[USER=29]@Kris Morgan[/USER] . That's a fine piece of analysis. Your formula gives the sum of the first (n - 1) integers and seeing that 7 points create 6 unique lines and so on, and then finding a formula, may just qualify you as a math nerd.:)
We teach that as (n + 1)n/2 in order to get the sum of the first n integers, but we make the students derive it from a theoretical beginning. It's interesting to do some Googling and see how Gauss found the sum of the first 100 integers as an elementary student.
I wish we could convince more people that math is fun.
Kris, you get a lot of vectors, but they are not independent. Each new measurement gives only one new independent vector. The rest are completely determined by those few you can treat as independent. That means you don't have anywhere close to 30 independent measurements for statistical purposes.
Jones, post: 389647, member: 10458 wrote: [USER=50]@Holy Cow[/USER] and [USER=7674]@MathTeacher[/USER]
.....This board was made up of Principles, teachers, and parents.
So many boards don't have any principles......it's nice to see one that does. 😀
Pal = human = principal
[USER=87]@Bill93[/USER] I agree I don't have 30 measurements to one point, but with 8 points, I have 28 different measurements across an old tract between control points. So, if I view the point as the sample, I agree, but if I view the original traverse or control network as 1, then I do have the requisite measurements to constrain and evaluate with, statistically speaking. To me, and my stats professor in college, it's about what you're trying to sample.
If you set up a base and take GPS data on N additional points, you have N independent vector measurements from the base. The many other vectors from point to point can be calculated, but provide no new information to help the statistics. To get the 28 or whatever to be statistically useful, you have to measure each of the combinations, not just calculate them from the N original measurements.
I always get into trouble when I talk about measurements and adjustments. At the risk of getting into trouble, I'll share this link to the NCDOT GPS guidelines. Page 4 gives a very brief description of independent baselines.
Please forgive me if it's off target.