Ib Maths Sl Portfolio Lacsap Fraction
IB Maths SL TYPE I
Lacsap’s Fractions Portfolio
Lacsap’s fraction
Introduction:
Lacsap’s fraction is a symmetrical triangle that has the following pattern in the first five rows
The shape is similar to Pascal triangle. It has the same quantity of symmetrical triangle as Pascal triangle. And Lacsap is the inverse alphabet order of Pascal. These make me think about Pascal triangle and I made an assumption that elements in Lacsap triangle may have the same relationship as in Pascal triangle. However, the elements in Lacsap’s fraction triangle may or may not have the same relationship as Pascal triangle so I ignore my hypothesis about Pascal triangle and decide to find the relationship by not referring to Pascal triangle. I believe that every element in Lacsap’s triangle must be in a sequence and the task for this portfolio is to find the relationship between each element.
This portfolio will be divided into five parts; finding numerator relationship, finding denominator relationship, test the accuracy of the statement, finding additional rows and limitations of the statement.
The notations in this portfolio are * X = the element place * N = row number * En(x) = The xthelement on the nthrow
Numerator Relationship:
First thing I notice about the Lacsap is that the numerators are the same in the same row.
The numerators are the same in each row
My first statement about Lacsap’s fraction is the numerators are the same in each row.
Considering the second diagonal row may give me some clue about how to find the numerator. If I can find the numerator for the second diagonal, the numerator for that row is revealed because the numerators are the same in the same horizontal row.
Second diagonal row
Row number | Numerator | 1st difference | 2nd difference | 1 | 1 | - | - | 2 | 3 | 2 | - | 3 | 6 | 3 | 1 | 4 | 10 | 4 | 1 | 5 | 15 | 5 | 1 |
I can see that the numerator’s 1st difference is 2, 3, 4 and 5 for the first five
Lacsap’s Fractions Portfolio
Lacsap’s fraction
Introduction:
Lacsap’s fraction is a symmetrical triangle that has the following pattern in the first five rows
The shape is similar to Pascal triangle. It has the same quantity of symmetrical triangle as Pascal triangle. And Lacsap is the inverse alphabet order of Pascal. These make me think about Pascal triangle and I made an assumption that elements in Lacsap triangle may have the same relationship as in Pascal triangle. However, the elements in Lacsap’s fraction triangle may or may not have the same relationship as Pascal triangle so I ignore my hypothesis about Pascal triangle and decide to find the relationship by not referring to Pascal triangle. I believe that every element in Lacsap’s triangle must be in a sequence and the task for this portfolio is to find the relationship between each element.
This portfolio will be divided into five parts; finding numerator relationship, finding denominator relationship, test the accuracy of the statement, finding additional rows and limitations of the statement.
The notations in this portfolio are * X = the element place * N = row number * En(x) = The xthelement on the nthrow
Numerator Relationship:
First thing I notice about the Lacsap is that the numerators are the same in the same row.
The numerators are the same in each row
My first statement about Lacsap’s fraction is the numerators are the same in each row.
Considering the second diagonal row may give me some clue about how to find the numerator. If I can find the numerator for the second diagonal, the numerator for that row is revealed because the numerators are the same in the same horizontal row.
Second diagonal row
Row number | Numerator | 1st difference | 2nd difference | 1 | 1 | - | - | 2 | 3 | 2 | - | 3 | 6 | 3 | 1 | 4 | 10 | 4 | 1 | 5 | 15 | 5 | 1 |
I can see that the numerator’s 1st difference is 2, 3, 4 and 5 for the first five