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

You are not logged in. #51 20130405 01:06:48
Re: Non Intersecting chordsThe number of legal ways to arrange parentheses is exactly the number of chords that do not intersect! 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. #52 20130405 01:11:00
Re: Non Intersecting chordsI somewhat got it now. '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 #53 20130405 01:13:58
Re: Non Intersecting chordsNothing at all except it is a legal ordering of the parentheses which (()( is not. 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. #54 20130405 01:16:15
Re: Non Intersecting chordsOne more thing I would like to ask is how can you make sure that the cases of legal expression and nonintersecting chords are equivalent? '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 #55 20130405 01:21:36
Re: Non Intersecting chordsThat is done by empirically getting 1,2,5,14 and then consulting the Oracle at Delphi. This is one of the chief advantages of doing experimental  computational mathematics! 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. #56 20130405 01:23:05
Re: Non Intersecting chordsOh so you just compare the cases? Last edited by Agnishom (20130405 01:23:30) '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 #57 20130405 01:26:50
Re: Non Intersecting chordsThe Oracle at Delphi is from Greek mythology. Apollo would speak to anyone consulting the Oracle providing unlimited knowledge and understanding of all things. 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. #58 20130405 01:29:00
Re: Non Intersecting chordsWow! '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 #59 20130405 01:31:51
Re: Non Intersecting chords4th Catalan number. 4 for the number of chords over 7 * 5 * 3 * 1 = 2 / 15 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. #60 20130405 01:35:25
Re: Non Intersecting chordsThanks a lot but please answer the first question in #56 '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 #61 20130405 01:38:38
Re: Non Intersecting chordsCompare the cases? I am not following you. 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. #62 20130405 01:41:06
Re: Non Intersecting chordsI mean is it just by mere observation that you know that the cases of the chords and that of the brackets are equivalent? '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 #63 20130405 01:45:13
Re: Non Intersecting chordsThe first few numbers you do by hand or you use a computer. Then you take them over to the Oracle( remember ) and it will do the rest. 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. #64 20130405 01:49:40
Re: Non Intersecting chordsBut you need a proof to say that that will work for all of them! '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 #65 20130405 01:54:26
Re: Non Intersecting chordsThat proof is provided by the site I am referring to. This is a well known combinatorics problem solved long ago.
We will discuss this somewhat old fashioned concept a little bit later. Just let me say that much math is done with a proof connected to it. 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. #66 20130405 02:29:57
Re: Non Intersecting chordsExperimental math? Huh? '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 #67 20130405 02:31:38
Re: Non Intersecting chordsOnce we have some portion of the sequence we can now look it up and find all pertinent information. 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. #68 20130405 02:35:14
Re: Non Intersecting chordsMaybe I would look up the Online Enclycopedia of integer sequences '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 #69 20130405 02:42:28
Re: Non Intersecting chordsI would use the book. The internet is also one of the cornerstones of experimental math.
Wiser than the Oracle at Delphi it is! Check it and you will see your whole problem already solved. Recurrences, generating functions, references. 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. #70 20130405 02:43:51
Re: Non Intersecting chordsIf you had nothing, how could you do it all from a scratch? '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 #71 20130405 02:51:11
Re: Non Intersecting chordsDo I need to? I also could not get 1000! from nothing. Technology is here, it is ruining the environment, we at least should use it. 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. #72 20130405 02:55:43
Re: Non Intersecting chordsYou do not need 1000! at all. '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 #73 20130405 02:59:35
Re: Non Intersecting chordsOnce we take the formula for the Catalan numbers and put it over the formula for the double factorial and simplify we will get the formula that I posted earlier. 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. #74 20130405 03:04:01
Re: Non Intersecting chordsI somewhat understand '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 #75 20130405 03:12:35
Re: Non Intersecting chordsDid you know that many famous mathematicians were not very big on proofs. The names of Eudoxus, Poincare and Bernhard Riemann come to mind.Did you know your countryman, who many call the greatest mathematician of the twentieth century never proved anything? 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. 