This investigation explores patterns in Lacsap’s Fractions, developing general rules which illustrate the rules for finding the numerators and denominators of these fractions. I will start with the fo
This investigation explores patterns in Lacsap’s Fractions, developing general rules which illustrate the rules for finding the numerators and denominators of these fractions. I will start with the fo
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This investigation explores patterns in Lacsap’s Fractions, developing general rules which illustrate the rules for finding the numerators and denominators of these fractions. I will start with the following:
1 1
1 3/2 1
1 6/4 6/4 1
1 10/7 10/6 10/7 1
1 15/11 15/9 15/9 15/11 1
I initially noticed the following:
Row Number Numerator in Previous Row Numerator in Current Row Difference of Numerators Row Number Equals Difference?
2 1 3 2 Yes
3 3 6 3 Yes
4 6 10 4 Yes
5 10 15 5 Yes
To find the numerator in the 6th row, 6 must be added to 15 because with each successive row, the row number is added to the previous numerator to find the current numerator, as illustrated by the above table. Next, I decided to graph the relation between the row number and the numerator: