopes And Pascals By Jeffrey C. Jacobs Back to messages on this topic. Back to geometryresearch. previous analogs of the triangle, tetrahedron, simplex Does pascals triangle ennumerate the elements of all http://mathforum.com/epigone/geometry-research/swerdprougil/8cqpfejkvmwb@forum.s
Pascal's Triangle Pascal's triangle and related triangles THIS PAGE IS UNDER CONSTRUCTION Fractal geometry Pascal's triangle mod 2, and mod n, etc at coefficients of (x+y+z)n will be like constructing a version of pascals triangle on a pyramid. http://www.hverrill.net/pages~helena/pascal
Extractions: URL http://shimura.math.berkeley.edu/~helena/pascal/ Pascal's Triangle and related triangles THIS PAGE IS UNDER CONSTRUCTION Pascal's triangle comes up all over the place, in lots of lovely ways; there must be whole books devoted to applications of Pascal's triangle and related triangles, but I don't know them - if you do, please let me know! Pascal's triangle gives the coefficients of (x+1) n Probably the best place to find out all about Pascal's triangle is at Math Forum web pages on Pascal's triangle Here are some pages that will show you rows of Pascal's triangle: Fractal Geometry - Pascal's triangle mod 2, and mod n, etc: For Children: More interesting links to Pascals triangle stuff: About Blaise Pascal
N-Dimentional Polytopes And Pascals By Bob Underwood Back to messages on this topic. Back to geometryresearch. next analogs of the triangle, tetrahedron, simplex Does pascals triangle ennumerate the elements of all the http://mathforum.com/epigone/geometry-research/swerdprougil/10607-3692CCA4-4@new
Extractions: Subject: N-Dimentional Polytopes and Pascals Author: runderwood@webtv.net Organization: WebTV Subscriber Date: 5 Jan 1999 21:58:53 -0500 David Paterson writing in Vol. 28(1) J. Recreaqtional Mathematics presents tables ( condensed from Coxeter) of the five regular polyhedra and the six regular 4-D polytopes. Two uestions: What is the number of regular convex hyperforms as a function of dimension? AND noting that thenumber of vertices, edges, faces(polygons), solids, Hypersolids, etc. for 3-D is1-4-6-4 and for 4-D is 1-5-10-10-5-, I wonder if The 5-D analog would be 1-6-15-20-15-6...? This applies only to higher dimensional analogs of the triangle, tetrahedron, simplex... Does Pascals Triangle ennumerate the elements of all the hyperdimensional tetrahedra ? Just curious. UNDERDOG The Math Forum
Extractions: Camden-Rockport Middle School Library Math Links 2000 Census info. for Camden and Rockport and area Rockport town profile Camden town profile (needs updating!) Discover our town: Camden Knox County census info. Moving to Maine: Midcoast Info. Math problem of the Week Stock Information CNN Quote Search Service 411 Stock Info. Yahoo! Finance PC Quote ... Invest Smart Personal Finance Math Topics Geometry Problem of the Week Geometry Hunt Tesselations Ask Dr. Math ... Math Puzzles TESSALATIONS Totally Tesselations Tesselations FRACTALS The Fractory - How to Understand Fractals What are Fractals? STOCK MARKET Investor Detective - The Stock Market ARICAN MATH Math in Africa ARCHITECTURE Architecture Links Architecture for Kids PASCALS TRIANGLE Pascals Triangle Pascal's Triangle activities FIBONACCI AND GOLDEN RATIO Fibonacci Numbers and the Golden Section Golden Ratio Extravaganza MATH IN MUSIC The Math of Music Music and Math ALBERT EINSTEIN Albert Einstein Albert Einstein Biography (short!)
Newmath Math Topics. geometry Problem of the Week pascals triangle. pascals triangle. Pascal's triangle activities http://www.fivetowns.net/METlib/newmath
Extractions: Camden-Rockport Middle School Library Math Links 2000 Census info. for Camden and Rockport and area Rockport town profile Camden town profile (needs updating!) Discover our town: Camden Knox County census info. Moving to Maine: Midcoast Info. Math problem of the Week Stock Information CNN Quote Search Service 411 Stock Info. Yahoo! Finance PC Quote ... Invest Smart Personal Finance Math Topics Geometry Problem of the Week Geometry Hunt Tesselations Ask Dr. Math ... Math Puzzles TESSALATIONS Totally Tesselations Tesselations FRACTALS The Fractory - How to Understand Fractals What are Fractals? STOCK MARKET Investor Detective - The Stock Market ARICAN MATH Math in Africa ARCHITECTURE Architecture Links Architecture for Kids PASCALS TRIANGLE Pascals Triangle Pascal's Triangle activities FIBONACCI AND GOLDEN RATIO Fibonacci Numbers and the Golden Section Golden Ratio Extravaganza MATH IN MUSIC The Math of Music Music and Math ALBERT EINSTEIN Albert Einstein Albert Einstein Biography (short!)
