mm-2959 ==== Subject: Re: Demon Chaos > In an extended field array of rectangular cells, each cell is assigned > an initial random level from 0 to 14. The field is then updated > repeatedly according to the rule that a cell will increase by one if > and only if there is a touching cell that is just one level higher. > Levels continue at mod 14, etc. When the 14 levels are represented by > 14 different colors, beautiful and interesting patterns emerge, first > as patch areas and then evolving to dynamic spirals. > Does anyone know why this occurs and why it works only with just 14 > levels ?! Neat! I like the patch areas the best, the spirals are far too static. The same thing happens with all numbers of levels, but the smaller levels generate more, smaller spirals which are harder to identify. I imagine that the spirals form from some kind of seed pattern. The pattern is WAY more interesting at levels=20! Nicholas Sherlock ==== Subject: Re: Demon Chaos Well this is strange. It's been quite some time now but the text from which I got this indicated that only 14 levels would work. I can remember trying it with a different number of levels and it just seemed to remain essentially random. Will have to try it again with 20 levels. On Mon, 30 Jan 2006 17:15:47 +1300, Nicholas Sherlock >> In an extended field array of rectangular cells, each cell is assigned >> an initial random level from 0 to 14. The field is then updated >> repeatedly according to the rule that a cell will increase by one if >> and only if there is a touching cell that is just one level higher. >> Levels continue at mod 14, etc. When the 14 levels are represented by >> 14 different colors, beautiful and interesting patterns emerge, first >> as patch areas and then evolving to dynamic spirals. >> Does anyone know why this occurs and why it works only with just 14 >> levels ?! >Neat! I like the patch areas the best, the spirals are far too static. >The same thing happens with all numbers of levels, but the smaller >levels generate more, smaller spirals which are harder to identify. >I imagine that the spirals form from some kind of seed pattern. >The pattern is WAY more interesting at levels=20! >Nicholas Sherlock ==== Subject: Re: Demon Chaos WOW! I take it back, it DOES seem to work with other numbers of levels. I must have made a programming error way back when I first tried something different from 14. What's worse, I can't seem to find the reference in the text. On Mon, 30 Jan 2006 13:34:30 -0500, Stephen G. Giannoni >Well this is strange. It's been quite some time now but the text from >which I got this indicated that only 14 levels would work. I can >remember trying it with a different number of levels and it just >seemed to remain essentially random. Will have to try it again with 20 >levels. >On Mon, 30 Jan 2006 17:15:47 +1300, Nicholas Sherlock > In an extended field array of rectangular cells, each cell is assigned > an initial random level from 0 to 14. The field is then updated > repeatedly according to the rule that a cell will increase by one if > and only if there is a touching cell that is just one level higher. > Levels continue at mod 14, etc. When the 14 levels are represented by > 14 different colors, beautiful and interesting patterns emerge, first > as patch areas and then evolving to dynamic spirals. Does anyone know why this occurs and why it works only with just 14 > levels ?! >>Neat! I like the patch areas the best, the spirals are far too static. >>The same thing happens with all numbers of levels, but the smaller >>levels generate more, smaller spirals which are harder to identify. >>I imagine that the spirals form from some kind of seed pattern. >>The pattern is WAY more interesting at levels=20! >>Nicholas Sherlock ==== Subject: Re: Demon Chaos RVh0U29mdHdhcmUAQWRvYmUgSW1hZ2VSZWFkeXHJZTwAAAAwUExURZSw9h2Xq+iGU7FmO7LK/6XA /97ir5CLgMv59HlEErDp5rfCnnHExLvR/7zS/0hW4hzk0QEAAAIKSURBVHjapJKJlsIgDEUzLI1I kf//28nK4jLqmRRoAu/yoAq3LwP+BTTrj9E2oGndKG7apJB+a7bOAyugfRkC9N5p0NZ94ErWfNQG c8Xb87TLMxzU5onDynY7UuIijaUkuyVPdSGZQyIgyYY8k7h1e1vaZEhzFlJ7+2wFcKldB323tExs 8+DVYIZq2aR5mdjhuxCAriejpzok6/s02LSMfcmp9znXtZ4OE+j9Dlg83SFt+7xw8DUYVxg+PvbU 963MIdMzh8fHB27UYckXZis3GjK9uclEzhWx8lPrbQjzmsAyAaw+NCpDKWVfHjtC1v05VXk9KYRj xJcHBKaWwxzH+SNBL4GwjmUnYRSkryL2oPTAI98FjATrucoFISK9BGI1/fV6vVAXgq7+CjjRgKvG