61. Gymnasieegnet Litteratur - Artikel Database Jean Pedersen Looking into Pascal's triangle Combinatorics, Arithmetic and geometry. BeskrivelseGiver med udgangspunkt i pascals trekant en http://www.imf.au.dk/Mathematics/ungdoms/artikelbase.html

TOP General Information Mathematics Vejledning for 3.g Gymnasieegnet litteratur - Artikel database ID: Viggo Brun: A generalization of the formula of simpson for non-equidistant ordinates Tidsskrift: Normat Year: Vol: Nr: page: Beskrivelse: Emneord: integralregning, simpsons formel, numeriske metoder ID: Henry Jensen: Om koordinater i de danske kort Tidsskrift: Normat Year: Vol: Nr: page: Beskrivelse: Emneord: kartografi ID: Erling Følner: Elementer af von Neumanns spilteori Tidsskrift: Normat Year: Vol: Nr: page: Beskrivelse: En matematisk teori omkring simple hasardspil, hvor ikke kun tilfældigheder råder, men hvor også spillerens dygtighed har indflydelse. Emneord: spilteori ID: Niels Pipping: Halvregelbundna Kedjebråk Tidsskrift: Normat Year: Vol: Nr: page: Beskrivelse: En gennemgang af forskellige typer uendelige kædebrøker i forbindelse med rationale approksimationer af reelle tal. Emneord: kædebrøker, rationale tal ID: Sven Danø: Lineær programmering Tidsskrift: Normat Year: Vol: Nr: page: Beskrivelse: Artiklen introducerer problemet i lineær programmering og angiver såvel en principiel som en praktisk metode (simpleks) til løsning. Kendskab til matrix-regning er nok en forudsætning. Emneord: lineær algebra, lineær programmering, simplex-metoden

62. Mathematical Biographies He wrote Geometria Indivisiblium or The geometry of Indivisibles He is most knownfor his Pascal triangle,which gives He also proved that pascals triangles work http://eva.silva.students.noctrl.edu/mathbiowbpg.html

to "Mathematical Biographies" Abel Agnesi Archimedes Apollonius ... Wilson Back to Home Page For More Info: Mac Tutor Site For more Mathematicians: Index of Mathematicians Thales (ca. 625-547 B.C.) He found that the height of a pyramid can be calculated by similar triangles. He is most known for five theorems: 1) A circle is bisected by any diameter. 2) The base angles of an isosceles triangle are equal. 3) The angles between two intersecting straight lines are equal. 4) Two triangles are congruent if they have two angles and one side equal. 5.)An angle inscribed in a semicircle is a right angle. for more info on Thales: link to Thales Site The result about angles subtended in a circle Greek Astronomy References for Thales back to top Pythagoras (ca. 580-500 B.C.) He is most well known for the Pythagorean Theorem: x + y = z He also has worked with triangular, even, and perfect numbers. for more info on Pythagoras: link to Pythagoras Site Pythagoras's Theorem References for Pythagoras back to top Democritus (ca. 460-370 B.C.) He found the volume of a cone to be 1/3 the volume of a cylinder with the same base and equal height. Also, he found the volume of a pyramid to be 1/3 the volume of a prism with the same base and equal height. He also has been known to dabble in circles, spheres, geometry, numbers, irrational lines and solids, and projections.

63. CyberSpace Search! SEARCH THE WEB. Results 1 through 6 of 6 for pascals triangle. http://www.cyberspace.com/cgi-bin/cs_search.cgi?Terms=pascals triangle

64. National Library Of Virtual Manipulatives pascals triangle – Explore patterns created by selecting elements of pascals triangle. TurtleGeometry – Explore numbers, shapes, and logic by programming http://matti.usu.edu/nlvm/nav/grade_g_4.html

All Topics (Grades 9 - 12) Virtual manipulatives related to the NCTM standards for grades Abacus Circle 0 Circle 99 Conways Game of Life ... Turtle Geometry Algebra (Grades 9 - 12) Algebra Balance Scales Algebra Tiles Base Blocks Coin Problem ... Triominoes Geometry (Grades 9 - 12) Cob Web Plot Geoboard Geoboard - Circular Geoboard - Coordinate ... Transformations - Translation Measurement (Grades 9 - 12) Converting Units Fill and Pour Geoboard Geoboard - Circular ... Contact

65. NRICH Mathematics Enrichment Club (1777.html) Maths and nature golden rectangle and Pascal's triangle out how the golden rectangle or pascals triangle relate to nature. numbers in the pascal triangle black and all of the http://www.nrich.maths.org.uk/askedNRICH/edited/1777_printable.shtml

