Trurl

You sound like you have some good math wisdom. I value your comments. I will have to evaluate the use of this geometric diagram. I didn't know there was a AutoCad viewer in Windows 10 store. I didn't know people actually used the store. I'll have to check it out. Anyways I was wrong. You did give a fair view of my problem. I misunderstood you comments about viewing the drawing. I have claimed in many posts ago on a different thread that I could solve SSA (side, side, angle). I did not want to bring that back up. But later I watch a math video on "The Great Courses" that the mathematician said he could solve SSA with some obtuse triangles. That is if I understood him right. This problem is not based on that. But again it is trying to find triangles knowing only 2 sides, with certain conditions known by other triangles. The following is not a religious statement. But in Christianity an non-believer would say if God is so strong can he make a boulder that he can't lift? If he can't he isn't all powerful. But you could extend it to this problem. If God is so powerful can he make a one-way function even he can't reverse? So do one-way functions exist? I believe as humans we are limited and one-way functions do exist. Knowing only N and finding 2 unknowns, knowing only a slight process in which N was encoded is a difficult if not impossible task. I have been working on this problem for a long time. I took a break to study Amateur Radio. But I would like to share the patterns in the multiplication I have found and based my equations. They are simplistic but I have to go through and list them all. Maybe someone will see something I missed. Anyways thanks for the comments. I don't always like being wrong, but I think it is more about being realistic with this problem. I don't know. Would you be interested in seeing a 5 step pattern in multiplication?

Obviously, you didn’t look at the drawing I posted. This is a science and engineering forum. There must be some viewer who has access to Autocad. I know you think, I’m stupid claiming to work with Prime numbers. And you don’t think I have a math background. I enjoy you reading my problem and telling me when something just doesn’t work. However, you should have viewed the drawing before dismissing my comments. If I am wrong your judgment is correct. However, there is no wrong. There are wrong techniques, but failures just mean that I try other approaches. In this problem, I am not asking you to find Prime numbers, I am asking the group to find techniques to find triangles with limited given. If you want to reverse a one-way function, you will have to use new ideas, because the old ones don’t work either. I understand why you think my problem is crap. But don’t think of it as supposed to solve Prime numbers. Think of it as a geometry problem where limited information is known about the angle. Yes, I could be wrong, but I believe I am right-on about the similar angles. The question is does it help me solve the unknown values of the triangle I need. As you said before a drawing will show everything. I don’t have any programs to draw triangles other than AutoCad 14. The AutoCad 14 files I shared in my last post should open in the current version. I am 20 years behind when it comes to CAD. They are just too expensive to buy. I have the student edition of Solid Works, but I have-to draw as I learn. So, if you can view my drawing. It may be awhile before I have a drawing in universal format.

I haven’t confirmed the Prime number part, but the triangles are drawn correctly. The only change is that triangle EDC is a right triangle and for triangle ABE to be similar another 4.789 chord must be drawn at a 30 degree angle from CD. So this new angle is similar. Similar to triangle ABE 4.789 comes from the fact that CE equals [the remainder of (N / Pi ) ] * 85 All of the equilateral sides of the main triangle = N = 85 I have a drawing but it is from AutoCAD 14 and an AutoCad 14 dxf file. I am working to convert. Also there are 2 more similar triangles. Triangle BED is similar to triangle AEC The problem is I can’t find out if triangle BED is also similar to triangle CEF We know s = CE and triangle syx is similar to triangle AFC Anyways I am now confused from looking at hundreds of angles. I need help to find if I have enough information to solve triangle AFC. Please help! My drawing is ready. I just have to fight to get it into readable format. This is more difficult than I thought: 32 and 64 bit; AutoCad 14 ; dxf; dwg; So now you will have to believe me that the values work. It really isn't that impressive. Especially unimpressive if I can still not solve for triangle syx as I originally intended to do. https://1drv.ms/f/s!Ao7PhUWlkaBtgQd7IjIjxkBjv3wz Here is a link if you can open AutoCad 14 drawings.

Ok so it looks like my triangle theory has failed. But it doesn’t matter. If an idea does not work it is just a dud. Here is why I designed the triangle the way I did. S = r * theta. In radians of course, but for the problem I converted it to degrees since my triangle is equilateral. I was looking for a triangle whose sides are proportional to the vector that with resultant of N, where N is the product of 2 Primes. I theorized that Pi radians or 180 degrees would divide into N and leave the remained of N/Pi (converted to degrees). And from this remainder N – the remainder; and CE = remained of N/Pi = s (on the unknown triangle) would solve the proportions of x and y, where x * y = N. We agreed that triangle syx was similar to triangle ACE. But I believe that triangle ECD is similar to triangle EBA. Of course, I have not proved it yet, but if true the triangle diagram would be useful. I began to think about drawing an accurate diagram. I am in the process I just wanted to run the idea by the message board. CE is much smaller part of N than my drawing shows. I am not claiming the triangles are similar, but I am going to do the work to find out. If this message is hard to understand, give it some leeway. I have not had a class in trig in 20 years. Also, it is difficult to explain why I choose to draw the diagram as I did. Over the next few weeks I will post the end. Right or wrong. Most likely wrong because of the difficulty of the problem. Even if this idea is a dud, I stand behind my previously posted equations. There is a pattern shown by the equations. It is just unfortunate that it is complex. But my next step will be to simplify the equations. My patterns come out of very simple patterns in multiplication. I want to post the patterns on my website to show how simple they are. I know that N = x *y is supposed to be a one-way function because there are 2 unknowns. However, I don’t believe in one-way functions. Yes, I know I’ve wasted a lot of time on an impossible problem, but it was geometry that gave me a lead. The problem is that no one believes your problem until you can prove it. So, in a few weeks, I will conclude my work on this ever-confusing drawing and post an improved diagram.

We are already in agreement that is wrong. I just didn’t update the drawing. I wanted to show I was using the same drawing. It takes longer to update the drawing. You are right. I meant to say AFC is similar to syx. FC = CE/cos(30 degrees) should be: CE + (CE/cos(30 degrees)) = FC, where CE = s = [remainder of N/PI) Proof: http://www.constructorscorner.net/ideas_and_gadgets/math/scos_ssin/scosinep1.htm Thanks again for bearing with me as I work through this problem. I will update later with a clearer drawing and definitions. I may seem that I’m an idiot throwing math together. But there is a design around this problem. This geometry might prove to be impossible to solve. Also it is confusing. Be assured that I am not intentionally trying to irritate you with bad math. I believe these corrections will let you better see how I approached the problem.

It is late 20170420…I still stand behind my triangles. You guys are more experienced mathematicians than me. You should have this thing solved already. I know the problem seems erroneous, but good math comes from new ideas. I mean if we always got a clear answer or it was too easy, there would be no point to doing the math. We’d all be English majors. But following is the latest attempt to show the Prime factorization problem may give clues on how to defeat it. It starts with an equilateral triangle, where all sides equal N. Then BC is subtracted by CE, where CE = the remainder of N / Pi. With alternating angles ECD = 30 degrees. FC = CE/cos(30 degrees). s = CE, which also equals the remainder of N / Pi. AEC is similar to syx. s/AC as x/FC as y/AF. Otherwise stated: s is proportional to AC as x is proportional the FC Currently I have not proven all my values. But they are based on a plan and not just random value assignments. Does this intrigue anyone? No, I am not claiming this works yet. I just wanted some feedback.

Thanks Dr. Strange, those are some excellent links and what I need.

Ok so I posted here asking for how pattern in genes are found and if there are already mathematical problems in the experiments already found. No response yet, probably because I’m an amateur and asking silly questions. But now I am going to up the ante. Reading only 2 chapters in the genetic textbook, this is a math pattern I believe needs investigated, if not already so. So the geometry of the genetic structure is a double helix. To me if I were going to map genes I wouldn’t be isolating single genes. I would look at the shape of the helix. It can’t be perfect. The connections would cause it to bend 3-dimentionally. The space between helixes could be measured and the slope in 3-axis could be measured. I chose this not knowing what work is done in the field. But in my original cryptography amateur research, I stated that a pattern in Prime numbers could be found with a logarithmic spiral. To me I look at the helix and see a 3D shape that looks like it originated from a 2D logarithmic spiral. Now I never proved that Prime numbers can be described by a logarithmic spiral, but all patterns I found in the Prime factorization problem, are based on my theory of the logarithmic spiral. So here is my theory. If you find the curve of the spiral that makes up the 3D Helix, then you can predict the size of the connections. It seems simple not to be already thought of, but the theory is the easy part. Finding the exact mathematics will prove difficult. But I believe my work with the logarithmic spiral and cryptography in the Prime factorization problem shows patterns in the logarithmic spiral. My work may have nothing to do with DNA, but if I am looking for a pattern in genes and the resulting proteins, I wouls simplify the calculations by looking for a geometric pattern.

