Learning Resources for Students, Families and Teachers

Search over 100,000 research quality URLs

StudySphere provides fast, easy and free access to a wide variety of research-quality child-safe websites organized for education online from home, school, study abroad and home school. StudySphere’s goal is to help students, teachers, librarians, and other researchers find both highly targeted and closely related information quickly.

Pascal's Triangle

/Home/Mathematics/Geometry/Pascal's Triangle


		American Scientist Online ^Votes:0 Home Current Issue Archives Bookshelf Online Features Marketplace Subscribe In This Section Search Book Reviews by Issue Issue Index Topical Index Author Index 1970-1997 Index Institutional Licensing American Scientist Classics Site Search Advanced Search Visitor Login Username Password Help with login Forgot your password? Change your username Archives FEATURED ITEM Computers, Paradoxes and the Foundations of Mathematics Gregory J. Chaitin Lots of things just can't be proved, yet mathematics moves forward Read More SECTION CONTENTS Welcome to the American Scientist Online archive of back-issue content. Members and subscribers have full access to the content published since 1998. Selected full-text "Classics" from earlier issues are also available, as is a complete listing of fea Read More Go to Site


		Blaise Pascal's Arithmetic Machine ^Votes:0 1640 AD Blaise Pascal's Arithmetic Machine As fate would have it, determining who invented the first mechanical calculator is somewhat problematical. Many references cite the French mathematician, physicist, and theologian, Blaise Pascal as being credited with the invention of the first operational calculating machine. Blaise Pascal. Copyright (c) 1997. Maxfield & Montrose Interactive Inc. a Pascal's Arithmetic Machine. Courtesy of IBM In 1640, Pascal started developing a device to help his father add sums of money. The first operating model, the Arithmetic Machine, was introduced in 1642, and Pascal created fifty more devices over the next ten years. (In 1658, Pascal created a scandal when, under the pseudonym of Amos Dettonville, he challenged other mathematicians to a contest and then a Read More Go to Site

		Cynthia Lanius' Fractals Unit: Sierpinski Meets Pascal ^Votes:0 Cynthia Lanius Sierpinski Meets Pascal Check it out! Table of Contents Introduction Why study fractals? What's so hot about fractals, anyway? Making fractals Sierpinski Triangle Using Java Math questions Sierpinski Meets Pascal Jurassic Park Fractal Using JAVA It grows complex Real first iteration Encoding the fractal World's Largest Koch Snowflake Using Java Infinite perimeter Finite area Anti-Snowflake Using Java Fractal Properties Self-similarity Fractional dimension Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Comments My fractals mail Send fractals mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received Notice the triangle above is all filled in. Now, what does this have to do with Sierpinski's Triangle? Try Read More Go to Site

		Cynthia Lanius' Fractals Unit: Sierpinski Meets Pascal ^Votes:0 Cynthia Lanius Sierpinski Meets Pascal Table of Contents Introduction Why study fractals? What's so hot about fractals, anyway? Making fractals Sierpinski Triangle Using Java Math questions Sierpinski Meets Pascal Jurassic Park Fractal Using JAVA It grows complex Real first iteration Encoding the fractal World's Largest Koch Snowflake Using Java Infinite perimeter Finite area Anti-Snowflake Using Java Fractal Properties Self-similarity Fractional dimension Formation by iteration For Teachers Teachers' Notes Teacher-to-Teacher Comments My fractals mail Send fractals mail Fractals on the Web The Math Forum Other Math Lessons by Cynthia Lanius Awards This Site has received Whose triangle is this, anyway? Have you ever seen the triangular pattern of numbers (above) named after the famous Frenc Read More Go to Site

		Development of Math in China3 ^Votes:0 Development of Mathematics in Ancient China Chinese Math Texts The history of Chinese math and mathematicians was mostly lost or destroyed over the centuries. For example, the despotic emperor Shih Huang-ti of the Ch'in dynasty (221-207 B.C.) ordered the burning of books in 213 B.C. Scholars in the following Han period (206 B.C. to 220 A.D.) had to transcribe China's literary and scientifice traditions from memory or remaining fragments of scroll. Knowledge of astronomy and other areas was often handed down from father to son, and only later recorded in texts. Unfortunately, very few texts dedicated to mathematical astronomy have survived. Since the 16 century, Chinese math history has also been denied and ignored in the Western dominance of science and technology, both inside and outside Read More Go to Site

		Ivars Peterson's MathTrek ^Votes:0 Ivars Peterson's MathTrek February 10, 1997 Pascal's Fractals Fascinating patterns can arise out of arrays of numbers defined by simple rules. For example, start with the number 1, and make it the apex of what will become a triangle of numbers. In the second row, write two 1s. For each subsequent line, add together adjacent numbers of the previous row and write the sums in the new row, then place 1s at both ends of the line. Here's what one gets for the first eight rows: ??????????????? ?????? 1 ??????????????????? 1 ??? 1 ????????????????? 1 ?? 2 ?? 1 ????????????? 1 ?? 3 ??? 3 ?? 1 ?????????? 1 ??? 4 ??? 6 ??? 4 ?? 1 ??????? 1 ??? 5 ?? 10 ?? 10 ?? 5 ??? 1 ? ??? 1 ?? 6 ?? 15 ??? 20 ??? 15 ?? 6 ??? 1 This set of numbers is now widely known as Pascal's triangle, named for French philosopher Read More Go to Site