Asked NRICH Maths and nature - golden rectangle and Pascal's triangle By Emily Tildesley (P3504) on Thursday, December 28, 2000 - 12:58 pm By Richard Samworth (Rjs57) on Tuesday, January 2, 2001 - 12:07 pm Emily, here this is of some use. I hope this helps. Richard By Brad Rodgers (P1930) on Tuesday, January 2, 2001 - 07:34 pm [For that picture, see the second link above. - The Editor] http://nrich.maths.org/askedNRICH/edited/1777.html

66. Everything Or Nothing Likewise with a pyramid. If the properties of geometry fit perfectly topascals triangle, they fit perfectly with a binary probability table. http://www.ebtx.com/wwwboard/messages/1259.html

everything or nothing Follow Ups Post Followup Ebtx D-Board FAQ Posted ByMatt on May 08, 2001 at 20:57:48: I remembered this the other day, and the more I think about it, the more it seems like a piece of the big puzzle. Before I can explain it, the relationship between pascals triangle and a probability table needs to be understood. (they are basically the same thing) Take a binary probability table. Only 2 things, 1 and 0. For every 1 OR 0, there is a 1 AND 0. It looks something like this. The + is a 1 AND/OR 0. Now take pascals triangle. A 1 on the first row, and each row adds up to twice what the previous row was. It looks like this. Pascals triangle is the same as the probability table. If you add up the ones in each section of the probability table, they are the numbers in pascals triangle. Basically, pascals triangle is the number of ones for every section of a probability table. Okay, here's what's been bugging me. I need to explain the simple geometry first. The simplest 1 dimensional thing, a line segment. 1 termination point on each end. So, 1 line, 2 points. The simplest 2 dimensional thing, a triangle (not circle, I'll explain). 3 points for the corners, and 3 lines connecting the points. So, 1 plane, 3 lines, 3 points.

67. Re: Everything Or Nothing Likewise with a pyramid. If the properties of geometry fit perfectly topascals triangle, they fit perfectly with a binary probability table. http://www.ebtx.com/wwwboard/messages/1278.html

Re: everything or nothing Follow Ups Post Followup Ebtx D-Board FAQ Posted By S. on May 10, 2001 at 12:40:26: In Reply to: everything or nothing posted byMatt on May 08, 2001 at 20:57:48: : I remembered this the other day, and the more I think about it, the more it seems like a piece of the big puzzle. : Before I can explain it, the relationship between pascals triangle and a probability table needs to be understood. (they are basically the same thing) : Take a binary probability table. Only 2 things, 1 and 0. For every 1 OR 0, there is a 1 AND 0. It looks something like this. The + is a 1 AND/OR 0. : Now take pascals triangle. A 1 on the first row, and each row adds up to twice what the previous row was. It looks like this. : Pascals triangle is the same as the probability table. If you add up the ones in each section of the probability table, they are the numbers in pascals triangle. Basically, pascals triangle is the number of ones for every section of a probability table. : Okay, here's what's been bugging me. I need to explain the simple geometry first. : The simplest 1 dimensional thing, a line segment. 1 termination point on each end. So, 1 line, 2 points.

68. Green Fields Mathmatics Highspeed links Pascal's triangle A project that can be used involving pascalstriangle; geometry games games that are playable such as rubik and others. http://www.greenfields.org/departments/internet/math/math_internet.htm

Links History of mathmatics The student can get historical information on different areas of math Math Homework Help: aids the student with any questions they have for math. Math Gives General knowledge of math Ask Dr. Math: Aids the sudent who has questions about math.. Highspeed links Pascal's triangle: A project that can be used involving pascals triangle Geometry games: games that are playable such as rubik and others. A fun game A geometric game using shapes and physics Other Cool Links A Geometry page : A shape used in Geometry This page was designed and tested by Brian Halbach '04 Please submit your comments to webmaster@greenfields.org Back to Links Menu

69. Nelson Thornes Online Education http//www.mathleague.com/help/geometry/polygons.htm. article on Generating Pascal'sTriangle at http CapeCanaveral/Launchpad/5577/musings/pascals.html Chapter http://www.nelsonthornes.com/secondary/maths/ks4_keymaths_links.htm

