Lacsap’s Fractions IB Math 20 Portfolio By: Lorenzo Ravani Lacsap’s Fractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’s fractions. The goal of this portfolio is to find an equation that describes the pattern presented in Lacsap’s fraction. This equation must determine the numerator and the denominator for every row possible. Numerator Elements of the Pascal’s triangle form multiple horizontal rows (n) and diagonal rows (r). The elements
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Yao Cia Hua Mathematics SL LACSAP’S Fraction-‐ Portfolio Type I LACSAP’S Fractions - Math SL Type I Name: Yao Cia Hua Date: March 22nd‚ 2012 Teacher: Mr. Mark Bethune School: Sinarmas World Academy 1 Yao Cia Hua Mathematics SL LACSAP’S Fraction-‐ Portfolio Type I Lacsap triangle is a reversed Pascal triangle. This task
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Portfolio #1 This portfolio surrounds the mathematical ideals of the LACSAP’s Fractions‚ and creating the task of answering certain questions about a specific symmetrical pattern. Through a work entirely of my own and without any unauthorized outside assistance‚ I answers all of the questions in this portfolio along with showcasing all my work‚ aided by the use of technology and patterns discovered by me. The symmetrical pattern provided possesses only 5 vertical rows‚ with number of elements
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| Math SL Portfolio-Lacsap’s Fractions | Type 1: Investigation Portfolio Greenwood High (An International School) | | | | | Table of Contents: Introduction……………………………………………………………………………………………………..……..…...Page 2 Patterns in Numerator………………………………………………………………………………….………………Page 2 and Page 3 Plotting Graph of Row Number and Numerator……………………………………………………………Page 4 to Page 7 Finding Denominator………………………………………………….………………………………………..………Page 8 to Page 9 Finding Further Rows……………………………………………………………………
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Lacsap’s Fractions The aim if this IA is to investigate Lacsap’s Fractions and to come up with a general statement for finding the terms. When I noticed that Lacsap was Pascal spelt backwards I decided to look for a connection with Pascal’s triangle. Pascal’s triangle is used to show the numbers of ‘n’ choose ‘r’(nCr). The row number represents the value of ‘and the column number represents the ‘r’ value. Eg. Row 3‚ colomn 2 = 3C2 =
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Exploration of Lacsap’s Fractions The following will be an investigation of Lacsap’s Fractions‚ that is‚ a set of numbers that are presented in a symmetrical pattern. It is an interesting point that ‘Lacsap’ is ‘Pascal’ backwards‚ which hints that the triangle below will be similar to “Pascal’s Triangle”. 1 1 1 1 1 1 1 1 1 1 There are many patterns evident in this triangle‚ for instance I can see
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In Lacsap’s Fractions‚ En(r) refers to the (r+1)th term in the nth row. The numerator and denominator are found separately‚ therefore to find the general statement‚ two different equations‚ one for the numerator and one for the denominator‚ must be found. Let M=numerator and let D=denominator so that En(r) = M/D. To find the numerator for any number of Lacsap’s Fractions‚ an equation must be made that uses the row number to find the numerator. Because the numerator changes depending on the row
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1 Introduction. Let us consider a triangle of fractions: Obviously‚ the numbers are following some pattern. In this investigation we will try to explain the theory behind this arrangement and to find a general relation between the element’s number and its value. The pattern above is called a Lacsap’s Triangle‚ which inevitably hints at its relation to another arrangement - Pascal’s Triangle (as Lacsap appears to be an anagram of Pascal). The algorithm behind it is very simple: each element
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Lacsap’s Fractions Laurie Scott SL Math Internal Assessment Mr. Winningham 9/5/12 Instructions: In this task you will consider a set of numbers that are presented in a symmetrical pattern. Pascal’s Triangle |n=0 |1 | |1 |0 | |2 |3 | |3 |6 | |4 |10
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Type I – Mathematical Investigation Lacsap’s Fractions The focus of this investigation is surrounding Lascap’s Fractions. They are a group of numbers set up in a certain pattern. A similar mathematical example to Lacsap’s Fractions is Pascal’s Triangle. Pascal’s Triangle represents the coefficients of the binomial expansion of quadratic equations. It is arranged in such a way that the number underneath the two numbers above it‚ is the sum. Ex. 1 1 1 1 2 1 1
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