Well I’ve been reading about genetics as a crash course. I am amazed at all the applications that bio-engineering has. But I did notice the intro chapter where there are arguments if bioengineering is safe or ethical. The book tries to be objective, but is really promoting the field. The author figures it has the same pro’s and con’s as any technology. I don’t know that I agree. As for a pattern, I picture a chemistry problem. You don’t mix all the chemicals in the chemistry set together. Chemistry improves our lives dramatically. But that doesn’t mean someone doesn’t take nitrates in an oxygen source and make a bomb. But in the bio-world there would be a one-way function to disarm the bomb. The bomb is easy to make, but not easy to reverse, if the only way to disarm the bomb is to add more chemicals to the mix. In other words, if something is genetically altered and becomes dangerous, how would you reverse it if it multiplies. I am not far enough in my study to find patterns in genes. But I just think of my chemistry example, where it is easy to add to a mixture of chemicals, but not as easy to neutralize the mixture of chemicals, by adding more chemicals to the solution. I have seen interviews on TV of the guy who lead the mapping of the human genome. He claims that he just proved evolution. But I’m not convinced until he can explain all the patterns that exists and cures complex, genetic diseases. So, if the math can be applied, and this isn’t the same math that says it’s a quintillion to 1 chance, like the March Madness bracket, I am going to ask the forum what are the simple strategies of finding patterns in genes? As I learn more I will be able ask better questions.

I think the $100 price tag for 700,000 traits is a deal. I do wonder why 23andme compares to prehistoric man. So, as I understand it, the genetic information is so vast it takes computer processing to find patterns. I don't know what kind of learning curve there would be. However, just by using N = p *q, I found 7+ patterns. All of which we found useless on this message board. But they were patterns even if they didn't solve the prime factoriation problem. Now I am asking where to start looking for genetic patterns. Are there some classifications that are starting points, like N=p*q for RSA? I am good at looking for patterns. I don't have a biology background. But I have read about networked science where amateurs provide an extra perspective working to classify stars or find genetic patterns. So please point me in the direction as to where to have a simple start to look for genetic patterns.

I will start the pseudo code. Notice that an x of 545 is positive and an x test value of 8756 yields a negative. I am arguing that with these test values the difference from PNP shows if the desired x is higher or lower than the test value. There is no reason that calculus won’t give a value when limit (equation) when PNP approaches 0. I know it takes more than that but do you agree the pseudo code will show an indication where x will fall at PNP? Please join this post. If you don’t believe my code, counter it. There should be a pattern in the pseudo-code. x = 545 y = 6737 PNP = 4639* y (((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2))) 545 6737 31252943 (566741960869155702888306342808481973/580236226342089968450) 566741960869155702888306342808481973/580236226342089968450 N[566741960869155702888306342808481973/580236226342089968450, 13] 9.767434971132*10^14 Sqrt[9.76743497113228416002242796713336`13.*^14] 3.125289581964*10^7 PNP - 3.125289581963931252118627996719126077423156917`13.\ 301029995663981*^7 47.18036 test second x x = 8756 y = 6737 PNP = 4639* y (((((x^2*PNP^4 + 2*PNP^2*x^5) + x^8)/ PNP^4) - ((1 - x^2/(2*PNP))))*((PNP^2/x^2))) 8756 6737 31252943 73243982077295884748898890760446202375/74884743323939619512464 N[73243982077295884748898890760446202375/74884743323939619512464, 14] 9.7808951231166*10^14 Sqrt[9.780895123116592692523297300191834`14.*^14] 3.1274422653530*10^7 PNP - 3.127442265353046080516318622627538568244967294`14.\ 301029995663981*^7 -21479.653530

Ok so my graphical representation has many flaws. I’m not finished with it yet. But did you guys look at the last attempt? But back to Post # ___16___ and ____19_____ I know it is no longer the Prime factorization problem if you test for values of x knowing N. I argue that with the test value of x you will know if the equation results in the given number N. The closer to the actual x the closer to the given, N. I know you guys don’t like pseudo-code. I am trying to write a program that will test x values. I know we have been down this road before but this is for an education project I am doing. I would explain the details but it would influence your input. I am going to write a program to efficiently test x. If you graph “x” you know where it approaches N. My arguments are in past posts. But I ask to move away from the Prime Factorization to a trail-and-error computer program. Yes, I believe my equation can eliminate calculations on large Semi-Prime numbers. But this is all you need to know for now. Please try and write pseudo-code if not to prove me wrong but to promote education. Thank you for your participation.

https://soundcloud.com/quitteriel/connor-dickiesynbiota-synbio-experiments-for-all What do you think of a kit like this? They start at $45. Also from what you said. Is it safe to share my DNA with Ancestry.com? They give you access to the genome. But would I be able to analyze it?