Pascals Triangle Patterns found in Pascal's triangle. There are many patterns thatcan be found in Pascal's triangle. Some of the patterns that can http://www.ga.k12.pa.us/academics/us/Math/Geometry/stwk00/sloanelikemen/paterns.
Extractions: Patterns found in Pascal's Triangle There are many patterns that can be found in Pascal's Triangle. Some of the patterns that can be found include: The Hockey Stick pattern, The Sum of the Rows, and The Magic 11's. Here you can learn more about each of these interesting relationships. To further understand these patterns you can refer to the completed diagram of Pascal's Triangle at the bottom of the page. The Hockey Stick pattern To form the "hockey stick", and understand the basis of this neat pattern, first draw a diagonal line downwards from one of the number 1's on the triangle. After you have selected your diagonal, you must then choose a number that is adjacent to the diagonal below it. It should then look like a hockey stick, hence the name for the pattern. What is interesting about this pattern is that when you add up the numbers in the diagonal the sum of the numbers inside the selection is equal to the number below the end of the selection that is not on the same diagonal itself. Look at the triangle with the numbers filled at the bottom of the page and try to find a "hockey stick" for your self. Here are some examples like below; the numbers that are being added up are the ones in the diagonal and the bottom part of the "hockey stick" or the blade of the stick is the number that the diagonal equals.
National Library Of Virtual Manipulatives Koch triangle geometry (68), geometry (9-12) pascals triangle Numbers Operations (9-12) http://www.matti.usu.edu/nlvm/applets/controller/query/query.htm?qt=
Pascals Triangle Patterns In this section, you will learn the many patterns thatcan be found in pascals triangle. These patterns include The http://www.ga.k12.pa.us/academics/us/Math/Geometry/stwk00/sloanelikemen/
Extractions: History of Pascal Here you can find a part of the histoy on the Philosopher Blaise Pascal along with a breif introduction to his accomplishments and how he created "The Triangle." Patterns In this section, you will learn the many patterns that can be found in Pascals Triangle. These patterns include: The Hockey Stick Pattern, Sum of the Rows, and Magic 11's. Take the Quiz! To test your knowledge of Pascal and his triangle, take our quiz and try to complete some of the the other activities that there are here to offer. Links to Other Pascal Pages To find more information on this interesting topic, check out some of these other awesome links. BACK TO THE GA HOME PAGE
National Library Of Virtual Manipulatives 5). Mandelbrot and Julia Sets geometry (68), geometry (9-12). Mastermind 12).pascals triangle Numbers Operations (9-12). Pattern http://matti.usu.edu/nlvm2/applets/controller/query/query.htm?qt=
Pascal's Triangle Fractal geometry Pascal's triangle mod 2, and mod n, etc Moreinteresting links to pascals triangle stuff http://hverrill.net/pages~helena/pascal/
Extractions: URL http://shimura.math.berkeley.edu/~helena/pascal/ Pascal's Triangle and related triangles THIS PAGE IS UNDER CONSTRUCTION Pascal's triangle comes up all over the place, in lots of lovely ways; there must be whole books devoted to applications of Pascal's triangle and related triangles, but I don't know them - if you do, please let me know! Pascal's triangle gives the coefficients of (x+1) n Probably the best place to find out all about Pascal's triangle is at Math Forum web pages on Pascal's triangle Here are some pages that will show you rows of Pascal's triangle: Fractal Geometry - Pascal's triangle mod 2, and mod n, etc: For Children: More interesting links to Pascals triangle stuff: About Blaise Pascal
Great Web Links This web site has all the main patterns found in pascals triangle including Catalan Maths Through The Ages Probability geometry The Computer http://members.tripod.com/mathsmission/greatweblinks.htm
Extractions: Great Web Links Back Home The Fibonacci Home Page Rating: url: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html This is the Home page for the Fibonacci numbers, the Golden section and the Golden string. There is a large amount of information at this site (more than 200 pages if it was printed), so if all you want is a quick introduction then the first link takes you to an introductory page. Pascals Triangle and It's Patters Rating: url: http://members.tripod.com/~absolutebow/ptri2.html Pascal's Triangle was originally developed by the ancient Chinese, but Blaise Pascal was the first person to discover all of the patterns it contained. On this page, I explain how the Triangle is formed, and more importantly, many of its patterns. Pascals Triangle Rating: url: http://forum.swarthmore.edu/workshops/usi/pascal/pascal_numberpatterns.html This web site has all the main patterns found in pascals triangle including : Catalan Numbers, Fibonacci Numbers, Hexagonal Numbers, Natural Numbers, Triangular Numbers, Tetrahedral Numbers and more. Cut The Knot Rating: url: http://www.cut-the-knot.com/games.html
