Trurl

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About Trurl

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    http://www.constructorscorner.net

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    applied mathematics
  1. Prime Products just one last time

    As you know I have a complex equation describing semi-Primes. The fact is I cannot at this time solve the polynomial. But instead, it is more of a guessing attack to discover Prime factors knowing only N. What I have discovered is more of a series. It only works with Prime factors. More importantly, the series works with the same Prime factor multiplied by other Prime factors. So: · The series is a guess attack, comparing N to computed N. · The series only works for semi-Prime factors that are Prime numbers. · The series works for a given Prime number and infinite other, different, Prime number factors, multiplied for different results of different N’s. (If the equation did not work for multiple factors, multiplied by the same factor, the equation would be useless.) · The equation that produces the series can be used to test if a number is truly Prime. Other significant facts of the equations: · The equation is too complex and factors with imaginary numbers. · The equation is simple algebra. · Even though the equation cannot be solved with a perfect mathematical answer, the series is beneficial to computer algorithms. · The equations may have relationships to logarithmic spirals. I have been working with Prime numbers and Logarithmic spirals since 2006. But have recently tried to switch my efforts to other projects. I haven’t posted to SFN for 5 months, in this thread. But instead of trying to defeat RSA and use my math series to factor p and q knowing only N; there is a twist. If you know p (also what I usually refer to as x), you can test to see if it is a Prime number by multiplying by Prime number test values. If the equations hold true, then a test for Primality exists. https://www.3dbuzz.com/forum/threads/200441-New-One-Way-Function I don’t know if anyone believes me when I say this series is significant. But I posted the link to me “old” work from the time before I found the more useful equations. Much of that work is just plain wrong. But it will show you how I ended up with the equations I promote now. So, if you think there is any meaning to my equations, please post me a message in this thread to let me know. I will respond with more information.
  2. How to get ,The Area of Trapezium from Triangle.

    Congrats on the minor discovery. Any discovery however little, is significant. But the next thing I would do is see where the discovery applies. It may seem like a simple polygon, but it is also a geometric construction. (What I am calling is using drawing and geometry to form shapes with measurable properties. Like dividing a line in half with 2 arcs of a compass.) I know it seems like the use for drawing this way is minor. However, what if this drawing method was applied to computer graphics. Imagine drawing a polygon mesh in 3DS Max and have that mesh be measurable by your polygons. It is difficult to come up with a major application, because this isn’t my design, but if you expand it to polygons of more sides with the inside of those polygons measured; you’d have a brick to build a polygon block and measure it at the same time. Now that isn’t a little discovery.
  3. I hope this is the right place to post this, but where is imatfaal? I always enjoyed her comments. I wanted to get her opinion. I don't know her. She could be anyone, as this is an Internet forum. But I was wondering why she hasn't returned.
  4. What is the Infinitesimal sign?

    I was wondering this the other day. How many infinity symbols are there? There is the car Infinity whose symbol I'm not sure what infinity it is. I wonder if infinity has the most symbols representing it than any other math symbol. For example this is infinity:
  5. Prime Products just one last time

    Ok, this is my final post to this thread, unless someone asks a question. I will continue to work on this problem. And I thank the community of SFN for letting me share my math problem, even when it sounded impossible. I wish more would have commented. As of this post it has been viewed 10,500 times. That is a significant amount. I am also asking permission to use my post in other writings. I know the forum is free, but is it still permissible to use those posts of members who ask questions? I am using them only so my posts make sense, in the proper context. Anyway, I hope you have enjoyed the work I put in on these posts. And I hope I made you believe that reversing the N = p * q problem is possible. But often in math, the idea is just as important as the solution. If you did not believe me these equations would solve anything, perhaps you considered it for one moment. Now that it has concluded, feel free to post any of your thoughts. I thought this problem would lead to great conversations. Don’t let a math thread get less response than one on astrology.
  6. Prime Products just one last time

    In[50]:= PNP = 85 x = 5 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] Out[50]= 85 Out[51]= 5 Out[52]= Sqrt[4179323/2]/17 In[53]:= N[F] Out[53]= 85.0333 Ok, the important thing about the above equations is equation F is the Cumulative Distribution Function of the factors of PNP! The values below are to show that with the proper x, F will equal (within small error) PNP. This is just to show that it works for Semi-Primes that are a little harder to do on a calculator. If someone knows how to program large numbers: millions of digits, then they could find larger Prime numbers or break encryption that use factorization as a one way function; RSA for example. But wait. If you put F into the following programming logic you have created a Normal Distribution Function! If [PNP - F > 0, x = x + Sqrt[PNP - F + x]] If [PNP - F < 0, x = ( x - Sqrt[F - PNP + x]) /2 ] These logic statements create a normal distribution when graphed. Of course it is centered at zero and can be used to correct the error of equation F. But we must note it is mirrored in the x-axis. But know we know where the distribution of the smaller factor that is multiplied to equal PNP. We have a Bell Curve; almost. I am only calling it that because that is what is usually though of with normal distribution. But I think as you read this it may add more credibility to my work. In[41]:= PNP = 2999* 6883 x = 2999 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] Out[41]= 20642117 Out[42]= 2999 Out[43]= Sqrt[40378385476407827918859/2]/6883 In[44]:= N[F] Out[44]= 2.06434*10^7 20180213NormalDistribution7PM02.nb
  7. Prime Products just one last time