There are still problems. s does not equal N/Pi but angle AFC should. That is if the triangles are similar. The only place that the sides of the triangle should be an integer is at x and y. AFC = (remainder(N/Pi)) * Pi (In theory)

Ok, sorry I haven’t replied sooner. I have changed that s is now the remainder of N/Pi. That is a 180 the max angle (straight line). I did this because I couldn’t remember the modulus definition. I am saying that if N is much larger than x and y the Prime factors that x would wrap around the half circle (180 degrees) N/Pi times. The remainder would form a triangle where x and y would add to find the remainder of N/Pi as the similar triangle AFC. So triangle AFC is similar to triangle xys. (Yes I know the label isn’t standard.) Why did I do this? There is no guarantee this will make the solution simpler. But I already have proven equations for x and y as related in terms of x and N. I was going to use these equations and place them to the sides of the triangle and use the equations we know about triangles to solve for a pattern. This is a long shot, but I have always pictured the Prime factorization as a logarithmic spiral. That is why I wrapped x at an angle around the circle. I realize this theory has somehow gotten away from me. It is extremely confusing. But I stand behind my underlying theory. As you read my earlier post on this thread, I have found patterns in the Prime factorization. The resulting equations are just impossible to solve to be useful. I thought since I cannot solve the polynomial equation, I would make a graphical representation, but I need to reevaluate this. Perhaps if I map out the entire idea, you guys could assist me in making it makes sense. I am have been busy and it takes time but I think I should explain more, even though this post is an attempt to explain. But in the coming weeks I will work on this. Try not to laugh at me too much.

OK, first off I’m sorry l haven’t replied sooner, but I have been busy. Second, I think you guys overestimate my knowledge of biology and genetics. I want to look for patterns in the genetic code. I have did a little research and I don’t know what the information needs. I need a starting point. You guys gave me excellent information. But I cannot test the DNA myself. I have an upper-level chemistry book that says to place a specimen in a spectrophotometer. I have googled it and it is affordable. My chemistry book does not list steps however. It has theory then puts a list of 7 steps on what to do without a complete lab explanation. I should explain more what I want to do. I want to look for patterns in genetics. As you guys stated that a lot of information is shared. I think it is like a networked science where the public looks at the data, like finding constellations in telescope pictures. I’m not claiming to be able to discover anything. I have tried to find patterns on the Prime factorization problem. I have found some patterns, but I don’t have a solution to the problem. As you can see from my math post on SFN. So I suppose my question is can I do any meaningful experiments. And by meaningful I mean worth the price of a $500 spectrophotometer to do amateur experiments and have some fun. I also have a question of the value of my own DNA. I was thinking of doing the Ancestry.com DNA test. But if I give my DNA do I compromise my privacy? I have DNA on record from being in the military. The military has a great DNA base of every member since approximately 1996. They are only supposed to use the DNA for identification, but imagine the information they collect on everyone with both nature vs. nurture. But I imagine a world where cryptography and identity will utilize the genetic information. Is it safe to give Ancestry.com genetic fingerprint? BTW, when I was talking about God, it was not in a religious way. I was asking does a one-way function exist. If an all-powerful being can create a function can they reverse it? If they can there are no one-way functions. But if the being can’t reverse it, one-way functions exist. Either way some would say that either would mean they are not all knowing. The boulder problem is a non-religious person’s argument. But I mention this only as the meaning of a one-way function. It is not intended to prove any religious viewpoint right or wrong. It is just a conundrum.

https://1drv.ms/i/s!Ao7PhUWlkaBthGPYxf06XrWnNzKL Definitely some problems with my geometric representation. Does this look better?

