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You are not logged in. #76 20121208 20:53:06
Re: A few questionsI see
Any article or anything you would suggest me to read for clearing my idea on mods? '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 #77 20121208 21:07:31
Re: A few questionsHi Agnishom; 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. #78 20121209 01:23:05
Re: A few questionsWould you suggest any good book that is freely available for Number Theory? '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 #79 20121209 07:14:03
Re: A few questionsHi Agnishom; 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. #80 20121209 07:33:37
Re: A few questionsHi phrontister! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #81 20121209 08:34:32
Re: A few questionsHi Agnishom; 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. #82 20121209 16:04:39
Re: A few questionsThanks! I will try to find it '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 #84 20121210 02:58:04
Re: A few questionsExcuse me noelevans, I think we had been talking about Triangles '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 #85 20121210 21:30:54
Re: A few questions
Let the sides be . The perimeter is and the area is by Heron's formula.
Hence Setting : Since are sides of a triangle, we can make the substitution , , , which gives Thus are integers, as are integers; they are also positive as the sum of two sides of a triangle must be strictly greater than the third side. Substituting in the above equation: So the RHS is divisible by 4. This means either (i) two of equal 2, or (ii) one of equals 4. In case (i) we have (taking WLOG) , an absurdity. So case (ii) must hold. WLOG let . Then Thus must be an integer or , which gives or . Substituting back gives or . Hence the only triangle with equal area and perimeter is the one with sides 6, 8, 10. Last edited by scientia (20121210 21:58:27) #86 20121210 21:53:10
Re: A few questionsSorry, I made a mistake. This means that either are integers or of the form for . There may be other answers. #88 20121210 23:25:02
Re: A few questionsYeah, as I said I made a mistake. Let , , , where are positive integers (so themselves are not necessarily integers). This gives which is what is required to be solved. I haven't gone very far, have I? Last edited by scientia (20121210 23:25:49) #89 20121211 08:03:09
Re: A few questionsHi scientia; 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. #90 20121211 14:18:25
Re: A few questionsWhat are these x,y and z? '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 #91 20121211 23:28:28
Re: A few questionsHi Agnishom! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #92 20121212 01:15:48
Re: A few questionsExcuse me noelevans, What if the triangle isn't right angled? '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 #93 20121212 01:18:00
Re: A few questionsHi Agnishom; 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. #94 20121212 01:52:46
Re: A few questionsThen How did you work them out? '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 #95 20121212 01:57:58
Re: A few questionsThe proof supplied the 5 answers. I checked them using geogebra and that was not easy either. 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. #96 20121212 03:05:28
Re: A few questionsDo you have the proof? '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 #97 20121212 03:09:32
Re: A few questionsHi; 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. #98 20121212 03:13:19
Re: A few questions
Why? Whats wrong? '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 #99 20121212 03:16:01
Re: A few questionsFor one thing, it could be wrong! If I do not understand it how can I explain it or be satisfied with it? Oh, he/she is right with the five solutions he gives. I checked them and they are correct. But supposing there are a couple of more solutions? 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. #100 20121212 03:18:20
Re: A few questionsPlease show me '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 