    This is a question to the mathematicians on the forum: when you're trying to solve an open problem in pure mathematics, what are the first things you do? Do you test the conjecture with a few example problems? Do you look up recent theorems related to the question, or do you just dive right in? I wanted to answer your question without killing your thread and leave it to professional mathematicians to answer, so I answered here. I do math for fun. And I choose my topics simply by what interests me. I use an intuitive method. I try to picture the problem completely and think if I have any techniques that will take me in the direction I feel that will solve the problem. But most likely will revel other problems and become a learning experience. Now with the Internet, math research is easily accessed. This is great to research, but it often leads to an overwhelming amount of information or confusion when piecing together conflicting evidence. This is why finding your “own” problem you want to work on is difficult, because the start point is a judgement call. But nothing helps with math problems than just searching and solving as many as you can. The process comes with practice, because you must develop a personalized technique. I have read books on “Flow” where a psychologist is trying to figure what makes someone creative. I think it helps to know how they approach a problem and though processes they go through. But I also think you can be consumed by someone else’s methods while it is more important to develop your own. I will give you an example on a problem I want to research. Everyone is mining Ethereum, the most popular digital currency. I have been working on an algorithm that will test values to see if they are factors. (Yes, I know it needs improved.) So, the first thing I look at is the enciphering protocol that Ethereum uses for its contracts. I have a little understanding of RSA, but a search reveals AES is used. I look at AES and more reading reveals that this encryption standard is well proven and nothing to do with factoring. But more reading on Wikipedia gives me a layman’s explanation on how substitution and movement in many iterations across matrices. Ok so I have a little knowledge of matrices from linear algebra. And I know a public key is used to encipher the message. But there is no way I can solve the pattern the computer enciphers with. But I look to what I know. We often use matrices to solve vectors. And if I took plain text and enciphered it with the known, public key it may show more than expected. If I could somehow give values to the plain-text and treat it as a vector addition, isn’t the public key the resultant of the matrices. I know there are a lot of unknowns here. And the idea is just a hunch; an intuitive idea. But that doesn’t mean the hunch does not need explored further. But what if a free-body-diagram with the forces being “movements of data” and the result force being the public-key. I know the idea probably won’t work. I just wanted to share an idea and how it can lead to something worthwhile. For this reason, I put so much effort in “The Products of Primes” here in this thread.
  8. Prime Products just one last time

    Taking a break on rather you agree or disagree that my equation has any value to the products of semi-primes. Back in 2003, I was with a group of friends whom were killing time. There was talk about a simple check-book-balancing sheet. However, the discussion was not yet about math and we were not doing school work. But we found ourselves in a common room that had a clock. Somehow someone in our small group noticed this clock was different from his wrist-watch. After everyone became interested, someone in the group ask if both clocks continued to run how much would on clock have to lose each hour to eventually have the same time as the other clock. Yes, I now know we were discussing the modulus. However, there is a twist here. The test to see if the times will ever be the same is testing to see if the times are relatively Prime to each other. Also, if you pick the time lost in order to synchronize the clocks, you may actually increase the difficulty of the problem. But what if you add more clocks or use smaller time increments such as seconds and fractions of seconds. I know this problem, though original to our group, has been thought of before. But this problem is an extension of the common modulus represented by a clock. This may be significant to the semi-Prime products, because the problem of many small clocks is the same one to find products. Let me know what you think. I wrote this, and I think it has some solid thought. It has been awhile since we had this idea and I hope a recall it factually. The important part is that the idea stuck with me. I tried to keep the description short here. Adjusting one clock will affect how the other clocks need adjustment. I think the multiple-clock-description fits nicely with cryptography.
  9. I don’t follow your method, but what I think you are trying to do is have an equation explain an unknown, irregular graph or shape. That would be gold dust that would allow any graph to be easily described. I think of it as 3D Studio Max. You are drawing a shape that is irregular from pieces of “molded” shapes. The drawing file in Max must be mathematically described, but is not an elegant equation describing the contours. But remember when you draw you draw starting with the basic shapes. As in your transformation from one graph to the other, it appears you have no reference graph. Perhaps you should try a known, defined graph and try to modify it to from the “transformed graph.” Remember in subjects like electricity, much descriptions are transformations of the Sine curve. I am not a math expert, obviously. However, I now you must simplify this problem. I don’t understand the transformation you did in your drawing. However, do not let that stop you, because how you explained it may be entirely different that the method I understood. But as I have personally learned, explaining the math problem is as important as finding the answer.
  10. Introducing the Piangle