Ok, for my background I am a college student. I confess to not knowing biology or genetics or even engineering for that matter. I have read some books on genetics and I am particularly interested in gene-therapy. But I have read that genetics is related in many ways to cryptography. I have tried here at SFN in a math post to solve the Prime-product problem. I have had little success so far. I have a polynomial which if you already know the Prime numbers proves true, but by itself I cannot solve the resulting equation. I have tried geometry and am currently looking at other methods. My question is how do you read the genetic code chemically? I have seen some basic experiments in a Make biology book. Also what are the cytological algorithms? From my brief research the math problem is complex and differs from gene pattern to pattern. So not only do you have to solve a genealogic one-way-function, but you don’t know the algorithm that pattern is based on. And most gene knowledge is not shared due to the fact it is a big-money intellectual property. So with most researchers working alone it is no wonder mathematicians haven’t solved it. My approach is to find a pattern that not only describes the RSA Key algorithm, but will find patterns where patterns don’t seem to exist. I believe in creation, but will not preach but list this to note something very important. A nonbeliever asked if God is so powerful can He make a bolder so heavy even he can’t lift. This sounds ignorant. The nonbeliever would say he isn’t all powerful if he can’t lift the bolder and if he can’t lift hit he can’t lift the heaviest boulder. I know it sounds like nonsense. But my question is can God make a function that cannot be reversed? Obviously I don’t know what God is capable of. There are easily one-way functions we cannot reverse. However I don’t see genetics as something that can’t be figured out. Some scientist, see genetics as chemical proof God does not exist. I believe the pattern just shows his work. The fact remains that knowledge of genetics is as dangerous as the fruit from the Tree of Life. That is just my perspective. I don’t want to argue if genetics proves we evolved. I am just stating why I am interested in genetics. I want to find patterns in them. Obviously I am limited in what I can do. I don’t have a lab or biology background. But I found this article which described a one-way biological function. Also you should check out my post in the math forum. Please share if you know any simple genetic experiments. I have the catalog of American Scientific’s “Amateur Scientist” columns. I have a professional microscope, power tools, Internet, cryptography books, and an impossible to solve polynomial. I’m not intending to cure cancer, but I want to look at patterns in DNA that could relate to cryptography. http://www.asee.org/documents/sections/middle-atlantic/fall-2009/01-Biological-One-way-Functions.pdf http://www.scienceforums.net/topic/95813-prime-products-just-one-last-time/

Imatfaal, I am not arguing that 60 deg = 1 radian. 1 rad is 180/Pi. I am only looking to find a symbolic value of angle AFC. The entire point of drawing the triangle with side N is to find angle AFC. As for degrees, it would be fine to find angle AFC in degrees. The question is can anyone symbolically find this angle. If you can I will tell you why I want to know its equation for.

https://1drv.ms/i/s!Ao7PhUWlkaBthFy7UgDHUGEIh2Lm Here is my updated drawing. It could still be wrong. I may have some flawed logic. But I am seeing this idea develop, but I cannot explain it. It is abstract. I know if I write it out and keep it as simple as possible, maybe someone else will be able to see it also. That is what I hope. Let me know what you think. This is only the start of the problem. But I need some input that the vector addition with sides x and y (the 2 Prime numbers multiplied together with an angle between them (the angle approaches the limit of Pi radians) have a resultant of N (where N is the product of the 2 Prime numbers x and y). Let me know if this conveys anything. An idea is not as valuable when no one else can understand what you are trying to do.

Very interesting. The question to answer is how it differs from a regular gear. Inter-locking the forces on the gear could be distributed differently. I am not sure of the inter-locking would allow circular motion. They would be in conflict during rotation. However don't be deterred. If certain Pokadoves were stationary while others rotated as a gear you could produce custom orbits. That is irregular non-circulat orbits. Think unsemetric objects like a space station. This is good work. I'm just giving my opinion. I am no authority on the subject. But you need to research gears in a machine design book. Again cool shape; creative design; I'm just not sure how it moves. Are you suggesting to use it as a mag wheel? Or is it to inter-lock as a tool?

Yes, my drawing and explanation are off. But don’t disregard the idea yet. This is a one of the graphical representations of my algebraic work posted earlier in this post. Things to remember when looking at this drawing: This is a vector. Both x and y are Prime numbers We are looking for the smallest lengths x and y possible. (They represent Prime numbers after all. There are no angle sides multiples of x and y. Again, these are prime factors. So, there is no 2x or 2y or 3x and 3y. As the lengths of x and y increase, the angle between them decreases. This is significant because the vector addition of x and y is less than N. And for my solution x < y. sin(60 degrees) = 0.866025404 sin(1 radian) = 0.841470985 cos(60 degrees) = 0.5 cos(1 radian) = 0.540302306 This relates to the same error of my equations. I am working on this problem off and on. I will try and produce a better and corrected drawing.