		Ladja's Report on Pascal's Triangle ^Votes:0 --> Pascal's Triangle Blaise Pascal was born in France in 1623. He was a child prodigy, who was fascinated by mathematics. When Pascal was 19, he invented the first calculating machine which actually worked. This was something another mathematician named Fibonacci had tried to do before, but failed. One of the topics which interested Pascal was the likelihood of an event occurring. His interest was triggered by a gambler. The gambler asked Pascal to help him make better guesses, about which scores would be most likely to occur when 2 dice were thrown. In the course of his investigations, Pascal produced a triangular pattern of numbers which now bears his name. The pattern was known to the Chinese 300 years before Pascal, but it was Pascal who fully developed it. Pascal's triangle is a tria Read More Go to Site

		Math Forum - Ask Dr. Math ^Votes:0 Associated Topics \|\| Dr. Math Home \|\| Search Dr. Math An Explanation of Pascal's Triangle Date: 27 Feb 1995 22:57:04 -0500 From: Anonymous Subject: Probability and Pascal's Triangle My 10th grade daughter is having trouble finding a simple explanation of Pascal's Triangle and its application. So far we've discovered that, in lieu of prozac, Pascal turned to math and came up with the arithmetical triangle as an aid for his gambling buddies. But that's where our information runs out. Any help would be gratefully appreciated. Erin and Dale in Helena, Montana Date: 28 Feb 1995 14:19:21 -0500 From: Dr. Ken Subject: Re: Probability and Pascal's Triangle Hello there! Well, since I'm not quite sure how much you know about Pascal's Triangle (for instance, you seem to know that it is connected to th Read More Go to Site

		Math Forum Electronic Newsletter ^Votes:0 --> Volume 2, Number 17 Back to Table of Contents 28 April 1997 Vol. 2, No. 17 THE MATH FORUM INTERNET NEWS Math & Energy Conservation \| Devlin's Angle \| Pascal's Triangle MATHEMATICS AND ENERGY CONSERVATION http://ecep1.usl.edu/ecep/math/math.htm Math Activity Guides created for the vocational technical schools in Louisiana as part of the Energy Conservation Enhancement Project. Starting with addition and subtraction and moving up through word problems, algebra, fractions, decimals, percentages, measuring, area and volume, ratio, proportion, and graphing, these practical lessons present math operations for solving real-world problems involving energy in home construction. Examples include: - calculating insulation choices for a home; - figuring the cost of energy-related goods and service Read More Go to Site

		Pascal's Triangle ^Votes:0 Pascal's Triangle to Row 19 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1 1 11 55 165 330 462 462 330 165 55 11 1 1 12 66 220 495 792 924 792 495 220 66 12 1 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1 1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1 1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1 1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1 1 18 153 816 3060 8568 18564 31824 43758 48620 43758 31824 18564 8568 3060 816 153 18 1 1 19 171 969 3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628 3876 969 171 19 1 Read More Go to Site

		Pascal's Triangle ^Votes:0 Pascal's Triangle Step 1: Fill in the missing numbers in Pascal's Triangle Check the answer here Step 2: Color the odd and even numbers with two distinct colors Check the answer here. Surprise? Pictures presented in this section are all provided by Dale Seymour Publications <--- back Contents (c) Copyright 1994,1995,1996,1997, 1998, 1999, 2000, 2001, 2002, 2003, and 2004 by Mary Ann Connors. All rights reserved. If you wish to use any of the text or images in Exploring Fractals please contact its author Mary Ann Connors at the following address. Thank you. Dr. Mary Ann Connors Department of Mathematics & Statistics Lederle Graduate Research Tower University of Massachusetts Amherst, MA 01003 Email: mconnors@math.umass.edu mconnors@math.umass.edu Read More Go to Site

		Pascal's Triangle Interface ^Votes:0 Pascal's Triangle Interface Pascal's Triangle Interface INSTRUCTIONS This form interface lets you visualize the entries of Pascal's triangle with respect to a modulus between 2 and 16. Select values for the number of rows, modulus, and the size of the image, and then submit. Otherwise the default values should generate an interesting image. Output Image Rows (max 100): Modulus (2 to 16): Image size: Read More Go to Site

		Recipe for the week of November 27 - December 3, 1995 ^Votes:0 The Cook Book Recipe for the week of November 27 - December 3 A Holiday Chestnut: Pascal's Triangle mod N Some rather pleasing patterns can be made by painting Pascal's Triangle of binomial coefficients modulo N . In other words, if N is 2 or more, color a number k in the triangle one of N colors (using your favorite palette) according to the remainder when k is divided by N. In our scheme, a remainder of 0 yields dark blue, remainder 1 green, etc. (Black is the background for the checkerboard lattice.) Note that you need not compute actual values in the triangle to determine a pattern; for given N, the modular arithmetic defines a simple rule whereby any interior color is a consequence of the two colors located just above. In other words, these are space-time diagrams of additive one-dime Read More Go to Site

		Visuals Patterns in Pascal's Triangle ^Votes:0 Visuals Patterns in Pascal's Triangle Visuals Patterns in Pascal's Triangle Ulysses Harrison Dunbar Vocational High School 8435 South Wood Street 3000 South King Drive Chicago IL 60620 Chicago IL 60616 (312) 239-6333 (312) 534-9000 Objectives : 1. To use a phenomenological approach to impress upon students the many visual patterns and number patterns that are present in the sequence of numbers that make up Pascal's Triangle. 2. To convince students that they are able to construct Pascal's Triangle on their own without use of notes after the conclusion of this presen- tation. 3. To encourage students to explore on their own patterns that exist in Pascal's Triangle, but which they were previously unaware. Materials Needed : Overhead Projector Three (3) prepared overhead displays of Pascal's Read More Go to Site

StudySphere is an outstanding resource for homework help, special education, music school, cooking school, charter schools, art schools, technical schools, traffic school, film schools, catholic schools, etc.