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About Simpson17866

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    Earth, give or take a galaxy
  • Favorite Area of Science
    Theoretical Physics, Mathematics

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  1. Anything to do with Mentalism. When somebody's using physical tools and tricks, I know that there's a physical gimmick to what he's doing, even if I don't know what the gimmick is. Telling 4 people to pick 3 numbers at random each, then providing the receipt of a shopping trip from a week ago which predicted that exact sequence of numbers... That is crazy in the best possible way How is that different from the special effect of a movie Magic doesn't fool us because we're dumber than the magicians, magic fools us because magicians are smarter than we are. What they do is completely real (just not what it looks like) and it makes perfect sense (just not to us). Rationality that I don't understand is still rationality
  2. So I've known ever since I discovered this formula that it was an extremely special case that skipped the vast majority of the magic squares that have square numbers in the center and the corners, but I'd thought that a formula that would look at all of the magic squares with square numbers there would be too complicated to use. I just found a formula that looks almost exactly the same, but that I believe covers every single magic square that could possibly have 5 square numbers in the corners and center E+n = (2p^2 + 4pq + q^2)^2 (2r^2 + 2rs + s^2)^2 E-n = (2p^2 - q^2)^2 (2r^2 + 2rs + s^2) E = (2p^2 + 2pq + q^2)^2 (2r^2 + 2rs + s^2)^2 E+m = (2p^2 + 2pq + q^2)^2 (2r^2 + 4rs + s^2)^2 E-m = (2p^2 + 2pq + q^2)^2 (2r^2 - s^2)^2 For which my original formula was the special case where q and s were both equal to 1. PS Do I need a certain number of posts before I can use LaTex? Or is that an option in the toolbar that I just haven't found yet?
  3. All of them. In a bee colony, there are hundreds of infertile female workers for every one fertile queen. Is it "unnatural" that this rampant infertility was not naturally selected out of the gene pool? "By definition, infertility could not possibly continue from one generation to the next"?
  4. Googling "homosexuality in nature" provides a lot of useful information.
  5. You don't have to write it in terms of X and Y, that was just how my personal approach developed. The general form is just E+n = a^2 E-n-m = b^2 E+m = c^2 E-n+m = d^2 E = e^2 E+n-m = f^2 E-m = g^2 E+n+m = h^2 E-n = i^2 And I happened to find one specific set of partial solutions defined by two variables that I happened to designate as x and y. Other partial solutions wouldn't take this specific form, and a lot of them are probably better than mine.
  6. That's the plan. The basic form of any magic square is E+n; E-n-m; E+m E-n+m; E; E+n-m E-m; E+n+m, E-n For any arbitrary values of (E, n, m), the 3 rows, the 3 columns, and the 2 diagonals will all add up to the same "magic sum" of 3E. Setting E=5, n=1, and m=3 gives the "classic" magic square that uses each digit from 1 to 9 exactly once each: 6; 1; 8 7; 5; 3 2; 9; 4 (magic sum: 3*5 = 15) This contains 3 perfect square numbers: 1; 4; and 9. Whereas, if you set E=25, n=11, and m=24, then you get a magic square that contains 4 square numbers instead of just 3: 36; -10; 49 38; 25; 12 1; 60; 14 The challenge is to find a magic square that uses 9 different square numbers instead of just 3 or 4. So far, the best anybody's managed is 8/8 sums the same, 7/9 square numbers 9/9 square numbers, 7/8 sums the same Nobody knows whether or not it's possible to make it all the way to 8/8 sums being the same by using 9/9 square numbers. If it is possible, though, then the numbers would have to be horrendously large (the minimum for any one of them would have to be 10,000,000^2, and it's possible that googol^2 might not be big enough) That is considered cheating
  7. I found a formula for a magic square that guarantees 5 out of the 9 numbers to be perfect square numbers (the 4 corners and the center) for any value of (x,y) And before Microsoft Excel succumbed to rounding errors, I found four specific values of (x,y) which bring this up to 6 out of 9 (the 4 corners, the center, and one of the 4 sides) (1,3) with a central value of 125^2 = 15,625 and a right-hand value of 95^2 = 9,025 (1,10) with a central value of 1,105^2 = 1,221,025 and a right-hand value of 529^2 = 279,841 (1,59) with a central value of 35,405^2 = 1,253,514,025 and an upper value of 2,831^2 = 8,014,561 (3,41) with a central value of 86,125^2 = 7,417,515,625 and a bottom value of 108,455^2 = 11,762,487,025 Have other mathematicians already tried magic squares of this form? If so, has this formula already been ruled out as being incapable of generating 9 perfect square numbers out of 9?
  8. Because any "God" who's existence can be scientifically demonstrated in one way or another is a false god who exists as a physical entity within the universe. Looking for physical proof of God's existence is like the springs of a watch asking which gear is the watchmaker.
  9. I've always believed that somebody with natural talent and deliberate training will get further than somebody with only one or the other.
  10. Hello everybody My name is Simpson, and I am a lifelong math and science nerd. I recently realized that I wasn't going to be a professional mathematician, but this is still my favorite hobby, and I am constantly finding new math problems to work on (my current favorite is the 3x3 Magic Square of Squares problem). I have taken Calc I-III and Differential Equations courses, but matrices have always been one of my main weak points.
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