Secondary Mathematics at Nelson Thornes Maths Home Key Stage 3 Key Stage 4 Scotland Contact Us You are here: Nelson Thornes Secondary Maths Key Stage 4 Books ... Intro Books Online Resources Curriculum Links IT Support Links For Key Maths GCSE Foundation Intermediate I Intermediate II Higher Foundation Chapter 1 Explore the Virtual Reality Polyhedra site http://www.georgehart.com Another very good site for finding out about polyhedra, and how to make them, is found at http://www.geocities.com/SoHo/Exhibit/5901/indexe.html Chapter See all kinds of polygons at this site http://www.mathleague.com/help/geometry/polygons.htm Chapter Pupils can investigate the patterns in Pascal's triangle at this site. http://mathforum.com/workshops/usi/pascal/ The Saint Andrews University site has a Biography of Pascal http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html There is an article on Generating Pascal's Triangle at: http://www.geocities.com/CapeCanaveral/Launchpad/5577/musings/Pascals.html

70. Keyed-in http//www.mathleague.com/help/geometry/polygons.htm. an article on Generating Pascal'sTriangle at http CapeCanaveral/Launchpad/5577/musings/pascals.html Unit http://www.nelsonthornes.com/secondary/maths/keyed_in/teachfound.html

Maths Home Keyed-in Home Ed's puzzle page Key Maths Quest ... Teacher file Key Maths - GCSE Links - Foundation Unit 1 Explore the Virtual Reality Polyhedra site http://www.georgehart.com Another very good site for finding out about polyhedra, and how to make them, is found at http://www.geocities.com/SoHo/Exhibit/5901/indexe.html Unit 3 See all kinds of polygons at this site http://www.mathleague.com/help/geometry/polygons.htm Unit 9 Pupils can investigate the patterns in Pascal's triangle at this site. http://mathforum.com/workshops/usi/pascal/ The Saint Andrews University site has a Biography of Pascal http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html There is an article on Generating Pascal's Triangle at: http://www.geocities.com/CapeCanaveral/Launchpad/5577/musings/Pascals.html Unit 11 Data for probability can be found at the UK National Lottery site.

71. Who Is Blaise Pascal time and went to his new found past time, geometry. The first seven rows of Pascal'sTriangle look like There is anouther theory or pascals trialngle which is http://www.wchs.srsd.sk.ca/Barteski/Computers 9/Savannah Botts (bliase plascal)

Who is Blaise Pascal? Blaise Pascal was born at Clermont on June 19, 1623, and died on August 19, 1662 in Paris. When Pascal was little he asked his tutor what geometry consisted of, the tutor responded " it was the science of constructing exact figures and of determining the proportions between their different parts " , after hearing this he gave up his play time and went to his new found past time, geometry. in a few weeks he found that his proof simply consisted in turning the angular points of a triangular piece of paper over so as to meet in the centre of the inscribed circle: a similar concealment can be found by turning the angular points over so to meet at the foot of the upright drawn from the prevailing angle to the other side The first seven rows of Pascal's Triangle look like: 1 n=0 1 1 n=1 1 2 1 n=2 1 3 3 1 n=3 1 4 6 4 1 n=4 1 5 10 10 5 1 n=5 1 6 15 20 15 6 1 n=6 There is anouther theory or pascals trialngle which is very similar to the above example. That would be called "Pascals Theory" The triangle is constructed as in the figure below, each horizontal line being formed form the one above it by making every number in it equal to the sum of those above and to the left of it in the row immediately above it;

72. The Math Forum: Geometry-research Web Discussion com ignore no reply 27 Jun 2002 2 some questions on measure theory 25 Jun 20023 a triangle problem 19 Jun 2002 1 Alternating Series, geometry, Theory of http://mathquest.com/epigone/geometry-research/all

Web Discussion: geometry-research all topics Subscribe/More Information Search this discussion Search all geometry discussions View all messages ... View recent messages Back to all discussions View by month: September 1992 October 1992 November 1992 January 1993 February 1993 March 1993 April 1993 May 1993 June 1993 July 1993 August 1993 September 1993 October 1993 November 1993 December 1993 January 1994 February 1994 March 1994 April 1994 May 1994 June 1994 July 1994 August 1994 September 1994 October 1994 November 1994 December 1994 January 1995 February 1995 March 1995 April 1995 May 1995 June 1995 July 1995 August 1995 September 1995 October 1995 November 1995 December 1995 March 1996 April 1996 June 1996 July 1996 September 1996 October 1996 November 1996 December 1996 January 1997 March 1997 April 1997 May 1997 June 1997 July 1997 August 1997 September 1997 October 1997 November 1997 December 1997 January 1998 February 1998 March 1998 April 1998 May 1998 June 1998 July 1998 August 1998 September 1998 October 1998 November 1998 December 1998 January 1999 February 1999 March 1999 April 1999 May 1999 June 1999 July 1999 August 1999 September 1999 October 1999 November 1999 December 1999 January 2000 February 2000 March 2000 April 2000 May 2000 June 2000 July 2000 August 2000 September 2000 October 2000 November 2000 December 2000 January 2001 February 2001 March 2001 April 2001 May 2001 June 2001 July 2001 August 2001 September 2001 October 2001 November 2001 December 2001 January 2002 February 2002 March 2002 April 2002 May 2002 June 2002 July 2002 August 2002 September 2002 October 2002 November 2002

