# Fred Kline

Seattle, WA

Age: 70

Contact: rudytoody.AT.comcast.DOT.net

I retired in 2006 and bought Mathematica and a stack of math books with the goal to teach myself to become a world-class mathematician. I am on pace to achieve that goal sometime shortly after the next Ice Age.

I consider myself a Mathematical Mutt (no papers) who occasionally ventures off the back porch to play in the yard with the big dogs.

I donate regularly to the The OEIS Foundation.

When I look at the patterns, I can hear the wheels turning. When I look at the math, I find out the hamsters have died.

 Dec 11 comment Accuracy of distance and bearing between GPS locationsPerhaps, you can use the nearest cell-tower location to reduce the uncertainty. Dec 11 comment Accuracy of distance and bearing between GPS locationsI believe you need a 3rd device whose location is known. Dec 9 awarded Caucus Dec 7 comment Alternate proofs for Collatz 1-Cycles@GottfriedHelms,I have an outside-the-box approach that uses symmetry, proportionality, and rigidity, all of which require a great amount of setup. This is an attempt to overcome the NP-ness of the proof (countably infinite cases). Contact me via my email in my profile or we could get a chat room. This explanation may take some time. (It implies that the count of all numbers is a square). Dec 7 comment Alternate proofs for Collatz 1-Cycles@GottfriedHelms, If you evaluate the main inequality for a few $r$'s you will see it has $t\geq1$ for all $r\geq3.$ Basically, we're proving for all $t\geq1$. Try setting $t=1\land r=3$ you will get True for the Waring part of the equation. Dec 7 comment Alternate proofs for Collatz 1-Cycles@GottfriedHelms, If all I need to do is show how Mathematica came up with the value, then it should be easy. The reason this works vs Waring's problem, is that we are proving for one $r$ at a time. When we try to do it for multiple $r$'s, we won't succeed. The advantage here is that $r$ is defined, so we precompute the exponentials and the Ceiling, then manually show the solution for each predefined $r.$ It is a proof by cases with infinite cases. It just so happens that the 1-Cycles occur at $r=2.$ Dec 7 comment What do these contour maps tell me about my Collatz expression?@GottfriedHelms, I posted the preliminary proofs of the 1-Cycle: math.stackexchange.com/q/1055394/28555 Dec 7 asked Alternate proofs for Collatz 1-Cycles Dec 5 comment What do these contour maps tell me about my Collatz expression?@GottfriedHelms, thanks. The sequence above shows all the potential 1-cycles per my definition. I have two inequalities that show that the first item is the only cycle. I can show this for all potential cycles. My definition of cycles is different from the usual, but I can show it covers all numbers $\in\textbf{Z}$. Dec 5 comment What do these contour maps tell me about my Collatz expression?@GottfriedHelms, Is this sequence $$\left\{2,\frac{8}{5},\frac{14}{9},\frac{20}{13},\frac{26}{17},\frac{32}{21}, \frac{38}{25},\frac{44}{29},\frac{50}{33},\frac{56}{37}\right\}$$ the 1-cycle? Dec 4 comment $\zeta(0)$ and the cotangent functionFrom Edwards, p 12, (1): for $n=0$,$$\zeta (2 n)=\frac{(-1)^{n+1} 2^{2 n-1} \pi ^{2 n} B_{2 n}}{(2 n)!}=\frac{(-1)^{n+1} 2^{2 n-1} \pi ^{2 n}}{(2 n)!}=-\frac{1}{2},$$ with and without the Bernoulli number. Dec 4 comment $\pi + e$ is rational or $\pi-e$ is rationalI seems to me that the OR should be AND in the OP and title. The truth value is False as noted by Martin Brandenburg in his answer. Dec 4 comment Name for sum of reciprocals$\frac{1}{n}$ is called a unit fraction. Dec 4 revised Software, techniques and tricks of experimental mathematics to conjecture possible closed formsadded comment about third book Dec 3 accepted What do these contour maps tell me about my Collatz expression? Dec 3 revised What do these contour maps tell me about my Collatz expression?added motivation and a tag Dec 3 comment What do these contour maps tell me about my Collatz expression?+1 for pointing out the extraneous assumptions. Dec 3 asked What do these contour maps tell me about my Collatz expression? Dec 1 answered How many different perfect matchings are there in this graph? Dec 1 answered How do I learn all the weird symbols and notations?