Fibonacchi 3+5=8 etc This sequence can also be found in pascals triangle Maths Through TheAges Probability geometry The Computer Tutor Revision Dictionary Calculators http://members.tripod.com/mathsmission/fibbonna.htm
Extractions: ...and the golden number... Leonard of Piza, also known as Fibonacci was one of the greatest mathematicians of his time. He even devised his own number sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 etc... which was approapriately named Fibonacci's sequence. The sequence is made by adding the previous two numbers together to get the next number, e.g. 0+1=1 1+1=2, 1+2=3, 2+3=5, 3+5=8 etc...This sequence can also be found in Pascals triangle: Here you add the numbers in the cells in a diagonal to get the Fibonacci numbers. If we were to divide each number by the number before it we would find the following sequence: 1/1 = 1, 2/1 = 2, = 1·61538... It is easier to see what is happening if we plot the resulting numbers on a graph: As you can see the numbers are getting closer and closer together in value. The average of these numbers is called the golden number, the golden mean or phi. The thing to remember about phi is that the number gets more accurate as you keep dividing, but I have approximated it to 1.625. But what if we if we do it the other way round, and divide each number by the one
Enrichment - Secondary School realms of our solar system and learn estimation, geometry, and problem topics includemagic squares, topology, pascals triangle, Fibonacci numbers, polyominoes http://www.awl.ca/school/math/mr/enr/books/enrbooks.html
Extractions: The little insights and ideas we all so laboriously discovered for ourselves come together in this carefully-structured, systematic book about mathematical proofs. Once students understand and analyze the structure of proofs, theyll be able to follow the more informal versions in texts and learn to create their own. Number Treasury
Enrichment Posters - Secondary Level art and architecture through a carefully designed sequence of geometry and algebra Patternsin pascals triangle Poster (Grade 7 and Up) Dale Seymour SS60-86651 http://www.awl.ca/school/math/mr/enr/posters/enrpstxt.html
Extractions: What do a pyramid, the Parthenon, an egg and a human body have in common? All have dimensions that approximate a unique ratio (1:1.618) called the Golden Section. Students learn about this amazing ratio and its many applications in nature, art and architecture through a carefully designed sequence of geometry and algebra problems.
Mathematics FRACTAL geometry. FRACTAL geometry The world of mathematics usually tendsto be thought of as abstract. Complex pascals triangle. pascals http://www.digitaltermpapers.com/members/Mathematics/
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Mathematics Trigonometry demonstrations; The joy of pi; Angle geometry Fuzz angles Fractals Sierspinskitriangles; pascals triangle; Famous Curves; Index of Java Applications; http://www.wellington-college.school.nz/intra/courses/maths.htm
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Pascal Lines: Steiner And Kirkman Theorems II Projective geometry lied abandoned for about two hundred years; and Pascal's result Next,have a look at the following triangle formed by three pascals http://www.cut-the-knot.com/Curriculum/Geometry/MorePascal.shtml
Extractions: Recommend this site At the age of sixteen B. Pascal proved a remarkable theorem The three intersections of the pairs of opposite sides of a hexagon inscribed in a conic are collinear. It is said [ Bell , p. 78] that from that result (and two other lemmas) Pascal derived all Apollonius' theorems on conics and more, no fewer than 400 propositions in all. Little wonder he called it the Mystic Hexagram Hexagrammum Mysticum ). The original manuscript (that was lost) was examined and praised by Leibniz. Descartes was been stunned to learn that the work had been performed by a sixteen years old. A shorter version written a year later has survived, see [ Source , p. 326-330], but contains no derivation. The theorem is clearly of projective nature, and in the surviving manuscript Pascal leaves no doubt of his intention to imitate the methods of Projective Geometry that Desargues introduced a short time beforehand. In the 17 th century, identification with Desargues' work was certainly detrimental to any discovery. The ridicule with which his concepts and notations were met caused Desargues to give up on mathematical research. Projective Geometry lied abandoned for about two hundred years; and Pascal's result had shared its fate. However, in the 19