hZGfs+I7h4vpOc7zqPdngjy/KQEknHpKjwqPDtqw4EHEAASlDwtTIg0sAQIqE34FkROAfgoVOsVA JEK+rADyB8FQ0CR+IDA9ASEIIj+2/DcQQyzrWRa5OIQQEPmPyoHIdSxDZtsPgAjyMIY6p5E889z4 CaGIRQxHCOc8yXqeSZQSOYjEeAQq0TfNM7lHiljFSPrIxDzHbuAQ/SIU9EYyIrMC4Dd4cNjjjEJE NlHZosWniOqV+GvrlSCm6LE+QujXK9xKQfgs+FuxR/ycYLl4lPditIvbPYT4FWAAn7M7WmFO0k8A AAAASUVORK5CYII= > WOW! I take it back, it DOES seem to work with other numbers of > levels. I must have made a programming error way back when I first > tried something different from 14. What's worse, I can't seem to find > the reference in the text. The higher levels take longer to set up large areas, and finally, spirals. More interesting as long as it actually gets started with the random pattern you generate. Nicholas Sherlock ==== Subject: Re: Demon Chaos BTW, Text = The Mathematical Tourist by Ivars Peterson I HIGHLY RECOMMEND IT ! On Tue, 31 Jan 2006 08:48:56 +1300, Nicholas Sherlock >> WOW! I take it back, it DOES seem to work with other numbers of >> levels. I must have made a programming error way back when I first >> tried something different from 14. What's worse, I can't seem to find >> the reference in the text. >The higher levels take longer to set up large areas, and finally, >spirals. More interesting as long as it actually gets started with the >random pattern you generate. >Nicholas Sherlock ==== Subject: Re: Demon Chaos > In an extended field array of rectangular cells, Is there any significance to them being rectangular? > each cell is assigned > an initial random level from 0 to 14. That's 15 values. >The field is then updated > repeatedly according to the rule that a cell will increase by one if > and only if there is a touching cell that is just one level higher. Exactly one cell? More than one cell? What does touching mean? Are diagonals considered touching like they are in the Game of Life? > Levels continue at mod 14, etc. That's 14 values. > When the 14 levels are represented by > 14 different colors, beautiful and interesting patterns emerge, first > as patch areas and then evolving to dynamic spirals. > Does anyone know why this occurs and why it works only with just 14 > levels ?! http://www.homestead.com/giannoni/sa18.html ==== Subject: Re: Demon Chaos On 29 Jan 2006 18:53:44 -0800, mensanator@aol.com >> In an extended field array of rectangular cells, >Is there any significance to them being rectangular? Must have 4 cells touching via edges and 4 cells touching via corners; really think this must be a rectangular array of cells. >> each cell is assigned >> an initial random level from 0 to 14. >That's 15 values. Yes, yes, I meant 0 - 13 or mod 14 ... >>The field is then updated >> repeatedly according to the rule that a cell will increase by one if >> and only if there is a touching cell that is just one level higher. >Exactly one cell? More than one cell? What does >touching mean? Are diagonals considered touching >like they are in the Game of Life? At least one cell, touching as in the game of life sense, or as described above. >> Levels continue at mod 14, etc. >That's 14 values. >> When the 14 levels are represented by >> 14 different colors, beautiful and interesting patterns emerge, first >> as patch areas and then evolving to dynamic spirals. >> Does anyone know why this occurs and why it works only with just 14 >> levels ?! >> http://www.homestead.com/giannoni/sa18.html ==== Subject: Re: Demon Chaos BIG CORRECTION ! ONLY EDGE TOUCHING CELLS COUNT, NOT THE CORNER CELLS. SORRY ... On Mon, 30 Jan 2006 11:01:49 -0500, Stephen G. Giannoni >On 29 Jan 2006 18:53:44 -0800, mensanator@aol.com > In an extended field array of rectangular cells, >>Is there any significance to them being rectangular? >Must have 4 cells touching via edges and 4 cells touching via corners; >really think this must be a rectangular array of cells. > each cell is assigned > an initial random level from 0 to 14. >>That's 15 values. >Yes, yes, I meant 0 - 13 or mod 14 ... >The field is then updated > repeatedly according to the rule that a cell will increase by one if > and only if there is a touching cell that is just one level higher. >>Exactly one cell? More than one cell? What does >>touching mean? Are diagonals considered touching >>like they are in the Game of Life? >At least one cell, touching as in the game of life sense, or as >described above. > Levels continue at mod 14, etc. >>That's 14 values. > When