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

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

2. Math Tools Support Material:
Lesson Plans Teacher Information pascals triangle. Author National Library of Virtual Manipulatives (Utah State Rect coordinate geometry. geometry in the plane. geometry in space
http://mathforum.com/mathtools/support.html?&new_id=424

3. 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

4. Pascals Triangle
At the top of Blaise Pascal s triangle is the number 1. The very topnumber 1 lies in Row Zero. Row One contains two number 1 s.

Extractions: 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.

5. Math Tools Support Material:
Lesson Plans Pascal's triangle Lessons. Tools pascals triangle. Author Doctor Math Rect coordinate geometry. geometry in the plane. geometry in space
http://mathforum.com/mathtools/support.html?&new_id=240

6. Math Tool: Pascals Triangle
combs., Pascal s triangle, Recurrence relations. BROWSE. Site Map. COURSES. AllCourses. PreK. Kindergarten. Math1. Math2. Math3. Math4. Math5. Math6. Math7.geometry.
http://mathforum.org/mathtools/tool.html?tp=9.3&id=424

7. Pascal's Triangle
Interactive Pascal's triangle. Pascal's triangle interface. Fractal geometry Pascal's triangle mod 2, and mod 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

8. Math Tool: Pascals Triangle
Pascal s triangle. Fractions. Percentages. Integers. Algebra expressions. Equations functions. Linear relationships. Ratio proportion. Rect coordinate geometry.
http://mathforum.org/mathtools/tool.html?co=m7&tp=9.3&id=424

9. Untitled
integral 29 queries convolution 28 queries geometry 28 queries probability 27 queries lagrange queries unit vector 3 queries pascals triangle 3 queries index group 3
http://aux.planetmath.org/misc/pmsearches_200205230243.txt

10. FUCHS MIZRACHI SCHOOL Middle And Upper School Math Curriculum
TOPIC CONTENT geometry Unit 1 Measurement, Capacity Weight US Customary Metric Expansion by pascals triangle Binomial Expansion by Binomial Theorem geometry TOPIC CONTENT
http://www.fbsm.org/MS-US Math Curriculum.pdf

11. TI-92 BASIC Math Programs - Ticalc.org
0104-29. Analytic geometry v2.0. The most comprehensive geometry (analytic) program for TI-89 and TI-92 This stores many rows of pascals triangle to a matrix for easy
http://www.ticalc.org/pub/92/basic/math

Extractions: This is a collection of several programs I have recently been working on. They are all calculus-related, except for a program to solve three equations simultaneously. I have included programs to help you use Newton's Method to approximate roots for the Nth iteration, a program for finding tangent points on a curve to a given point, a program for finding tangent points on two curves (tangent to each other), programs for both the regular Mean Value Theorem and the Mean Value Theorem for integrals, and the aforementioned program for solving three equations. These should help you speed up some tedious calculations in calculus class. acst.zip

12. User:Jaredwf - Wikipedia, The Free Encyclopedia
projection (cartography) Orthographic projection (geometry) Paul Bachmann pascals triangle Spline (mathematics) Timeline of algorithms Translation (geometry)
http://en.wikipedia.org/wiki/User:Jaredwf

Extractions: Server will be down for maintenance on 2004-06-11 from about 18:00 to 18:30 UTC. A cultivated person's first duty is to be always prepared to rewrite the encyclopedia. Umberto Eco Table of contents 1 Local pages 2 Topics of interest 3 Current projects 4 Pages created ... edit edit Mathematics ... Computational geometry and Computer graphics Computability theory and Computational complexity theory edit edit Approximation error Axis-aligned bounding box Bounding volume Buffon's needle problem ... edit Ambiguous grammar Bézier splines Cross product Finite state machine ... edit DFAexample.png Graphstructuredstack jaredwf.png Leftmostderivations jaredwf.png Line Segment jaredwf.png ... edit Views Personal tools Navigation Search Toolbox What links here Related changes User contributions Special pages This page was last modified 22:54, 28 May 2004.

13. National Library Of Virtual Manipulatives
Ladybug Mazes  geometry (PreK2), geometry (3-5), Measurement (PreK-2),Measurement (3-5). pascals triangle  Numbers Operations (9-12).
http://matti.usu.edu/nlvm/applets/controller/query/query.htm?qt=

14. Pearson Education
Chaos and Fractal geometry. Collaborative Investigation Generalizing the AngleSum Concept. Chapter 9 Test. Using pascals triangle and the Binomial Theorem.

15. A Brief History
work on conics and published several papers in the field of geometry. this provedthe theory of baromic pressure, he created pascals triangle (1654) which
http://www.bath.ac.uk/~ma1mrw/history.html

Extractions: Interesting Patterns In Pascal's Triangle Main Page A brief history Sum of the rows Hockey stick pattern ... Petal Pattern A Brief History Pascals Triangle is a well known and famous mathematical pattern. Athough this pattern was originally discovered in China it was named after the first westener to study it. According to Yuhnze He the triangle was first developed during the Song Dynasty by a mathematician named Hue Yang. Blaise Pascal was a French mathematician who was alive in the 17 th century. His mother was Antoinette Begon and his father was Etienne. His mother died when Pascal was three and his father had the responsibility of bringing up Pascal and his two sisters Gilberte and Jaqueline. In 1635 Pascal began his studies and had mastered Euclid's Elements by age 12. This won him great respect in mathematical circles. Instead of going to school Etienne took Pascal to lectures and mathematical gatherings at the "Academie Parsienne". By age 16 Pascal was playing an active role here as the principle disciple of Girard Desargues, a proffesor in geometry. Pascal began work on conics and published several papers in the field of geometry. In fact, in June 1639 Pascal had already made a significant discovery with his mysical hexagram. In 1641, a bad case of ill health delayed his research for a year.

various modules triangle module, pentagon moduel, sonobe module, pascals trianglemodule, that The connection with geometry is clear and yet multifaceted; a

17. 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.org/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

18. Do You Speak Mathematics?
Projective geometry lay 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.org/ctk/Mathematics.shtml

Extractions: Discourses and Enchiridion , Classics Club, 1944, p. 47 Do you speak mathematics? is a very valid question assuming mathematics is a language. Many think it is. Josiah Willard Gibbs gave a speech on that account. Galileo and R. Feynman thought so. Mathematics is even judged to be a universal language, the only one suitable to initiate extraterrestrial communication [ Jacobs , p. 1]. Some object. For example, Jean-Pierre Bourguignon argues [ Basis , p. 173] that For some people, mathematics is just the language of the quantitative . This opinion is shared by some of our fellow scientists. ... We mathematicians know how wrong this opinion is, and how much effort goes into building concepts, making new links, establishing facts, and following avenues we once thought plausible but turned out to be dead ends. I generally accept the above sentiment with reservations concerning mathematics being just the language of quantitative The potency of the bond between mathematics and its language is such that many mathematicians do indeed identify the two [ Spectrum , p. 112]:

19. 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

20. Patterns - Secondary Level
In this book, students study history and geometry as they arithmetic, symmetry,design transformation, Latin squares, pascals triangle, repeating circles
http://www.awl.ca/school/math/mr/pat/pattxt.html

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