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tan(x) = sin(x)/cos(x) question
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tan(x) = sin(x)/cos(x) Problem: If tan(x) = 5/12, find sin(x) and cos(x) My answer: I know this can be solved by drawing a right-angled triangle and using Pythagoras's theorem to find the hypotenuse. Using this method gives sin(x) = 5/13, cos(x) = 12/13. But by looking at tan(x) = 5/12, I'm thinking sin(x) = 5 and cos(x) =... more »
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JSH: But is quadratic residue idea new?
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Finding a result is one thing but often I wonder afterwards, why is this result new? Now I'm in pondering mode as I consider something so trivially simple that it seems weird if it's NOT previously known. Because of the way congruences work, it's possible to do something interesting with quadratic residues, where I've simplified from the... more »
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New technology competition
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Hi all, Seen in Techcrunch, this competition should interest the group: [link]. The company is looking for best ideas for games, laptops, phones, music using this new tech: the 5 winnings ideas get $6,000, and more. Ideas can be submitted by Nov 30, competition ends Dec 13th: the more... more »
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JSH: Understanding quadratic residues result
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Using very simple mathematics I've found a fascinatingly simple connection between the solution for a quadratic residue, and a factorization, where it is unbelievable how simple the mathematics is, so explaining it is trivial. Given a quadratic residue q, modulo N, where N is odd, I've found that given... more »
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JSH: Your broken system
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So now I found a way to solve for quadratic residues, which also works with composites as well as primes, and there is no denial to claim that's been done before. With one year gone since I first came up with this approach the reality of what mathematicians in our modern world have become can not be denied: they are show people.... more »
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