the 14 levels are represented by > 14 different colors, beautiful and interesting patterns emerge, first > as patch areas and then evolving to dynamic spirals. > Does anyone know why this occurs and why it works only with just 14 > levels ?! > http://www.homestead.com/giannoni/sa18.html ==== Subject: Re: Demon Chaos > On 29 Jan 2006 18:53:44 -0800, mensanator@aol.com > In an extended field array of rectangular cells, >>Is there any significance to them being rectangular? > Must have 4 cells touching via edges and 4 cells touching via corners; > really think this must be a rectangular array of cells. my screensaver (xscreensaver, demon) also does it with triangular cells. ==== Subject: Complex Locus Could anyone please help me with the folowing: The point P representing z(= x + iy) in the Argand diagram lies on the line 6x + 8y = R, where R is real. Q is the point representing (R^2) / z. Prove that the locus of Q is a circle, and find its centre and radius. I can't get going on this, I know it's simple, I have the answer (Centre (3R, -4R), radius 5R) but need to understand the method. Mitch. ==== Subject: Power of 2 divisible by 3 I cannot seem to find a power of 2 divisible by 3. I did all of the to try to find a power of 2 divisible by 3, but it couldn't find any. So the number must be above 2^32. But what is the smallest power of 2 divisible by 3? Does a number x such that log2(x) is an integer and x/3 is an integer even exist? Is there a way I might go about proving or disproving the existence of such a number? ==== Subject: Re: Power of 2 divisible by 3 > I cannot seem to find a power of 2 divisible by 3. Good! you won't. > Does a number x such that log2(x) is an integer and > x/3 is an integer even exist? No. >Is there a way I might go about proving > or disproving the existence of such a number? there must be. if you accept that for a number x to be evenly divisible by a number n then x must have all the prime factors of n (in greater or equal quantities) then all you need to do is show that powers of two are only have the prime factor two. ans that two is not three. -- ==== Subject: Re: Power of 2 divisible by 3 > I cannot seem to find a power of 2 divisible by 3. I did all of the > to try to find a power of 2 divisible by 3, but it couldn't find any. > So the number must be above 2^32. But what is the smallest power of 2 > divisible by 3? Does a number x such that log2(x) is an integer and > x/3 is an integer even exist? Is there a way I might go about proving > or disproving the existence of such a number? If you think about this for a few seconds it's going to suddenly become obvious. A power of 2 is 2x2x2x2x2x2x2x2x2 ... for some number of 2's. A number divisible by 3 must have a 3 somewhere when it's broken down into prime factors. Prime decomposition is unique ... in other words for any given number, its prime power decomposition either does or does not contain a 3. ==== Subject: Re: Power of 2 divisible by 3 > I cannot seem to find a power of 2 divisible by 3. I did all of the > to try to find a power of 2 divisible by 3, but it couldn't find any. Don't use computers, they're stupid, have never taken a math class, never passed a math exam and don't have a math degree. Learn number theory. > So the number must be above 2^32. But what is the smallest power of 2 > divisible by 3? Does a number x such that log2(x) is an integer and > x/3 is an integer even exist? Is there a way I might go about proving > or disproving the existence of such a number? Yea, unplug the computer and learn number theory. Oh, by the way 2^(log 3/log 2) = 3 ==== Subject: Re: Power of 2 divisible by 3 Are you being serious? A number can only be broken down into prime factors in one way so if a number is a power of 2 (ie 2 x 2 x 2 x ... x 2) then 3 can't be a factor also since they are both prime. >I cannot seem to find a power of 2 divisible by 3. I did all of the > to try to find a power of 2 divisible by 3, but it couldn't find any. > So the number must be above 2^32. But what is the smallest power of 2 > divisible by 3? Does a number x such that log2(x) is an integer and > x/3 is an integer even exist? Is there a way I might go about proving > or disproving the existence of such a number? ==== Subject: Help with word problem.. 