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The question above about Goldbach's conjecture got me wondering. It seems there are a number of famous conjectures or unproven theorems which have been subjected to brute-force searches for counterexamples. For example, the Goldbach article says it has been verified for n up to around 1017. I imagine Fermat's Last Theorem received similar attention. A layman like me might be tempted to think that a search to high numbers like that makes it a pretty good bet that any further searching is likely to be unsuccessful. My question is, have any of these large-scale searches simply not gone high enough, and a solution was later found by other means? Are there any interesting mathematical relationships that only kick in for enormous values? --TotoBaggins 00:30, 27 February 2007 (UTC)
Good answers, thanks! --TotoBaggins 16:27, 27 February 2007 (UTC)
Is there a way of getting the next sequence with the tedious effort of solving the polynomial? 202.168.50.40 02:07, 27 February 2007 (UTC)
And, for a rough approximation, we can notice that each term is about half as far from 0.5 as the previous term, with this relationship becoming closer with each term. Thus, we can guesstimate 0.5005 for the next term. If anyone actually solves this, please let me know how close my guesstimate came. StuRat 15:36, 27 February 2007 (UTC)
Jane Smith picks up her husband everyday at exactly 6pm at the local train station. One day her husband John Smith arrived back early at 5pm. Rather than waiting an hour for his wife, he started walking back at a constant speed of 4 km/hour. Jane Smith, departed from her house at the usual time and met her husband on the road. He got into the car and she drove home and arrives back at the house 20 minutes earlier than normal.
What is Jane Smith driving speed? For this problem you must assume that Jane Smith drives at a constant speed all the time, there is no traffic on the road and there is no traffic light on the road.
Good Luck! 202.168.50.40 02:17, 27 February 2007 (UTC)
I'm trying to find out how to describe circular objects that are supposed to be concentric, but are not quite. How does one describe non-concentricity? What would the unit of measure be? Thanks, ( 4crates 05:58, 27 February 2007 (UTC))
The general area of finding appropriate descriptions for quantities like this is metrology, but Wikipedia's coverage of that area seems lacking. Lambiam's answer makes sense if the circles really are circles, but if they're lacking in concentricity they may well also be lacking in circularity. Maybe a Google search will find something more relevant? — David Eppstein 17:28, 27 February 2007 (UTC)
I understand that this is impossible with just a pair of compasses and a straight-edge, but is it possible with compasses and a ruler? How would the ruler have to be marked? Do we need the sqrt(pi) marked on the ruler, or would any two points suffice? Is it possible to produce a ruler that has a tick at exactly sqrt(pi) from the zero-tick? Vonity 23:24, 27 February 2007 (UTC)
A "straight edge" is a ruler. Or is it the other way around? Either way you cannot square a circle using only rational numbers. So what if you have the sqrt(pi) marked on your ruler? You cannot multiply two numbers on a ruler.
Pi*r*r = B*B
So B = sqrt(pi) * r
So how do you plan to "multiple" sqrt(pi) with r using your ruler? 202.168.50.40 00:52, 28 February 2007 (UTC)
Mathematics desk | ||
---|---|---|
< February 26 | << Jan | February | Mar >> | February 28 > |
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. |
The question above about Goldbach's conjecture got me wondering. It seems there are a number of famous conjectures or unproven theorems which have been subjected to brute-force searches for counterexamples. For example, the Goldbach article says it has been verified for n up to around 1017. I imagine Fermat's Last Theorem received similar attention. A layman like me might be tempted to think that a search to high numbers like that makes it a pretty good bet that any further searching is likely to be unsuccessful. My question is, have any of these large-scale searches simply not gone high enough, and a solution was later found by other means? Are there any interesting mathematical relationships that only kick in for enormous values? --TotoBaggins 00:30, 27 February 2007 (UTC)
Good answers, thanks! --TotoBaggins 16:27, 27 February 2007 (UTC)
Is there a way of getting the next sequence with the tedious effort of solving the polynomial? 202.168.50.40 02:07, 27 February 2007 (UTC)
And, for a rough approximation, we can notice that each term is about half as far from 0.5 as the previous term, with this relationship becoming closer with each term. Thus, we can guesstimate 0.5005 for the next term. If anyone actually solves this, please let me know how close my guesstimate came. StuRat 15:36, 27 February 2007 (UTC)
Jane Smith picks up her husband everyday at exactly 6pm at the local train station. One day her husband John Smith arrived back early at 5pm. Rather than waiting an hour for his wife, he started walking back at a constant speed of 4 km/hour. Jane Smith, departed from her house at the usual time and met her husband on the road. He got into the car and she drove home and arrives back at the house 20 minutes earlier than normal.
What is Jane Smith driving speed? For this problem you must assume that Jane Smith drives at a constant speed all the time, there is no traffic on the road and there is no traffic light on the road.
Good Luck! 202.168.50.40 02:17, 27 February 2007 (UTC)
I'm trying to find out how to describe circular objects that are supposed to be concentric, but are not quite. How does one describe non-concentricity? What would the unit of measure be? Thanks, ( 4crates 05:58, 27 February 2007 (UTC))
The general area of finding appropriate descriptions for quantities like this is metrology, but Wikipedia's coverage of that area seems lacking. Lambiam's answer makes sense if the circles really are circles, but if they're lacking in concentricity they may well also be lacking in circularity. Maybe a Google search will find something more relevant? — David Eppstein 17:28, 27 February 2007 (UTC)
I understand that this is impossible with just a pair of compasses and a straight-edge, but is it possible with compasses and a ruler? How would the ruler have to be marked? Do we need the sqrt(pi) marked on the ruler, or would any two points suffice? Is it possible to produce a ruler that has a tick at exactly sqrt(pi) from the zero-tick? Vonity 23:24, 27 February 2007 (UTC)
A "straight edge" is a ruler. Or is it the other way around? Either way you cannot square a circle using only rational numbers. So what if you have the sqrt(pi) marked on your ruler? You cannot multiply two numbers on a ruler.
Pi*r*r = B*B
So B = sqrt(pi) * r
So how do you plan to "multiple" sqrt(pi) with r using your ruler? 202.168.50.40 00:52, 28 February 2007 (UTC)