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Is it true that for all k, the sum of the reciprocals of the numbers which contain k factors all different diverges? So for example for k = 4, the sequence starts out 1/(2*3*5*7) + 1/(2*3*5*11) + 1/(2*3*5*13) + 1/(2*3*7*11) +... Naraht ( talk) 14:20, 6 April 2014 (UTC)
I am not a mathematician. I am involved in some applied aspects due to my hobby so to speak although it is more serious than a simple hobby. Also I want to reassure you, it is not a homework. I read the article "Sphere" in the Wikipedia and could not find what I need.
Imagine a 2-sphere of radius R = 1 with a North Pole and a great circle which is the Equator. Given a point on the sphere which is distinct from the North Pole and the Equator (it is defined by an angle θ between a radius pointing to the point in question and the one going to the North Pole) I want to know the length (in relative units) of a small circle running through this point parallel to the equator. I would appreciate if someone would give me this answer. Thanks, - -- AboutFace 22 ( talk) 15:01, 6 April 2014 (UTC)
Wow! So fast! Thank you very much. StuRat is here as always! I don't see the proof though. It seems to be more like intuitive? I hope you guys are correct. It is definitely correct in two extreme cases, theta = 0 and theta = 90. Looie496, thanks. Thanks again. -- AboutFace 22 ( talk) 15:24, 6 April 2014 (UTC)
Again, I appreciate it. Thanks, -- AboutFace 22 ( talk) 19:58, 6 April 2014 (UTC)
Well, I am back here. Either there is something wrong with the formula or I am making a mistake somewhere. First I have a small globe in front of me. Then I decided to calculate the latitude as you call it or a small circle on the sphere which is just 3 degrees removed from the North Pole. It is a tiny distance, in fact. This is what I get. The sine ( θ ) = 0.052359... I don't know how to use calculators, it is easy for me to write a short piece of code, so it is C#. Then using your formula I multiply 6.28 * 0.052359 and I get 0.3284. It seems too large a value for me. Could it be true? Thanks, -- AboutFace 22 ( talk) 21:29, 6 April 2014 (UTC)
Quondum, thank you but I do not understand what you are trying to say? First you said "correct." In what sense am I correct? That I made a mistake or the result I posted is correct? And what digit did I miss? Could you be more specific? Yes, I am talking about circumference. It is the length of the small circle I meant. On the other hand my result appears to be around 5% of the Equator (great circle). -- AboutFace 22 ( talk) 22:05, 6 April 2014 (UTC)
Thank you StuRat and especially Quondum. Now it is all clear. A rephrased statement did the trick. -- AboutFace 22 ( talk) 00:41, 7 April 2014 (UTC)
Mathematics desk | ||
---|---|---|
< April 5 | << Mar | April | May >> | April 7 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Is it true that for all k, the sum of the reciprocals of the numbers which contain k factors all different diverges? So for example for k = 4, the sequence starts out 1/(2*3*5*7) + 1/(2*3*5*11) + 1/(2*3*5*13) + 1/(2*3*7*11) +... Naraht ( talk) 14:20, 6 April 2014 (UTC)
I am not a mathematician. I am involved in some applied aspects due to my hobby so to speak although it is more serious than a simple hobby. Also I want to reassure you, it is not a homework. I read the article "Sphere" in the Wikipedia and could not find what I need.
Imagine a 2-sphere of radius R = 1 with a North Pole and a great circle which is the Equator. Given a point on the sphere which is distinct from the North Pole and the Equator (it is defined by an angle θ between a radius pointing to the point in question and the one going to the North Pole) I want to know the length (in relative units) of a small circle running through this point parallel to the equator. I would appreciate if someone would give me this answer. Thanks, - -- AboutFace 22 ( talk) 15:01, 6 April 2014 (UTC)
Wow! So fast! Thank you very much. StuRat is here as always! I don't see the proof though. It seems to be more like intuitive? I hope you guys are correct. It is definitely correct in two extreme cases, theta = 0 and theta = 90. Looie496, thanks. Thanks again. -- AboutFace 22 ( talk) 15:24, 6 April 2014 (UTC)
Again, I appreciate it. Thanks, -- AboutFace 22 ( talk) 19:58, 6 April 2014 (UTC)
Well, I am back here. Either there is something wrong with the formula or I am making a mistake somewhere. First I have a small globe in front of me. Then I decided to calculate the latitude as you call it or a small circle on the sphere which is just 3 degrees removed from the North Pole. It is a tiny distance, in fact. This is what I get. The sine ( θ ) = 0.052359... I don't know how to use calculators, it is easy for me to write a short piece of code, so it is C#. Then using your formula I multiply 6.28 * 0.052359 and I get 0.3284. It seems too large a value for me. Could it be true? Thanks, -- AboutFace 22 ( talk) 21:29, 6 April 2014 (UTC)
Quondum, thank you but I do not understand what you are trying to say? First you said "correct." In what sense am I correct? That I made a mistake or the result I posted is correct? And what digit did I miss? Could you be more specific? Yes, I am talking about circumference. It is the length of the small circle I meant. On the other hand my result appears to be around 5% of the Equator (great circle). -- AboutFace 22 ( talk) 22:05, 6 April 2014 (UTC)
Thank you StuRat and especially Quondum. Now it is all clear. A rephrased statement did the trick. -- AboutFace 22 ( talk) 00:41, 7 April 2014 (UTC)