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 r increasing by 1 per new row created, and with r=0 representing the first element on each. However, one of the tasks requires finding the 6th row and its elements through patterns found in the pattern itself. Through a close analysis of the symmetrical pattern, which resembles Pascal’s Triangle in many ways, I found a relation between the numerators of the 1st element of every row, with r=1. As the first element of row 1 equals 1 (which can also be written as 11), the first element of row 2 equals 32. Just through that it can be seen the difference between numerators equaling 2. And as the first element in the third row is 64, the difference between numerators of second and third rows equals 3. And as I continued to analyze the numerators on the any elements of each of the following two rows, I came to the conclusion there was a pattern between their numerators and their row numbers. Therefore, the numerator of any element in any row will result from next numerator=previous numerator+(previous difference+1) equation. To be more mathematical, I developed the equation of numerator(row n)=n2+n2 , with n equaling the row number. To validate my general statement for finding numerators for rows, I tested it for finding the 6th row’s numerator, common to all of its elements. I calculated numerator6th row=n2+n2= 62+62=36+62=422=21, and through re-checking the patterns I’d found earlier and applying it to that row I came to the same results. However, the task was not fully...

...Lacsap’sFractions
IB Math 20 Portfolio
By: Lorenzo Ravani
Lacsap’sFractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’sfractions. The goal of this portfolio is to ﬁnd an equation that describes the pattern presented in Lacsap’sfraction. This equation must determine the numerator and the...

...Exploration of Lacsap’sFractions
The following will be an investigation of Lacsap’sFractions, 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...

...Type I – Mathematical Investigation
Lacsap’sFractions
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’sFractions 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...

...Lacsap’sFractions
The aim if this IA is to investigate Lacsap’sFractions 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...

...INTRODUCTION
Lacsap’s triangle-The set of numbers in concern are basically an inverse of the Pascal’s triangle. These terms themselves are fractions which follow different series themselves. There is a specific function that can accurately predict the fractional numbers accurately. Using the graph plots we can calculate this function and predict the numbers accurately. The whole process for finding the adequate function would involve the use of different smaller...

...1 1
1 32 1
1 64 64 1
1 107 106 107 1
1 1511 159 159 1511 1
The aim of this task is to find the general statement for En(r). Let En(r) be the element in the nth row, starting with r = 0.
First to find the numerator of the sixth row, the pattern for the numerator for the first five rows is observed. Since the numerator is the same in each row...

...
Yao
Cia
Hua
Mathematics
SL
LACSAP’SFraction-‐
Portfolio
Type
I
LACSAP’SFractions - 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...

...Lacsap’sFractions
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...