'Aircraft Bearing I need help trying to figure out how to solve this word problem.. An aircraft going from city A to city B on a bearing of S69E is traveling at a speed of 430 miles per hour. The wind is blowing out of the north to south at a speed of 25 miles per hour. Find the ground speed and the plane's true bearing. ==== Subject: Re: Help with word problem.. 'Aircraft Bearing > I need help trying to figure out how to solve this word problem.. > An aircraft going from city A to city B on a bearing of S69E is traveling > at a speed of 430 miles per hour. The wind is blowing out of the north to > south at a speed of 25 miles per hour. Find the ground speed and the > plane's true bearing. Is this for a pilot's exam or part of an introduction to vector addition? I could tell you the answer but that won't help you if I know how to read S69E -- ==== Subject: Re: Help with word problem.. 'Aircraft Bearing > I need help trying to figure out how to solve this word problem.. > An aircraft going from city A to city B on a bearing of S69E is traveling > at a speed of 430 miles per hour. The wind is blowing out of the north to > south at a speed of 25 miles per hour. Find the ground speed and the > plane's true bearing. I understand S 69 E to mean 69 degrees East of South - which is the same as 21 degrees South of East or several other expressions, but we could suppose that there is some convention about which to prefer. To make sense of the question, S 69 E has to be the plane's on-board compass direction. The wind from the northblows it slightly to the south, and slightly faster, for a true bearing of S 66 E and a ground speed of 440 mph. ==== Subject: Re: Help with word problem.. 'Aircraft Bearing On 31 Jan 2006 01:50:23 -0800, bert I need help trying to figure out how to solve this word problem.. >> An aircraft going from city A to city B on a bearing of S69E is traveling >> at a speed of 430 miles per hour. The wind is blowing out of the north to >> south at a speed of 25 miles per hour. Find the ground speed and the >> plane's true bearing. >I understand S 69 E to mean 69 degrees East of South - which is the >same as 21 degrees South of East or several other expressions, but we >could suppose that there is some convention about which to prefer. >To make sense of the question, S 69 E has to be the plane's on-board >compass direction. The wind from the northblows it slightly to the >south, and slightly faster, for a true bearing of S 66 E and a ground >speed of 440 mph. I agree with your interpretation of S 69 E, and for that matter, the interpretation of the whole question, but I think it is worded badly. Normally in these type of questions I would expect to see the term heading when referring to the planes magnetic compass reading. And going from city A to city B on a bearing of S69E is ambiguous. Is the bearing from city A to city B S69E? A much clearer statement would be something like: An airplane is flying with a heading of S69E and an airspeed of 430 mph. The wind is blowing due south at a speed of 25 mph. Calculate the plane's ground speed and (resultant) direction. My 2 cents worth. --Lynn ==== Subject: Re: Help with word problem.. 'Aircraft Bearing > I understand S 69 E to mean 69 degrees East of South - which is the > same as 21 degrees South of East or several other expressions, but we > could suppose that there is some convention about which to prefer. > To make sense of the question, S 69 E has to be the plane's on-board > compass direction. The wind from the north blows it slightly to the > south, and slightly faster, for a true bearing of S 66 E and a ground > speed of 440 mph. Aaah, but how much flaps are applied? Is the direction of airflow the same at the craft's current altitude or has it sheared west? Is there convergence? Convection? Inversion? What is the polar efficiency of this particular craft? Is it a hang-glider or a 747? Even air density and temperature will have an influence on velocity. Seriously, this is a good example why word questions suck and should be outlawed. :) ==== Subject: Re: Help with word problem.. 