1. Pascals Triangle Patterns found in Pascal's Triangle There are many patterns that can be found in Pascal's Triangle. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Pascals Triangle how he created "The Triangle." Patterns In this section, you will learn the many patterns that can be found in Pascals Triangle. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Pascal's Triangle - AskTheBrain.com Bermuda Triangle Equilateral Triangles Blaise Pascal Triangle Geometry Sponsored links Pascals Triangle Explore patterns created http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Pascal's Triangle Pascal's Triangle. Home Geometry Home Geometry Project Library Books http//www.danenet.wicip.org/heron/grea. .. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Pascals Triangle The History of Blaise Pascal and How His Triangle is Constructed http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. ENC Online Curriculum Resources Pascal's Triangle (ENC-012432 Featured in Digital Dozen Subjects Mathematics Fibonacci sequences. Geometry. Numbers. Pascal's triangle. Patterns. Triangles. Visualization. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Pascal's Triangle Math Search Algebra Geometry Graphing Calculator Calculator Volume Polygons Pascal's Triangle Right Triangles http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Pascals Triangle important advances in geometry, but perhaps his most famous creation was a triangle that isn't really a triangle. Called 'Pascal's Triangle http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Activity Resources - Pascal's Triangle Recover password Contact us Privacy statement Terms Conditions. Activity Resources Geometry Books(Geometry) Pascal's Triangle 270 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Math Forum Pascal's Triangle = good places to begin Triangle grid paper (to print out) of primes and twin primes, divisors, factors, combinatorics, and geometry. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Home - Search Geometry geometry. pi geometry. pentominoes geometry. pascals triangle geometry. origamipaper folding geometry. geometry. euclidean geometry. analytic http://www.algebraic.net/cgi-bin/988.cgi?q=geometry&show_page=1

12. Math Tools Problem about a Parallelogram, Parallelogram (geometry), Java Applet, Tool, 0. pascals triangle, Pascal s triangle (Math 5)+, Java Applet, Tool, 1. http://mathforum.org/mathtools/newitems.html?sortBy=&offset=2050 &limit=25

13. Pascal S Triangle By Mathan a new topic Back to geometrycollege Subject pascal s triangle Author mathan mathankumar@sancharnet different applications of pascals triangle for students http://mathforum.org/epigone/geometry-college/twimgendtwimp

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14. Pascals Triangle Take the Pascal s triangle Quiz Along with Other Activities to Test Your Pascal s triangle Quiz. 1. ­ 2. Name or describe two patterns that can be found http://www.germantownacademy.org/academics/US/Math/Geometry/stwk00/sloanelikemen

Take the Pascal's Triangle Quiz Along with Other Activities to Test Your Knowledge on His Triangle Pascal's Triangle Quiz 3. Using binomial expansion, what are the numbers in Row Four of Pascal's Triangle? 4. How many pizzas can you make using two toppings out of five possible toppings available? 5. What is the sum of the numbers in row six of the triangle? Tony's Pizza Place Tony's Pizza Place has a wide variety toppings: pepperoni, sausage, ham, pineapple, anchovies, and olives. How many different pizzas can be made with 3 different toppings on it? Here's one method of doing it. You could write out every possible combination like this: pep, sau, ham pep, sau, pin pep, sau, anch pep, sau, oli pep, ham, pin pep, ham, anch pep, ham, oli pep, pin, anch pep, anch, oli sau, ham, pin sau, ham, anch sau, ham, oli sau, pin, oli sau, anch, oli ham, pin, anch ham, pin, oli ham, anch, oli pin, anch, oli If you just counted all of the possibilities above, then you should have gotten 20 pizzas for the answer. However, using Pascal's Triangle, you could arrived at that answer much quicker. What if there were no toppings? How many pizzas can you make? 1. How about if there was only 1 topping that you could choose from, how many can you make then? There are 2 (1 without topping and 1 with one topping). What about if there were 2 toppings that you could choose from? 4 (1 without any, 2 with only one topping, and 1 with both). If you look at the numbers here, you will see that they match up with the rows in Pascal's Triangle. This is how you use Pascal's Triangle to figure out a problem like this.