    Ok I am going to suggest something that may be wrong, but it will show my thinking. If you take the Pi Angles here and multiply “every other” circular value by a number less than the next angle divided by the “every other” angle, you would get an ellipse on the graph. This would give an ellipse whose equation is represented in a different way than x^2/a^2 + y^2/b^2. You can build any circular function. I believe they are called conic sections. Does anyone have any thoughts on this? There are many series that could be used and in various patterns. Suppose the circle that the values were rolled out to the right, was a logarithmic spiral instead of an involute. Combine that with different combinations and different series and you could draw anything. If I am wrong or my explanation is confusing (which it is), I will clarify, but I believe anyone familiar with the coordinate plane will understand this. At this time, I can’t describe it well. But the idea is simple. Putting the math steps in words is difficult.
  11. Prime Products just one last time

    Ok for the new year I wanted to clarify the equation I posted here. With the following equations I wanted to show the test value of x produces a PNP – the calculated PNP approaches zero that test values of x equal p, in N = p* q. So, when F approaches PNP the value of x is the p, in N = p * q. I have included 2 if-statements that test this. And as you can see, an x equal to PNP (85 in this case) is zero, but those numbers larger than the correct x of 5, increase in value as they approach 5 and those test values smaller than 5, increase until they reach zero. (That is in my IF-Statements.) Yes, I know that the test value is too small. The problem is the accuracy of the PNP calculation relies on the square root of a large value. This is causing a margin of error in values of PNP greater than 3 digits. But I show this because the estimate is significant. How do I make the square root of the polynomial in F in this code to be more accurate? I hope you agree this equation is significant. PNP = 85 x = 85 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] If [PNP - F > 0, x = x + Sqrt[PNP - F + x]] If [PNP - F < 0, x = ( x - Sqrt[F - PNP + x]) /2 ] 85 85 161 Sqrt[4123/2] 1/2 (85 - 7^(3/4) Sqrt[23] (589/2)^(1/4)) N[1/2 (85 - 7^(3/4) Sqrt[23] (589/2)^(1/4))] -0.249277 PNP = 85 x = 5 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] If [PNP - F > 0, x = x + Sqrt[PNP - F + x ]] If [PNP - F < 0, x = ( x - Sqrt[F - PNP + x]) /2 ] 85 5 Sqrt[4179323/2]/17 1/2 (5 - Sqrt[-80 + Sqrt[4179323/2]/17]) N[1/2 (5 - Sqrt[-80 + Sqrt[4179323/2]/17])] 1.37825 PNP = 85 x = 7 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] If [PNP - F > 0, x = x + Sqrt[PNP - F + x ]] If [PNP - F < 0, x = ( x - Sqrt[F - PNP + x]) /2 ] 85 7 (11 Sqrt[45773587/2])/595 1/2 (7 - Sqrt[-78 + (11 Sqrt[45773587/2])/595]) N[1/2 (7 - Sqrt[-78 + (11 Sqrt[45773587/2])/595])] 1.88414 PNP = 85 x = 3 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] If [PNP - F > 0, x = x + Sqrt[PNP - F + x ]] If [PNP - F < 0, x = ( x - Sqrt[F - PNP + x]) /2 ] 85 3 Sqrt[847772947/2]/255 3 + Sqrt[88 - Sqrt[847772947/2]/255] N[3 + Sqrt[88 - Sqrt[847772947/2]/255]] 5.69458 PNP = 85 x = 1 F = Sqrt[(((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2)))] If [PNP - F > 0, x = x + Sqrt[PNP - F + x ]] If [PNP - F < 0, x = ( x - Sqrt[F - PNP + x]) /2 ] 85 1 (7 Sqrt[13123/2])/85 1 + Sqrt[86 - (7 Sqrt[13123/2])/85] N[1 + Sqrt[86 - (7 Sqrt[13123/2])/85]] 9.90669 Above is the input and output of my code. The test values are separated by spaces.
  12. Prime Products just one last time

