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  1. 1001 Fibonacci Numbers: The Miracle Begins with Unity and Order Follows by Mr. Effectiveness, 2010-01-13

1. 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
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

2. 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
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Re: N-Dimentional Polytopes and Pascals by Jeffrey C. Jacobs
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Subject: Re: N-Dimentional Polytopes and Pascals Author: timehorse@unforgettable.com Date: The Math Forum

3. 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
URL http://shimura.math.berkeley.edu/~helena/pascal/
Pascal's Triangle and related triangles
THIS PAGE IS UNDER CONSTRUCTION
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4. 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
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N-Dimentional Polytopes and Pascals by Bob underwood
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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

5. Newmath
Tesselations. Ask Dr. Math. geometry Puzzles. Fun Stuff. Architecture Links; Architecturefor Kids pascals triangle. pascals triangle; Pascal's triangle activities
http://www.sad28.k12.me.us/METlib/newmath
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

6. Newmath
Math Topics. geometry Problem of the Week pascals triangle. pascals triangle. Pascal's triangle activities
http://www.fivetowns.net/METlib/newmath
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

7. 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.
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.
The Sum of the Rows The sum of the numbers in any row is equal to 2 to the nth power (n is the number of the row). Here are some examples of this:

8. 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=

9. 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/
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

10. 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=

11. 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/
URL http://shimura.math.berkeley.edu/~helena/pascal/
Pascal's Triangle and related triangles
THIS PAGE IS UNDER CONSTRUCTION
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12. 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
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

13. 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
...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

14. 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
Titles for Enrichment
Seconday Level Reading, Writing, and Doing Mathematical Proofs
Daniel Solow (Grades 10-12)
SS6-0-86651-148-2, 288 PP, $29.10
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.
  • two workbooks tailored to the high school curriculum
  • short, easy-to-follow lessons followed by exercise sets with solutions
Number Treasury
Stanley Bezuszka and Margaret Kenney (Grades 7-12)
SS6-0-86651-078-8, 208 pp., $29.10
This resource offers an extensive source of information about number patterns, classical and modern.
  • covers prime and composite numbers, plane and figurate numbers, digital patterns, and more
  • solutions included
Math Space Mission
Regional Math Network

Kay Merseth, Director (Grades 7-9)
SS6-0-86651-439-2, 256 pp., $33.45 Students explore the outer realms of our solar system and learn estimation, geometry, and problem solving with this four-module, spiral-bound kit.
  • activity book includes teaching notes, reproducible student worksheets and problem cards, answers, and more

15. 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
Enrichment Posters
Secondary Level
Prices with a (*) denote Ontario PST applicable
Practical Conic Sections (Grades 8-12)
J.W. Downs
SS6-0-86651-628-X, 100 pp., $16.00
This resource book describes ways to create and explore relationships among the ellipse, hyperbola and parabola.
  • over 90 illustrations help explain shapes and their many real-world applications
  • find out how conics relate to the reflection of light in telescopes, and the reflection of sound in microphones and amplifiers
  • includes historical information and discussion of characteristics of cones and conic sections
Conic Sections Poster
SS6-0-86651-629-8, 22 X 34, $14.55* A companion to the book Practical Conic Sections, this poster shows properties and applications of the ellipse, hyperbola and parabola. The Golden Section (Grades 7-12) Garth E. Runion SS6-0-86651-510-0, 184 pp., $21.80 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.
  • additional proofs and problems provided
The Golden Proportion Poster Trudi H. Garland

16. 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 Absolute Values in Radicals.
Absolute Values in Radicals By: Catreece E-mail: jupitter45@hotmail.com Absolute Values in Radicals Absolute values in radicals is a very easy concept, once it is mastered. Basically an absolute value is the positive square root of the sum of the squares o Albert Enstine.
Albert Enstine By: Ian E-mail: BIGFLOCK@HOTMAIL.COM Albert Einstein Einstein was born on March 14, 1879, in Ulm Germany. He lived there with his parents, Herman and Pauline. After a year in Ulm, due to the failure of his father's electrical and engineering Analytic Geometry.
Analytic Geometry By: Baa1313@aol.com Analytic geometry was brought fourth by the famous French mathematician Rene' Descartes in 1637. Descartes did not start his studying and working with geometry until after he had retired out of the army and settled dow Archimedes.
Archimedes By: Nana E-mail: much2lazy@bolt.com Archimedes was born in 287 BC in Syracuse, a Greek seaport colony in Sicily. Archimedes’ father was Phidias. He was an astronomer; this is all we know about his father and we learn this from Archimedes’ work, Aristotle.

17. :: Free Essays :: Paper Writing :: Book Reports :: Mathematics Essays ::
Deceiving Mathematical Codes Modular Arithmetics pascals triangle Pi PythagoreanTriples R. Buckminster Fuller Rene' Descartes Analytic geometry Self Reliance
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18. Mathematics
Trigonometry demonstrations; The joy of pi; Angle geometry Fuzz angles Fractals Sierspinskitriangles; pascals triangle; Famous Curves; Index of Java Applications;
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19. MetaCrawler Results | Search Query = Pascal's Triangle Patterns
pascals triangle http//www.ga.k12.pa.us/academics/us/Math/geometry/stwk00/sloanelikemen/paterns.htm(Fast) More like this. XYZ
http://search.metacrawler.com/texis/search?q=Pascal's Triangle Patterns

20. 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
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Pascal Lines: Steiner and Kirkman Theorems II
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

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