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    applied mathematics

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  1. Thanks for the links and programming advice 😊 Seems like it is pretty involved to do this kind of thing. I will use it to strengthen my programming. I was taught that that something written as say: 28/7 is in exact form. It is when you divide it is an approximation in decimal form. I read the article and they prove that the fractions are infinite. Here is what I was trying to do is invert the quotient and factor both the numerator and denominator. Divide and reduce those factors; then decide if there is any common modulus where the factors will reach a whole number. I guess you could say the fraction will terminate where the factors multiplied together will equal. (If they don’t terminate at a smaller modulus). I know you are thinking how do we know by division that this modulus will be reached. But it would simply be the modulus of the numerator by the denominator would tell how many iterations, until the infinite fraction terminates. We know the numerator and denominator will terminate at their original product. However there is no guarantee that the inverse quotient of those factors will terminate. I know this is flawed. But in the article they were testing fractions for accuracy. They prove the accuracy. But I am arguing that with infinite iterations the decimal may terminate. Yes, I know they went to Oxford and I went to Point Park, but this hypotenuse is why I was interested in this process in the first place. Hope this makes sense.
  2. If you know your exact position and magnitude of explosion (how long the sound took to reach you) the direction you were looking at the explosion, you may be able to determine the location based on arc length. You are at the tangent of that arc length. But the arc length is unique to you who measured it. Different magnitudes would have different arc lengths. I need someone to verify this. But I believe if you have your exact position you may be able to tell. It would be like finding the trajectory of someone shooting at you. The shot is a straight line and the angle. Reverse those and the arc lengths along the tangent to you is where the shooter is. The distance from you to the shooter would depend of the magnitude of the bullet. But to keep the same tangent the shooter would have to move along the same angle. If he shot with greater magnitude and a different field of vision it would be an entirely different arc. I believe what you are trying to say and a question I will asks is: With different positions having different arcs, do you have enough information to determine the location (knowing your current location) to solve the shortest distance you are from that arc? If you used that magnitude to measure from you to the original explosion? I hope this makes sense. Correct me if am wrong. But it seems you are asking can you find the distance without enough known.
  3. Does anyone know of any research or math records on determining when a decimal number will terminate based on the inverse of its factors? Yes I know that I would be working with whole numbers not integers. But for integers what if you took the factors of a quotient, say circumference divided by diameter and factored the numerator and denominator. The equation would be = to itself, but if you multiplied the factors together you already know that those factors terminate at the product. Someone has probably done a similar technique. But factoring large numbers is recursive and then you add to the process recursion again to do the multiplication and you get a problem you can’t solve. Also can someone explain the process that was used when they solved Pi to a trillion digits and don’t know where it stops. The stopping point is what I would describe by the multiplication of the factors. The factors multiplied together still equal the original number, but the product determines where the factors stop. Hope this makes sense.
  4. Would such sets be more tangible if related to computers? Like pointers which point to a memory address but are used to store a value they represent but are not equal to. I have had an idea of a computer algorithm to sort. Test a value s, to see if an element of array R. If s is not an element then set s equal to R. s is not an element of R but the equivalent of R. I hope I made sense. But I think there is model that helps picture the paradox.