73. Pascal's Triangle -- From MathWorld Pickover, C. A. Beauty, Symmetry, and Pascal's triangle. Ch. Wells, D. The PenguinDictionary of Curious and Interesting geometry. London Penguin, pp. http://mathworld.wolfram.com/PascalsTriangle.html

Discrete Mathematics Combinatorics Binomial Coefficients Number Theory ... Number Triangles Pascal's Triangle A triangle of numbers arranged in staggered rows such that where is a binomial coefficient . The triangle was studied by B. Pascal although it had been described centuries earlier by Chinese mathematician Yanghui (about 500 years earlier, in fact) and the Persian astronomer-poet It is therefore known as the Yanghui triangle in China. Starting with n = 0, the triangle is (Sloane's Pascal's formula shows that each subsequent row is obtained by adding the two entries diagonally above, In addition, the " shallow diagonals " of Pascal's triangle sum to Fibonacci numbers where is a generalized hypergeometric function Pascal's triangle contains the figurate numbers along its diagonals. It can be shown that and The "shallow diagonals" sum to the Fibonacci sequence , i.e., In addition, It is also true that the first number after the 1 in each row divides all other numbers in that row iff it is a prime . If is the number of odd terms in the first n rows of the Pascal triangle, then

74. JAVA Gallery Of Interactive On-Line Geometry transformations to move around on a game board shaped like Sierpinski's triangle,a famous Register Tell Us What You Think Up The geometry Center Home Page http://www.geom.umn.edu/java/

75. Blaise Pascal (1623 - 1662) Detailed biography reproduced from a 1908 history of mathematics.Category Kids and Teens School Time Scientists Pascal, Blaise...... and one day, being then twelve years old, he asked in what geometry consisted. inparticular the proposition that the sum of the angles of a triangle is equal http://www.maths.tcd.ie/pub/HistMath/People/Pascal/RouseBall/RB_Pascal.html

Blaise Pascal (1623 - 1662) From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. Among the contemporaries of Descartes none displayed greater natural genius than Pascal, but his mathematical reputation rests more on what he might have done than on what he actually effected, as during a considerable part of his life he deemed it his duty to devote his whole time to religious exercises. Blaise Pascal Elements , a book which Pascal read with avidity and soon mastered. In 1650, when in the midst of these researches, Pascal suddenly abandoned his favourite pursuits to study religion, or, as he says in his , ``contemplate the greatness and the misery of man''; and about the same time he persuaded the younger of his two sisters to enter the Port Royal society. His famous Provincial Letters directed against the Jesuits, and his , were written towards the close of his life, and are the first example of that finished form which is characteristic of the best French literature. The only mathematical work that he produced after retiring to Port Royal was the essay on the cycloid in 1658. He was suffering from sleeplessness and toothache when the idea occurred to him, and to his surprise his teeth immediately ceased to ache. Regarding this as a divine intimation to proceed with the problem, he worked incessantly for eight days at it, and completed a tolerably full account of the geometry of the cycloid. I now proceed to consider his mathematical works in rather greater detail.

76. ? v. 13, Total orderings of cardinality w1, v. 5, Re Geometryproblem, v. 9, Parallel vectors, v. v. 2, pascals triangle,v. 28 http://mathmag.spbu.ru/conference/sci.math/b206000/

77. Pascal An overview and selection of links.Category Society Philosophy Philosophers Pascal, Blaise...... however, his curiosity raised by this, started to work on geometry himself at theage of 12. He discovered that the sum of the angles of a triangle are two http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html

Blaise Pascal Born: 19 June 1623 in Clermont (now Clermont-Ferrand), Auvergne, France Died: 19 Aug 1662 in Paris, France Click the picture above to see six larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Blaise Pascal was the third of Etienne Pascal 's children and his only son. Blaise's mother died when he was only three years old. In 1632 the Pascal family, Etienne and his four children, left Clermont and settled in Paris. Blaise Pascal's father had unorthodox educational views and decided to teach his son himself. Etienne Pascal decided that Blaise was not to study mathematics before the age of 15 and all mathematics texts were removed from their house. Blaise however, his curiosity raised by this, started to work on geometry himself at the age of 12. He discovered that the sum of the angles of a triangle are two right angles and, when his father found out, he relented and allowed Blaise a copy of Euclid At the age of 14 Blaise Pascal started to accompany his father to Mersenne 's meetings.

