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Apr
28
comment Estimate the surface area of a 2D shape where the only known value is the length of the enclosing boundary
+1 @lhf: Thanks, the visuals on the wikipage for "isoperimetric inequality", combined with André Nicolas comment "The maximum area is obtained using a circle. There is no minimum", confirms it is not possible; to me. Big thanks for the amazingly fast answer! Cheers!
Apr
28
comment Estimate the surface area of a 2D shape where the only known value is the length of the enclosing boundary
+1 @André Nicolas: As you wish, your comment was a huge help, and was noted below the answer. Cheers!
Apr
28
comment Estimate the surface area of a 2D shape where the only known value is the length of the enclosing boundary
+1 @André Nicolas: Makes sense, feel free to post your comment as is, as an answer. Thanks!
Dec
2
comment Method of Modeling Problem Complexity
Given your background in software and mathematics, do you have any additional thought on how one might created a stable measure of a mathematical problems complexity? User474632 suggestion to use runtime appears to be unstable, for a proof of this see source-of-ruby-benchmark-irregularites. Again, thanks for the info!
Dec
2
comment Method of Modeling Problem Complexity
+1 @Thomas Klimpel: Agree, good point.
Dec
2
comment Method of Modeling Problem Complexity
Here's a better proof of the runtime stability issue, benchmark irregularites.
Dec
2
comment Method of Modeling Problem Complexity
clearly creating code is beyond the scope of the question, but the concept of runtime seems unstable as a measure of complexity. Any thoughts? Again, thanks!
Dec
2
comment Method of Modeling Problem Complexity
+1 @user474632: I went forward with modeling complexity based on runtime and appears based on my research to be a deadend; reason being I believe that runtime is effected by more than just the code run, and the environment impacts the code's runtime. Here's the code I used, which when run twice return different runtimes for the same problems "1+1"-vs-"1x2".
Dec
2
comment Method of Modeling Problem Complexity
+1 user474632: I'd thought about using runtime performance as a measure, but seems so brute force, and wanted to make sure I understood at least at a high-level that the approach would male sense. Findings that you explained make perfect sense, thanks for adding that!
Dec
2
comment Method of Modeling Problem Complexity
+1 @Thomas Klimpel: Yes, I'd wondered about the flow, thanks. Does this method seem related, or no, Cyclomatic Complexity.
Dec
1
comment Method of Modeling Problem Complexity
+1 @user474632: Yes, all true. The goal is not to create optimized execution plans, but to take a problem as is and assign it a complexity rating. Took a look at why Furer's algorithm for multiplication beats versions based on the Chinese Remainder Theorem, and it was way over my head. Guess the best answer for me would be an open-source software that was able to read problems formatted in a standard markup, for example MathML, and assign them a score; also guess either that's flawed, or does not exist.
Dec
1
comment Method of Modeling Problem Complexity
+1 @user474632: Thanks, your answer lead me to find this Computational complexity of mathematical operations - that said, looking for more of a complete way to take a set of problems and rank their complexity. Again, thanks and if you're still the best answer I'll award you the extra 50 points and select you as the answer. Cheers!
Jun
11
comment How to Generate Random Mathematical Equations that Equal an Integer
+1 @Doug Spoonwood: complexity was meant to be the inclusion of concepts such as: addition, subtraction, division, multiplication, roots, fractions, powers, Decimals, percentages, etc. until as many concepts had been used that would not result in getting an answer that would not equal [0-9]. That said, your idea was creative, addressed two of the three parts of the question as far as I'm able to tell - though, to me, incremental redundant patterns produce volume, not complexity. As very possible I've misunderstood your answer, either way thank you!
Jun
11
comment How to Generate Random Mathematical Equations that Equal an Integer
+1 @Gortaur: Thanks, stepped out, just got back. Answers looks fine, realized while I was out (looking at the question on my phone) that the question was flawed, though a good start, so I'm not going to edit the question since it's my error. Also, believe @amWhy is right, would you confirm that. Thanks!
Jun
11
comment How to Generate Random Mathematical Equations that Equal an Integer
@Gerry Myerson: Looked at your edit, and rolled it back, reason being that the solutions should be equations rather than integer themselves. Meaning I want to generate equations that resolve to a fixed integer (or in this case, a set of them), not integers that fit within an an equation. The generated equations should represent as many math mathematical concepts as possible while still resolving to [0-9].
Jun
11
comment How to Generate Random Mathematical Equations that Equal an Integer
@Gerry Myerson: "x + 3 = [0-9]" where x is TRUE, meaning [0-6] would be TRUE, [7-9] would be FALSE. All generated equations must evaluate as true.
Jun
10
comment How to Generate Random Mathematical Equations that Equal an Integer
@Gortaur: No, not attempting to make a CAPTCHA, though I thought that might be what you meant. And that's correct, no indeterminates should not be within the solution, or to be more clear, solutions should ONLY result in the following: 0,1,2,3,4,5,6,7,8,9.
Jun
10
comment How to Generate Random Mathematical Equations that Equal an Integer
@Gortaur: Just noticed I had not answer your question about the types of equations. Answer would be any that are possible, though randomly selected.
Jun
10
comment How to Generate Random Mathematical Equations that Equal an Integer
@Yuval Filmus: My motivation is a secret. Is there anything about the question and the solution it seeks that is unclear to you?
Jun
10
comment How to Generate Random Mathematical Equations that Equal an Integer
@Gortaur: Do you have links to the meanings of capture and smth?