  5. In[118]:= PNP = \ 1934366789178173879737044987039672886320217970368234273396727882248077\ 5276979813504845595034120393370152899748537330898548017116175240963843\ 8671061576515629388985879569844395850383900815310597936363427571127082\ 3949399560800528445239352682682607043790064999077825592888096779406064\ 2207210135237248313591984445102205903536129280729693873645010158968436\ 2023257379753594951333514783850699868022479467082630988357448219611018\ 0532168624955470298291740460265055263421172154319402790946210321183175\ 9214437760483022798117868041446071398803987275533080729349251435281331\ 126580312335348000444123257382275855627368919052416438211 x = PNP * (1/ 833333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333333\ 3) Sqrt[((((x^2 * PNP^4 + 2* PNP^2 * x^5) + x^8) / PNP^4) * ((PNP^2/ x^2)))] Out[118]= \ 1934366789178173879737044987039672886320217970368234273396727882248077\ 5276979813504845595034120393370152899748537330898548017116175240963843\ 8671061576515629388985879569844395850383900815310597936363427571127082\ 3949399560800528445239352682682607043790064999077825592888096779406064\ 2207210135237248313591984445102205903536129280729693873645010158968436\ 2023257379753594951333514783850699868022479467082630988357448219611018\ 0532168624955470298291740460265055263421172154319402790946210321183175\ 9214437760483022798117868041446071398803987275533080729349251435281331\ 126580312335348000444123257382275855627368919052416438211 Out[119]= \ 1934366789178173879737044987039672886320217970368234273396727882248077\ 5276979813504845595034120393370152899748537330898548017116175240963843\ 8671061576515629388985879569844395850383900815310597936363427571127082\ 3949399560800528445239352682682607043790064999077825592888096779406064\ 2207210135237248313591984445102205903536129280729693873645010158968436\ 2023257379753594951333514783850699868022479467082630988357448219611018\ 0532168624955470298291740460265055263421172154319402790946210321183175\ 9214437760483022798117868041446071398803987275533080729349251435281331\ 126580312335348000444123257382275855627368919052416438211/\ 8333333333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333333\ 3333333333333333333333333333333333333333333333333333333333333333333 Out[120]= \ 1119462642967601379625749889949236065777407216363091843656817758630897\ 2822004013012808616251428523303469194983368339224288931527755260370593\ 4564726982165021366914927214391866070447793539124105460668568853618924\ 3132905693874616958336079958862242579650280812660512453816275628067977\ 7721150419713278365400937039926619418164741229089532498330068239309776\ 1690074453198227284210005164670550843915175125291348603192500942129571\ 2160296397474642360130036975254240806723286365854612676445799004846266\ 7602028680911873106587947193189889293999449715734241944639662748710845\ 3864217222758522411029165882690689971923777751749568939373903823332879\ 0347862820497821662686301328739580127103593058742239980461079578843089\ 8938404770001288892056326897984920834525603021493609403571623845097415\ 9269047818150038841906826639724779147047347019045703317553593717846683\ 7809250765440348545752291612966122145077943669090956833677756556314535\ 3415742755622794040068289994068630691327156047081726660842339291269766\ 7917971187981886248629293392246074136458310437500753586451933193176668\ 2313587611783431933780044950953903564442478335965847599970260746987255\ 0731160508492599759339823308128315559840203913178785278415738419343860\ 320599550946803281571941063514234186096009901328/\ 5787037037037037037037037037037037037037037037037037037037037037037037\ 0370370370370370370370370370370370370370370370370370370370370370370370\ 3703703703703703703703703703703703703703703703703703703703703703703009\ 2592592592592592592592592592592592592592592592592592592592592592592592\ 5925925925925925925925925925925925925925925925925925925925925925925925\ 9259259259259259259259259259259259259259259259259259259259259259537037\ 0370370370370370370370370370370370370370370370370370370370370370370370\ 3703703703703703703703703703703703703703703703703703703703703703703703\ 7037037037037037037037037037037037037037037037037037037037037 In[121]:= N[%120] Out[121]= 1.934431447048015*10^616 Hopefully the code is readable. I need to use such operations in the guessing game. It is still trillions of digits off. But calculus can be used. I will need help with the calculus. I will also need advice on how to approach the programming to get large numbers into usable figures. But I hope you agree this definitely eliminates potential values. And is the large number a 1024 bit number?
