Lascap triangles Math Portfolio

by xrosraiser (student)

Lascap’s fractions

Bill LI

IB Math SL

Internal Assessment Type 1

Introduction

Pg.1

Finding the numerator

Pg.2

Graphical representation of correlation of the row number, n, and the numerator

Pg.3-4

Finding the sixth and seventh rows using patterns:

Pg.5

The general statement

Pg.6

Testing the validity of the general statement by finding additional rows

Pg.7

Conclusion

Pg.8

Introduction

Aim: In this task you will consider a set of numbers that are presented in a symmetrical pattern

Figure 1: The given pattern, Lascap’s fractions

1    1

1

1

1

1

1

1

1

1

Lascap’s fraction is in the form of a triangle where there is an increase of one element for each row that is increased. In this math portfolio Lascap’s fraction general formula will be disused and along with that how the general formula was formed due to patterns in the fraction themselves.

Finding the numerator:

First find the denominators of the rows in order from top to bottom and the differences of the denominators. The 1’s in this case are substituted for an equal fraction.

Figure 2: The difference of the numerators between each row of Lascap’s fractions

In this case the difference of the denominators is 2, 3, 4, and 5 going down the rows. Based on these numbers only, the pattern is a sum notation. Which ...