'Aircraft Bearing I will write that down, and ask my teacher to show me how to do that on paper. >> I need help trying to figure out how to solve this word problem.. >> An aircraft going from city A to city B on a bearing of S69E is >> traveling >> at a speed of 430 miles per hour. The wind is blowing out of the north >> to >> south at a speed of 25 miles per hour. Find the ground speed and the >> plane's true bearing. > I understand S 69 E to mean 69 degrees East of South - which is the > same as 21 degrees South of East or several other expressions, but we > could suppose that there is some convention about which to prefer. > To make sense of the question, S 69 E has to be the plane's on-board > compass direction. The wind from the northblows it slightly to the > south, and slightly faster, for a true bearing of S 66 E and a ground > speed of 440 mph. ==== Subject: Re: Help with word problem.. 'Aircraft Bearing >I need help trying to figure out how to solve this word problem.. > An aircraft going from city A to city B on a bearing of S69E is traveling > at a speed of 430 miles per hour. The wind is blowing out of the north to > south at a speed of 25 miles per hour. Find the ground speed and the > plane's true bearing. Just consider it as traveling in the direction of a compass 69 degrees clockwise from due north. Due east would be 90 degrees. Due south would be 180 degrees. I'll let you extrapolate due West :D Wait, I think that's right. S69E would say South East? It would actually be North East. Hmm... I'm not positive at this point. I did a search of the internet and saw nothing to clarify this. I would presume (proably wrongly) that this was refering to a compass bearing of 69 degrees as I stated. ==== Subject: Re: Help with word problem.. 'Aircraft Bearing The book has it labeled as S69*degrees*E. I would assume that's South East 69 degrees. I can tell you the answers they have as possible choices are... 422 Miles Per Hour; S66E 602 Miles Per Hour; S66E 426 Miles Per Hour; S67E 440 Miles Per Hour; S66E Hope that helps clarify. :-/ Cody >>I need help trying to figure out how to solve this word problem.. >> An aircraft going from city A to city B on a bearing of S69E is >> traveling at a speed of 430 miles per hour. The wind is blowing out of >> the north to south at a speed of 25 miles per hour. Find the ground >> speed and the plane's true bearing. > Just consider it as traveling in the direction of a compass 69 degrees > clockwise from due north. Due east would be 90 degrees. Due south would > be 180 degrees. I'll let you extrapolate due West :D > Wait, I think that's right. S69E would say South East? It would actually > be North East. Hmm... I'm not positive at this point. I did a search of > the internet and saw nothing to clarify this. I would presume (proably > wrongly) that this was refering to a compass bearing of 69 degrees as I > stated. ==== Subject: Binomial Coefficient Problem I have the following problem: I solved the probability of some event to be equal to: C(10,2)*C(k-10,18)/C(k,20). The problem asks to find the value of k for which that probability is maximized. So, I set C(10,2)*C(k-10,18)/C(k,20) = 1. Can somebody help me solve this problem? I think that some rule of binomial coefficients must apply to make this really simple, but can't think of which one. The answer is k=100, but I have no idea what procedure to follow to get it. ==== Subject: Re: Help on Boolean Logic > Given A, Given B, false is a tautology, Given that information prove > let say A OR B is a tautology. The symbol |= taut is a shorthand > notation for is a tautology. > A nd B are Well Defined Formulas. > Note, it is not given A AND B but Given A, and Given B as two separate > true formulas. > false is a tautology. > An examble is Given A,B |= taut (A => B) > that is t because A = t , B = t then (A = > B) = t > Another example Given A,B |= taut (A => NOT B) > that is f because A = t, B = t and NOT B = f so (A = > NOT B) = f. > I hope this help to clear up the interpretation. > I am given a problem where A,B |= taut false, and I should prove > a tautology involving A some connective and B. (A OR NOT A) AND (B OR NOT B) |= taut is does use both A and B ;) (A OR NOT A) OR (B OR NOT B) |= taut they are also always correct. (A AND A) AND (B AND B) |= taut (A AND A) OR (B AND B) |= taut Does '|= taut false' mean a contradiction or just not all true? IE: what are the possible truth tables for A and for B? T,F or F,F. Does your problem mean: Given that A is not a taut, and B is not a taut, prove that A (something) B is a taut? Or your problem mean: Given that A => B is not a taut, Both T and F are valid prove that A (something) B