  6. I am using Visual Studio 2017. All of my skills in C++ are just out of school and learning how to make useful programs. I have seen how to import libraries (mainly C++ libraries). I know classes, but again I have the theory of overriding but not much experience. I am attempting to learn the Flint library. This is a library I have a book on, but I am not experienced to use it. I figured using the library is separate from understanding it, but I have found no clear-cut program that will let me plug and play large numbers. Obviously, this isn’t very easy, or I would have found a program that will let me plug and chug my 128-bit key into a mathematical equation. This is a learning process. I want to do this to show my math project works. I have the 128bit numbers if I could factor them it would be gold dust. Is there no ready-made program that will do this? Cheap is important. I don’t want to spend several hundred dollars. Is there something in Linux? If something like this isn’t ready made it should be. Obviously, someone before has faced this problem. There is a worthy project here for someone with programming skills. With limited expertise what are my options? I need to be able to complete the equation in the previous posts. It has N^6th power and then adding and diving it. So, I would take a 128-bit key and multiply it by itself 6 times creating a large monster. But it still needs only the 4 arithmetic operations of addition, subtraction, multiplication, and division. No recursion. I also only need to test 2 to 8 values in the equation. I need one below the factor and one above the factor. It will be a math guessing game for the factor.
  7. Ok Sensei, How do I put a very large number into this program? I am not sure why a large number would cause a memory leak. I know that computers can handle many digits. But programs like Mathematica are max at x^100 power. If I am only using the 4 arithmetic operators: addition, subtraction, multiplication, and division, why wouldn’t the computer just take more time. Yes, I have researched it myself. I will not be using recursion to factor. That is where computers crash. But it is possible. People have factored Pi to a billion digits. I am only using a workstation. I have looked at libraries that handle large number digit operations. I believe C++ console cannot handle larger than double, because of the way it manages variables. You can’t put in a large number and expect it to go through many functions. But if I could limit it to just arithmetic operations. So after reading that, my question is: How do I approach working with a 128 bit number? I did not learn this in school. And it appears it is a continuing computer puzzle. Oh and, Sensei and Sensei only, view my profile for the latest updates.
  8. Obviously Tomlin is a great coach and the other 48 are knowledgeable professionals. I'm not saying that I know the game more or could outcoach them. I'm saying apply science and math. There is something simple everyone is overlooking. Well Game Theory explained the Cold War and I saw an example where a goalie uses it to block left instead of right. But even though this is also strategy, Game Theory still applies. If Game Theory couldn't help make sense of complex decisions it wouldn't be useful. I have many other ideas to measure but I do not have access to game footage. So if anyone has access to any such game footage
  9. Thanks for the input, but I'm not far in left field here. But you are right I have to put it into something calculable. How bout this. I just heard you have to put pressure on Brady (the Patriot's quarterback), but he releases the ball too fast. So the game theory "decision" is to determine when Brady is throwing fast and when he needs more time for his receivers to get down field. The decision to make is stopping the small gains. The Steelers usually take away the deep allowing the short, but this doesn't work. The Pats march up the field with short passes. But the only way to stop such an offense is to solve when the Pats are short or long plays. My solution (recommendation (not mathematically proven)) is to make the receivers go deep. I say this because Brady is relying on his receivers to get open. The receiver goes short when the defender goes deep and will go deep if the defender tries to stop the short pass. So rush Brady if receivers go deep and don't rush Brady when you give up the short. This strategy correlates with Brady decision and time to release, and how he is allowing his receivers to dictate the march down the field. I know this sounds simplistic but I think we could test it scientifically. From my understanding game theory is simply decision making. I know not all football is logic, but the strategy is game theory even if it is too complex for math. But you guys insisted on a concrete example. Let me know if this is a more fundamental approach. I chose this example for a clear choice of when to rush Brady. Obviously the offense has the advantage. A few recivers going different routes and going deep or should would complicate the math. But I include this example if the Pats go undefeated this season this forum may be interested in how they are doing it once again.
  10. Yes the science of game theory. And how to design a football game scheme that will stop the Patriots offense. About 15 years ago there was an online Star Wars game. The Imperial forces strength far outweighed the Rebels. One Rebel-based player planned an attack the devestated the Imperial forces. It ruined the game but it should what an underdog can do. There is a branch of science called network science where the general public has access to the data. I'm saying if several thousand people were analyzing the game tape they would discover why the Pats always have better play calling. I know they have won the Super Bowl 6 of 8 times, but they have done it with different teams, often not the more talented teams. So I am asking is there a way to use science to insure the integrity of the game? Something that can be measured by the fans? Probality is out. I have read about people using computer football simulators. I don't know what they use. I have a $20 game I bought off Steam. But I end with this, with drafts and salary caps how is it possible for one team to dominate the game 20 years?
