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

You are not logged in. #1 20130821 16:37:52
Theory of CurvenessHi; "The most incomprehensible thing about the universe is that it is comprehensible." Albert Einstein #2 20130821 19:28:44
Re: Theory of CurvenessExplain... '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 #3 20130822 01:15:33
Re: Theory of CurvenessThe theory of curveness is true because any planet, satellite or star are always spherical in shape. "The most incomprehensible thing about the universe is that it is comprehensible." Albert Einstein #4 20130822 02:16:00
Re: Theory of CurvenessWell, nothing is exactly straight. Do you have some kind of a definition of a real world straight line? 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 #5 20130822 03:47:54
Re: Theory of CurvenessDefinition: A figure is said to be straight (in a three dimensional space) if the two endpoints of the figure are at minimal distance. '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 #6 20130822 03:53:59
Re: Theory of CurvenessMinimal as compared to? 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 20130822 04:03:17
Re: Theory of CurvenessIt is the least possible distance and only one such configuration exists. '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 #8 20130822 07:41:08
Re: Theory of CurvenessThe "least possible distance" depends on the metric used. Each space has it's own metric. 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 #9 20130822 17:15:18
Re: Theory of CurvenessWhat is a metric? '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 20130822 23:14:00
Re: Theory of CurvenessIt's a function that assigns values to distances. It also has to satisfy a few properties, but those are not important for what we're discussing. 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 20130823 00:01:11
Re: Theory of CurvenessIn the 3D space, I can only concieve of one kind of distance. Please explain if there exists others '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 #12 20130823 00:32:24
Re: Theory of CurvenessThe one you are thinking of is called the Euclidian distance. There exist others. There is quite a bit on this on the net. 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 #13 20130823 03:07:05
Re: Theory of CurvenessWith what keyword should I search for? '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 #14 20130823 03:33:41
Re: Theory of Curvenesshttp://en.wikipedia.org/wiki/Metric_%28mathematics%29 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. 