78. Orðasafn: P parallelism, (in elementary geometry) samsíðuskipan. parallelizability, () Pascal'striangle Pascalþríhyrningur, þríhyrningur pascals. http://www.hi.is/~mmh/ord/safn/safnP.html

P packing , troðsla. packing density troðsluþéttleiki. packing of spheres kúlnatroðsla, = sphere packing packing problem troðsluverkefni. $p$-adic , $p$-legur. $p$-adic integer $p$-leg heiltala, heil p-leg tala. $p$-adic number $p$-leg tala. $p$-adic valuation $p$-leg virðing. pair tvennd, raðtvennd, röðuð tvennd, = couple ordered couple ordered pair óröðuð tvennd, = non-ordered pair plain pair unordered pair pair of compasses hringfari, = compass pair of primes frumtalnatvíburar, = prime pair prime twins twin primes pair set tvístökungur, tveggjastakamengi, = two element set paired comparison paraður samanburður. pairing axiom frumsenda um lítil mengi, frumsetning um lítil mengi, = axiom of pairing pairwise , tveir og tveir. pairwise disjoint sundurlægir tveir og tveir, = mutually disjoint 2 pairwise independent óháðir tveir og tveir, = mutually independent palindromic number spegiltala. pandiagonal magic square heilsteyptur töfraferningur, = diabolic magic square perfect magic square Pappian , Papposar-, pappeskur. Pappian plane Papposarslétta, pappesk slétta.

79. World's Greatest Creation Scientists From Y1K To Y2K We speak of “pascals” of pressure, Pascal and mathematicians speak of Pascal’striangle. on conic sections, projective geometry, probability, binomial http://www.creationsafaris.com/wgcs_2.htm

Home: creationsafaris.com Bible-Science Resources: creationsafaris.com/bisci.htm creationsafaris.com/teach.htm From to by David F. Coppedge c. 2000 David F. Coppedge, Master Plan Productions PART II Science Takes Off in All Directions Blaise Pascal Blaise Pascal was the youngest of three children, the only boy. His mother died when he was three years old. His father, Etienne, a tax collector, took to schooling the children himself. At age 19, Blaise started working on a mechanical calculator to help his father with his work. The Pascaline Pascal grew in reputation as a mathematician so that in his prime he corresponded with other notable scientists and philosophers: Fermat, Descartes, Christopher Wren, Leibniz, Huygens, and others. He worked on conic sections, projective geometry, probability, binomial coefficients, cycloids, and many other puzzles of the day, sometimes challenging his famous colleagues with difficult problems which he, of course, solved on his own. In physics, Pascal also excelled in both theory and experiment. At age 30, he had completed a Treatise on the Equilibrium of Liquids Provincial Letters (Thoughts). Nevertheless, enough was written to give believers and unbelievers alike a great deal of food for thought: on the nature of man, sin, suffering, unbelief, philosophy, false religion, Jesus Christ, the Scriptures, heaven and hell, and much more. The entire work is available online and highly recommended reading.

80. The History Of Computers: Blaise Pascal raised by this, started to work on geometry himself at the sum of the angles of atriangle are 2 One of pascals early desk calculators using the toothhed wheel http://www2.fht-esslingen.de/studentisches/Computer_Geschichte/grp1/seite4.html

The Calculating Machine Blaise Pascal hundreds, thousends, etc. The Number that is to be operated upon is represented by the tooth that faces the index above each wheel (a viewing window in an actual machine). For example, the number 456 is represented by the position of the toothed wheels. If you wanted to add 111 to this number, you would simply turn each wheel by one tooth (or noth), so that the theeth indicating 5,6, and 7 would face the index or viewing windows. The result of the addition of 456 and 111 appears at the viewing window. One of Pascals early desk calculators using the toothhed wheel principle, like this, Authors: H. Rentzsch G. Ottenbacher Back to the index-page

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