15. Pascals Triangle At the top of Blaise Pascal s triangle is the number 1. The very top number 1lies in Row So this is all you have to do to construct Pascal s triangle. http://www.germantownacademy.org/academics/US/Math/Geometry/stwk00/sloanelikemen

The History of Blaise Pascal and How His Triangle is Constructed Blaise Pascal was born in 1623-1662, in Clermont- Ferrand, France, but lived mostly in Paris. He was a religious philosopher, scientist, and mathematician. Besides the triangle, he also invented a calculating machine (1647), and later the barometer and the syringe. At the top of Blaise Pascal's Triangle is the number 1. The very top number 1 lies in Row Zero. Row One contains two number 1's. Each of the 1's is made by adding the two numbers above it (in this case, the two numbers are and 1, the being the number outside of the triangle). This is how you create the rest of the triangle; add the top two numbers to get the number below the two numbers. For example if you take Row Two, 1+0=1; 1+1=2; 1+0=1; And thus, Row Two's numbers are 1-2-1. So this is all you have to do to construct Pascal's Triangle. This means that there are many more rows in Pascal's Triangle than we show with our diagram (see Activity Page for diagram). There are actually an infinite amount of rows. Another way that you can find a number in the triangle is through the nCr (n Choose r) method. In this equation, "n" stands for the number of the row, and "r" is the number of spaces in that row that you want to find the number for. For example, in Row Three, the first 1 is the "zeroeth" element, the first 3 is the first element, the next three is the second element, and the last 1 is the third element.

16. The CTK Exchange Forums MSET99 Talk Games Puzzles Arithmetic/Algebra geometry Probability Eye Opener AnalogGadgets Subject pascals triangle link , Previous Topic Next Topic. http://www.cut-the-knot.org/cgi-bin/dcforum/ctk.cgi?az=read_count&om=310&forum=D

17. Pearson Education - Mathematical Ideas, Expanded Edition Chaos and Fractal geometry. Collaborative Investigation Generalizing the AngleSum Concept. Chapter 9 Test. Using pascals triangle and the Binomial Theorem. http://www.pearsoned.co.uk/bookshop/detail.asp?item=100000000036562

18. Sierpinski Gasket If the entry in pascals triangle is odd then it is part a 2D pyramid is an equilateraltriangle, and a The intuitive method of determining the geometry of a 4D http://astronomy.swin.edu.au/pbourke/fractals/gasket/

Sierpinski Gasket Written by Paul Bourke March 1993 See also: Photographs by Gayla Chandler PovRay rendering by Angelo Pesce Geometric models of the Menger sponge level 3 plain level 4 efficient level 3 crumpled Introduction The following is an attempt to acquaint the reader with a fractal object called the Sierpinski gasket. The gasket was originally described in two dimensions but represents a family of objects in other dimensions. This family of objects will be discussed in dimensions 1, 2, 3, and an attempt will be made to visualise it in the 4th dimension. Cantor set or Dust The nineteenth century mathematician Georg Cantor became fascinated by the infinite number of points on a line segment. The set of points described here has been attributed to Cantor because of his attempts to imagine what happens when an infinite number of line segments are removed from an initial line interval. To generate the Cantor set start with a closed interval [0,1] (includes the points and 1). On the first iteration replace the interval with 3 equal length pieces and remove the middle third, or ]1/3, 2/3[ (excludes the points 1/3 and 2/3) Subsequent iterations involve removing the middle portion of the remaining line segments.. The gap removed each time is usually called a trema from the Latin tremes = termite.

19. Enrichment - Secondary School This wide variety of exercises for exploring pascals triangle includes probabilities, Book One features investigations in geometry, patterns, http://www.pearsoned.ca/school/math/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

20. Patterns - Secondary Level In this book, students study history and geometry as they explore eight elegant Latin squares, pascals triangle, repeating circles, magic squares, http://www.pearsoned.ca/school/math/math/mr/pat/pattxt.html

Patterns Secondary Level Prices with a (*) denote Ontario PST applicable Line Design Poster Sets (All Grades) Dale Seymour Set A: SS6-0-86651-587-9, $14.95* Set B: SS6-0-86651-588-7, $14.95* The eye sees a series of graceful curves although these beautiful geometric designs are created with simple straight lines. Perfect for framing and enhancing any classroom. two sets available four posters per set each poster 11.5 x 11.5 Introduction to Line Designs (Grade 6 and Up) Dale Seymour SS6-0-86651-579-8, 292 pp., $32.00 Written especially for beginners, Line Designs helps students create string sculptures, curve stitchings and line designs. Explorations also explore line designs with personal computers, new geometry tools, and artistic creativity. complete with designs, instructions and examples The Pythagorean Theorem Poster Set and Book (Grades 8-12) Sidney J. Kolpas Book: SS6-0-86651-598-4, 48 pp., $13.50 4 posters: SS6-0-86651-597-6, 16" x 22", $24.70* Book and Posters: SS6-0-201-68657-0, $32.05* In this book, students study history and geometry as they explore eight elegant proofs of the Pythagorean Theorem from across the centuries. includes interesting facts, biography of Pythagoras and a list of concepts needed to understand the proofs

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