    Merry Christmas everyone! My present for you is a problem that was given to me by a friend Curtis Blanco. He proposed that I try and solve this geometry problem. I thought it would be best suited for a geometric construction. If you follow this link I have written it up 10 years ago. Here is the problem: Two buildings, I and II stand next to each other forming an alleyway between them. Two ladders, ladder A and ladder B in the alley cross each other touching at the point where they cross. The bottom of A sits against the base of building I, and leans over on building II. The bottom of ladder B sits against the base of building II, and leans over on building I. Ladder A is 3 meters long, ladder B is 4 meters long. The point where ladder A and ladder B cross is 1 meter above the ground. What is the width of the alleyway? http://www.constructorscorner.net/ideas_and_gadgets/math/math_hunch/hunch_00001/hunches_section0003_fellow_constructors/ladder_circles.htm It took me a while to figure out what I was trying to do back then, but I think it works. I bring this up because it now relates to my Prime problem. In the Travelling Salesman problem, I proposed using circles to find distances. When multiple circles intersect they give clues on what is the shortest path between points. The difficulty of the TSP is not finding the shortest line distance between points. Instead finding the point this way doesn’t always lead to the shortest distance, if the pattern is in a square for instance. The perimeter of the square is longer than navigating through the center. All of this learned from Wikipedia. I still need to research the problem. I show this here because I think it is interesting and plan to relate it to my overall problem of Primes. I know I have to make a better diagram. I am behind on drawing these diagrams. My job title was once “document specialist”. I know I should be better with this, but version updates in software packages, has made my old programs incompatible with Windows 64 bit. But follow the link and see if it solves the problem I listed. I will follow up to this post with more descriptive work, because I know how difficult it is to follow my description of the solution. But I hope it shows that with the TSP, circles are our friends.
  13. Introducing the Piangle

    Good job. Keep up the great work. I don’t think it is a thousand years old. You have just used an angle and may have unknowingly drawn an involute which is a type of logarithmic spiral. (In case you don’t know I love logarithmic spirals.) When you unroll each outline to the right; Can someone in this forum tell me if it is a linear representation of the involute? I have seen something graphical, similar to this unroll in a math reference. I can’t remember where, but I believe it was for gears. I don’t have any pictures of a logarithmic spiral to share yet. I want to be sure it relates to your post. But even if this work is rediscovered, it doesn’t mean you can’t relate it to something new. What I think you should try is to “put space between your Pi angles.” What I mean by this is that having a “series” between where 1/3 r and 2/3 r and r would change the shape of the involute to a special logarithmic spiral. I know it sounds like I’m talking babble, but I am not. If you are confused on what I am trying to say, let me know and I will try and describe my idea better. Simple put I would shift the new larger angles a distance (determined by a series) across the x-axis from the original triangle that was at the origin. This way you can craft series and describe them in a logarithmic spiral. I will post a picture of an ellipse determined by angles. It is not a logarithmic spiral, but it will demonstrate using angles to determine geometry. I will try to work on drawing a graphic representation of the logarithmic spiral I describe here. But this will work till then.
  14. Prime Products just one last time

    I know this doesn’t solve the problem. I am only trying to solve the triangle I constructed. But is it possible to find FE by subtraction. I may not be doing it right, but is it possible to do subtraction of the triangle segments to get FE? To me it seems possible, but when you go to do it, it is confusing. But it just feels possible. Remember I am only trying to solve for FE. AC = N [Absolute value [ AC – AE – (AC-CE) – CE]] = FE
  15. New TSP Method (p=np)

    I will stay out of the conversation after this post. I just wanted to clear up what I said. It may make more sense than you think. All I am saying is that geometric constructions may simplify the calculation. Let me know if this does or does not make sense. I am saying take a compass and draw a circle that encompass 2 points. Then with 3 points draw another circle from the 2 points closest together. Keep drawing circles from all points. When there are several points, the circles should intersect somewhere along the circle. Connect those intersections with lines and you have a polygon or the shortest path. Do you remember in high school when they taught us to find the center of a line by taking a radius more than half of the line and string 2 arcs from each side? The line between those arcs passes through the center of the original line. I propose if you did the same constructors of circles on the unknown points, geometric constructions such as finding the tangent of a circle (or any of the dozens of circle constructions) you would simplify the computer process. I don’t know how to put a drawing compass into a computer program, but you could always use a CAD script. But then again, I don’t know the algorithm to such a thing, as I have only spent 2 minutes coming up with a hypothesis. I would say that a radius of the circles, and arcs of those intersecting circles, would eliminate calculations that just can’t be done. I wouldn’t scrap the polygon idea. Instead, I’d use the polygon to form a path between the intersecting arcs. Also by using circles you have the advantage of all the circular functions. Do they still teach geometric constructions in geometry? Yes, I know the problem has N points, but this is a simple approach. As more and more points are formed you would have to erase (delete) some the circles no longer needed. And no, I don’t claim I can solve this problem. But I do like how the computer was run to solve this problem. Computers have already ruined chess and that game with squares. I’m glad there is much work to be done to solve this problem. I hope this is clearer. All I am saying is use geometric circle constructions. After all, you can build almost any shape with them. Someone has probably tried it, but before modern programming, such an idea wasn’t possible. Because in CAD you could program it to draw hundreds of points.