Hello again. This is my second blog entry. Last time, I had some good results, but this time, I wasn’t so fortunate and I do not have results that are as good, accurate, or relevant. I have found something different than I was looking for.
This time, the question I was investigating the question:
If you know the side lengths of a right triangle, can you predict what the angles will be?
I did not find the answer to that question. Instead, I found a semi-pattern that is not really a pattern. It seems like a pattern, but I didn’t find a pattern. Maybe you can find one. This is what I did.
My teacher us to find patterns, but I was stuck. So, my teacher gave me a clue. She said that the relationship was in the ratio of the legs. After getting that clue, I started experimenting with the legs. I divided the longer leg by the shorter leg in some of the Pythagorean triples. These are my results:
4 ÷ 3 = 1.33333333
12 ÷ 5 = 2.4
24 ÷ 7 = 3.42857143
40 ÷ 9 = 4.44444444
60 ÷ 11 = 5.45454545
84 ÷ 13 = 6.46153846
112 ÷ 15 = 7.46666667
…
The quotient increases by about 1 each time, but not exactly. In fact, I calculated the difference of every two numbers. These are the results for that:
4 ÷ 3 = 1.33333333
+1.06666667
12 ÷ 5 = 2.4
+1.02857143
24 ÷ 7 = 3.42857143
+1.01587301
40 ÷ 9 = 4.44444444
+1.01010101
60 ÷ 11 = 5.45454545
+1.00699301
84 ÷ 13 = 6.46153846
+1.00512821
112 ÷ 15 = 7.46666667
…
This time, the numbers decrease each time. I found the difference between those, too, but they don’t have a pattern them either, so I won’t bother posting them here. That is what I have done since my last entry. Thank you.
