Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20121005 10:29:58
New Puzzles 4Even more "Stephen Froggatt" puzzles:: "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20121005 17:21:44
Re: New Puzzles 4hi You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20121005 18:00:32
Re: New Puzzles 4Hi MIF; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20121006 11:55:05
Re: New Puzzles 4Great! I will put that in the solution. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #5 20121006 19:03:01
Re: New Puzzles 4Hi MIF; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20121007 03:57:19
Re: New Puzzles 4I would think there is one, thought it does seem GFs might be of use. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #7 20121007 07:29:21
Re: New Puzzles 4Hi anonimnystefy; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #8 20130304 23:04:21
Re: New Puzzles 4There is a problem with the "Three Of The Best" puzzle. MORE COMPLEX PROOF: The formula is the limit as n goes to infinity of the sequence defined by . Assume some exists (otherwise the sequence would be undefined). Define a sequence . We proceed by induction. Base step: Inductive Hypothesis: Thus we have proved by induction the relation for all . Since is a sequence of the form , this ratio converges to the golden ratio. Last edited by Thurhame (20130306 12:28:02) #9 20130304 23:15:36
Re: New Puzzles 4Wonderful, Thanks! 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #10 20130305 01:39:19
Re: New Puzzles 4Hi Thurhame The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #11 20130305 03:24:55
Re: New Puzzles 4Hi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20130305 04:23:07
Re: New Puzzles 4
Oh, my mistake, it just said there were two solutions to the formula. However, that's still wrong; my proof shows that any solution must be equal to the golden ratio, i.e. there are at most 1 solutions. Last edited by Thurhame (20130305 04:26:01) #13 20130305 05:30:13
Re: New Puzzles 4Hi Thurhame The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #14 20130306 12:27:40
Re: New Puzzles 4Ah, thanks for reminding me, my simple lessrigorous proof isn't adequate if i'm only proving the number of solutions, rather than the value. Removing it now. Hope the more complex proof doesn't make anyone's eyes glaze over. 