Ok, my last post wasn’t very clear. Here is what I was trying to do. N is known. x and y the 2 number that when multiplied together make N. I am trying to simplify the factoring by using a simple vector. This vector might be able to be solved to find the unknown factors x and y. Picture an angle between 2 lines. As the lines increase in distance so the angle stays the same, but the distance between the 2 lines also increases. So I start with a triangle whose segment opposite the (obtuse) angle between the lines equals N. Now I take this same length N and travel along the original 2 lines until the length along the lines approaches a segment between those lines as N. N is the point where the segment between the 2 lines will reach the limit of N. Beyond N the segment is bigger than N. This is where I need your help. Just to see if this is worth pursuing. The other limit (opposite end of the N segment) is 1 Radian with a radius of N. So, on a circle with radius N with 2 sides N and the angle between 1 Radian. I am not sure as you pointed out the triangle of 60 degrees is not 1 radian. But I am referring to the relative angle between side N and side N. So, the tangent of x equals N -x. N is known This is the tricky part! I have not solved this yet. But I am saying I could possibly use the equations I found a pattern in the Prime factors. Which until know is too complex. But Knowing N and the angle opposite N… I am saying there is a possibility of substituting the equations for x with a new simpler equation of x in this geometry. I am not claiming this works. It was just something I was thinking about. Remember this drawing is off. I need to make a clearer drawing. https://1drv.ms/f/s!Ao7PhUWlkaBtgQd7IjIjxkBjv3wz

I am going to keep this short, because it is just an idea I was working on and I have school work to do and not silly math ideas. But imagine a circle where N is the product of 2 Prime numbers. The radius of the circle is N, so in 1 radian a triangle is formed with a segment opposite the 1 radian angle is N. So an equilateral triangle is formed with all sides equaling N. But we want to know the angle of a triangle with the side opposite the obtuse angle is also of length N, but we have lengths "x" and "y" that are unknown sides. Could we take the N-equilateral triangle and subtract x from one of the end sides? The theory is that the y side would complete the triangle giving us the obtuse's angle in form of an equation with variables in N and x. Can anyone disprove that this will not geometrically solve an unknown triangle of one side N, which is known, and put into equation form x and y? I will add more to this when I have time. I can't insert the picture so it is difficult to visualize what I am describing. I know it sounds stupid, but there is some thought here. Let me know what you think. Trurl

Thanks for the link. The following is why I started researching this idea. It may seem silly but does anyone get anything from this? I'm not sure if anyone got anything from the previous posts but this is going to sound brilliant or a bunch of malarkey. Let me start by saying that this idea is just a theory and nothing is proven. This is just an example of how I approach a math problem. It is very much intuitive and visual. The idea: PNP is given and the unit circle will be used to find x and y. (These variables correspond to my previous equations.) The area encompassed by the angles on the unit circle will be used to form equations that find the values of x and y. Imagine a vector solved by the method of parallelogram addition. That is there is a triangle with 2 known sides x and y. Through vector addition and an angle of y/x radians between the sides the area can be found. This area is theoretically equivalent to N in value. The problem is N is the only value we know. To be useful we have to know y/x are at least some properties and proportions. We cannot use vector addition directly because N is only given. But it may be useful to use the unit circle to find which x and y will equal N. So a circle with radius x and a y arc length from an angle of y/x radians, has an area encompassed by the unit circle equal to N. This encompassed area is of angle y/x. If y/x is larger than 2Pi*x the angle encompasses one or more of the circle. That is the idea. I don’t know if it works, but it is how I go about math problems. This would relate to my theory of a logarithmic spiral that would show a pattern in the placement of Prime numbers. I have had this idea for quite some time. As seen in these URL’s: http://www.constructorscorner.net/ideas_and_gadgets/math/math_hunch/hunch_00001/hunches_section0005/trig_parabola.html http://www.constructorscorner.net/ideas_and_gadgets/math/math_hunch/hunch_00001/hunches_section0005/trig_parabola_verified.html http://www.constructorscorner.net/ideas_and_gadgets/math/math_hunch/hunch_00001/hunches_section0008/PrimeRevolutions.html If it is true this is just one step. There must be a way to solve the unknowns x and y in equation form. Remember PNP/y equals a distance of 1 radian. And remember this is only a preliminary idea I want input on. I am not clamming it works. I just think it is interesting enough to consider. Trurl [bJS1]