# LACSAP's Functions

LACSAP’S FRACTIONS

Tanya Zhandria Waqanika
Prince Andrew High School
IB Math SL Portfolio #1
Mr Brown

Task 1 – Find the Numerator
Task 2 – Plot relation between the row number and Numerator, write general statement about it
Task 3 – Find the 6
th and 7th rows
Task 4 – Find the general statement for E
n(r)
Task 5 – Find additional rows with General Statement
Task 6 – Discuss the scope/limitations of the General Statement

Task 1 - Finding the Numerator

Since ‘LACSAP’ is just ‘Pascal’ reversed, I decided to do some research about Pascal’s triangle. Through my research, I was able to come across the equation nCr, or n!/r!(n –r)! where n represents the row number and r represents the ‘element’ number, or the diagonal row number.

e.g. 3C2 = 3!/2!(3 – 2)! = 1 x 2 x 3/1 x 2 x 1 = 3

This equation is used to find any number within Pascal’s triangle. With 1 at the top of both pyramids representing n = 0, r = 0, I decided to compare Pascal’s triangle to LACSAP’s fractions.

Pascal’s triangle

LACSAP’S Fractions.

Since I’m trying to find the numerator, I was looking for any similarities between the two triangles. As it so happens, in Pascal’s triangle, when r = 2, the diagonal sequence is the same as the numerator order in LACSAP’s fractions. This sequence is called the Triangular sequence. Here is a table to show this.

Knowing this, in the equation nCr, r would have =2 in this case.  Afterwards, I decided to plot the row numbers of LACSAP’s fractions with the numerators and the newfound equation nC2, or n!/2!(n-2)!

Task 2 - Plot relation between the row number and Numerator, write general statement about it

This is a graph of Numerator (y – axis) vs Row Numbers (n) (x – axis)

In the equation nCr, n must be equal to or greater than r in order for it to work properly. Though the equation was coming up with the right numerators, they were coming ...