  11. Ok to show I don't just waste my time looking for patterns in factoring. I have also studied game theory. Not so much the rigorous math, but the protocols. With a little knowledge and possible outcomes you can make some good predictions. I don't know if my reference will be lost on those who don't follow American football but here it is. I predicted on January 10th 2019 that Antonio Brown would become a New England Patriot. I have proof in the YouTube video link following. But my simple approach to game theory does not end there. Simply put the Patriots are ruining football. What if we the fans could devise a game plan that would defeat the Patriots. We could use game theory and math. It would be a great challenge. youtu.be/SX1QAXp53f4 http://youtu.be/SX1QAXp53f4
  12. I've been told Linux is secure because the code is public. You se what is put on the system. In cryptography an open cipher is more secure than hidden. But is this true? The fact is we don't know what is going on when the computer is processing thousands or computarions. I warned a friend about software piracy. They just don't give software away it is loaded with viruses. I told him the movie files could hide viruses in the file. He says he knows it is virus free because he is extracting a pure movie file. I disagree because movie files are packaged with instructions for the codec. The question to ask is "is our Linux more secure?"
  13. What is the "logic" deleting the code. That is bad "syntax". Isn't the code the discussion? The reason to post code alone is to have the code be read entirely. But the code itself should not have been deleted. It erases the record of the post. I was going to reply to this post but didn't because I figured I'd kill it because of my previous thread where I claim I can factor semi Primes. I wanted to see what other more experienced coders thought.
  14. Thanks Sensei. This program is heading for a crash with large numbers. I believe float could handle large numbers but the Cmath library is limited in operation. Are there any math libraries on the net with easy implementation? I was thinking of programming it in Mathematica, but before it can be useful I have to compute the error.
  15. This is a program I wrote. It isn't very useful yet because I need a software library that handles large numbers. But if you read it you will see what I have been saying all along. Of course I could be wrong, but that goes without saying. I need some computer scientist to explain how I can run a program similar to this one with large numbers. /* This program utilizes factor patterns to estimate the value p in the N=p*q keys in RSA and other cryptography ciphers that use the product of semi-prime numbers. Note it is complex to program math into a programming language. Large values could easily crash this program. As an example I recommend testing 85 for N and 5 for x. Also note that finding the error between PNP and pnp_check is crucial to solving this problem. For this demenstration estimate is set to 7. Abviously to make this program usefull estimate must be determined exactly. For now this stands as a demonstration of the equation. */ #include "stdafx.h" #include <math.h> #include <iostream> using namespace std; int main() { bool testvalue = false; int PNP; double root, estimate = 7; float x, pnp_check; cout << "Input N the know product of 2 Prime numbers" << endl; cin >> PNP; do { cout << "Enter the small Prime factor of N as test value+." << endl; cin >> x; /* PNPcheck = sqrt[(((((x ^ 2) * (PNP ^ 4) + 2 * PNP ^ 2 * (x ^ 5)) + x ^ 8) / PNP ^ 4) * (((PNP ^ 2) / x ^ 2)))]; estimate = (2 * x ^ 5 / PNP ^ 2 + x ^ 8 / PNP ^ 4); */ pnp_check = (((( (x*x) * (PNP*PNP*PNP*PNP) + 2 * (PNP * PNP) * (x*x*x*x*x)) + (x*x*x*x*x*x*x*x)) / (PNP*PNP*PNP*PNP)) * ( ( (PNP*PNP) / (x*x) ))); root = sqrt(double(pnp_check)); if ((abs(root - double(PNP))) < ((estimate))) { testvalue = true; }; cout << "The root that compares to N is " << root << endl; if (root > PNP) { cout << "Chose lower x if program does not end." << endl; }; cout << pnp_check << endl; if (root < PNP) { cout << "Chose higher x if program does not end." << endl; }; } while (testvalue != true); cout << endl << endl << endl; cout << "The smaller Prime Factor is around " << x << endl; system("pause"); return 0; }
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