is a taut? In that case you can not guess anything about A, but you can tell that B can be F, it is the only way to get an F overall. A B A=>B T T T T F F F T T F F T I am not sure how much good this does you. If you know that A => B |= contradiction, then you can tell that the only way that this could happen is if A =T and B =F, then B=>A|=taut Am I getting close to what the question was about? ==== Subject: How would you calculate this??? The wording of this isn't as clear as it could be (for me anyway). How would you calculate the reimbursement amount based on the way this is worded? Reimbursement Amount shall be the product of: (i) the full amount of the Fee and (ii) the quotient of (A) 90 minus the number of days that Placed Candidate provided services to the Company and (B) 90. For example; Let's say that: * (i) is $10,000 (the full amount of the fee) * The service was provided for 60 days so (A) would be 30 What would be the Reimbursement Amount be after using the above calculation? ==== Subject: Re: How would you calculate this??? > The wording of this isn't as clear as it could be (for me anyway). How would > you calculate the reimbursement amount based on the way this is worded? > Reimbursement Amount shall be the product of: (i) the full amount of the > Fee and (ii) the quotient of (A) 90 minus the number of days that Placed > Candidate provided services to the Company and (B) 90. > For example; Let's say that: > * (i) is $10,000 (the full amount of the fee) > * The service was provided for 60 days so (A) would be 30 > What would be the Reimbursement Amount be after using the above calculation? Reimbursement Amount = full fee times [(90 - d)/90]. In your example that would be 10,000 * [(90 - 60)/90] = 10,000 * (1/3) = 3,333.33 ==== Subject: Simple math/geometry question I have a rectangle. I know the measurement from corner to opposite corner (kitty-corner) is 42 inches and the height to width ratio is 16:9. How do I find the height and width of the rectangle? ==== Subject: Re: Simple math/geometry question >I have a rectangle. I know the measurement from corner to opposite corner >(kitty-corner) is 42 inches and the height to width ratio is 16:9. > How do I find the height and width of the rectangle? >Try this: (9x)^2 + (16x)^2 = (42)^2 81x^2 + 256x^2 = 1764 337x^2 = 1764 x^2 = 1764/337 x^2 = 5.2344 x = 2.287 9x = 9(2.287) = 20.583 16x = 16(2.287) = 36.592 ==== Subject: Re: Simple math/geometry question >I have a rectangle. I know the measurement from corner to opposite corner >(kitty-corner) is 42 inches and the height to width ratio is 16:9. > How do I find the height and width of the rectangle? I think I may have figured it out. If I square the measurement 42, then divide by 25 (all parts of the ratio 16:9 added together) and multiply the result by nine, the square root of that result is 25.2 which unless I've made an error is the measurement of the width. The height would then be 33.6. ==== Subject: Re: Simple math/geometry question > I have a rectangle. I know the measurement from corner to opposite corner > (kitty-corner) is 42 inches and the height to width ratio is 16:9. > How do I find the height and width of the rectangle? Using the diagonal, we can make a triangle (not to scale) with sides | | l| e| n| g| diagonal t| h| | |_________ width length^2 + width^2 = diagonal^2 But width is ratio*length, so we can substitute giving us length^2 + (ratio*length)^2 = diagonal^2 length^2 * (ratio^2 + 1) = diagonal^2 length^2 = diagonal^2 / (ratio^2 + 1) length = sqrt(diagonal^2 / (ratio^2 + 1) ) ==== Subject: Re: Simple math/geometry question On Tue, 31 Jan 2006 17:17:24 -0600, Ernie Sty (kitty-corner) is 42 inches and the height to width ratio is 16:9. >How do I find the height and width of the rectangle? If the unknown side lengths are L and H, 1. What is the formula for the kitty-corner side? 2. What is it that gives 16 / 9? That should give you two equations in two unknowns which you can solve by substitution. --Lynn ==== Subject: 01.02.06 factorial date 1 x 2 x 3 = 6. 01.02.06 factorial date 1 x 2 x 3 = 6. 1 st february 2006. today's date. divisible by 9 ?? 0 ! = 1, then .. (n+1)! = (n+1)x n! .. recurrence relation, definition of factorial.. n is a non-negative integer. maths. stirling's approximation. n ! ~ (n/e)^n * sqrt(2 pi) ??? assymptotic convergence? don.lotto nz