Comments for Affine Mess http://affinemess.com/blog Math Musings, Math Circles and More Math. Fri, 03 Sep 2010 03:04:16 -0400 http://wordpress.org/?v=2.8.5 hourly 1 Comment on Four Points, Two Distances by affinemess http://affinemess.com/blog/2009/01/four-points-two-distances/comment-page-1/#comment-95 affinemess Fri, 03 Sep 2010 03:04:16 +0000 http://affinemess.wordpress.com/?p=3#comment-95 @Tumblemark: you can't have four collinear points having just two distinct distances. If the points are ABCD in order, then AB < AC < AD. @Tumblemark: you can’t have four collinear points having just two distinct distances. If the points are ABCD in order, then AB < AC < AD.

]]> Comment on Four Points, Two Distances by Tumblemark http://affinemess.com/blog/2009/01/four-points-two-distances/comment-page-1/#comment-94 Tumblemark Fri, 20 Aug 2010 20:21:06 +0000 http://affinemess.wordpress.com/?p=3#comment-94 My 8-year old daughter came up with an additional solution. She made the points colinear. Your challenge does not seem to preclude that. My 8-year old daughter came up with an additional solution. She made the points colinear. Your challenge does not seem to preclude that.

]]> Comment on Mathematical Reasoning is Non-Metric by Yiftach http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-93 Yiftach Sat, 26 Jun 2010 10:18:40 +0000 http://affinemess.com/blog/?p=158#comment-93 I think many mathematical problems are NP in their nature. They have a short solution which is easy to verify, but it might be quite hard to find the solution. Therefore, I do not like the tendency to look down on short proofs. I think many mathematical problems are NP in their nature. They have a short solution which is easy to verify, but it might be quite hard to find the solution. Therefore, I do not like the tendency to look down on short proofs.

]]> Comment on Mathematical Reasoning is Non-Metric by Gil http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-83 Gil Tue, 16 Feb 2010 16:13:57 +0000 http://affinemess.com/blog/?p=158#comment-83 Dear Alon, congratulations on joining the mathblogging circles! --Gil Dear Alon, congratulations on joining the mathblogging circles! –Gil

]]> Comment on Looking inside Tim Gowers’ Mind by Girish Bantwal http://affinemess.com/blog/2009/10/looking-inside-tim-gowers-mind/comment-page-1/#comment-78 Girish Bantwal Sun, 25 Oct 2009 06:30:45 +0000 http://affinemess.com/blog/?p=165#comment-78 I agree - its amazing the kind of transformational thought that Timothy Gowers, Terence Tao and the like seems to bring to this world. Yes, brainwaves and unusual insight and hard work and seclusion :-) forms the core of mathematicians and is considered unusual and looked upon with awe by laymen like me and others BUT its a whole lot more valuable when they contribute selflessly to a bigger and grander purpose of acknowledging that SUM of Parts is bigger :-) and reach out to source of knowledge unbiasedly. They make their prowess so humbling and achieve greatness. I agree – its amazing the kind of transformational thought that Timothy Gowers, Terence Tao and the like seems to bring to this world. Yes, brainwaves and unusual insight and hard work and seclusion :-) forms the core of mathematicians and is considered unusual and looked upon with awe by laymen like me and others BUT its a whole lot more valuable when they contribute selflessly to a bigger and grander purpose of acknowledging that SUM of Parts is bigger :-) and reach out to source of knowledge unbiasedly. They make their prowess so humbling and achieve greatness.

]]> Comment on Mathematical Reasoning is Non-Metric by affinemess http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-77 affinemess Sun, 11 Oct 2009 06:03:57 +0000 http://affinemess.com/blog/?p=158#comment-77 @ernie that's right, although since the numbers form a set (rather than a sequence) it is common to omit the "distinct" part. Just to be safe I'll update the post - thanks for the catch. @ernie that’s right, although since the numbers form a set (rather than a sequence) it is common to omit the “distinct” part. Just to be safe I’ll update the post – thanks for the catch.

]]> Comment on Mathematical Reasoning is Non-Metric by ernie http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-76 ernie Sat, 10 Oct 2009 06:42:27 +0000 http://affinemess.com/blog/?p=158#comment-76 I think you mean "Given 51DISTINCT integers between 1 and 100, prove that two of them are relatively prime. " I think you mean
“Given 51DISTINCT integers between 1 and 100, prove that two of them are relatively prime. “

]]> Comment on Mathematical Reasoning is Non-Metric by affinemess http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-75 affinemess Sat, 10 Oct 2009 02:48:12 +0000 http://affinemess.com/blog/?p=158#comment-75 What's 6^2-5^2? What’s 6^2-5^2?

]]> Comment on Mathematical Reasoning is Non-Metric by AM http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-74 AM Fri, 09 Oct 2009 22:43:34 +0000 http://affinemess.com/blog/?p=158#comment-74 Am I missing something here? The difference of two squares is: a^2 - b^2 = (a+b) . (a-b) Since, its the product of two quantities - it can't be prime! Am I missing something here? The difference of two squares is:
a^2 – b^2 = (a+b) . (a-b)

Since, its the product of two quantities – it can’t be prime!

]]> Comment on Mathematical Reasoning is Non-Metric by affinemess http://affinemess.com/blog/2009/09/mathematical-reasoning-is-non-metric/comment-page-1/#comment-73 affinemess Wed, 07 Oct 2009 02:53:56 +0000 http://affinemess.com/blog/?p=158#comment-73 That's very true - sometimes just knowing (or believing!) that there is a solution helps, and even more so if the solution is known to have be "elementary" in some sense, or to take a certain form. Still, hats off to you - I do believe the third problem is significantly harder than the first two, and solving it instantly is quite remarkable. That’s very true – sometimes just knowing (or believing!) that there is a solution helps, and even more so if the solution is known to have be “elementary” in some sense, or to take a certain form. Still, hats off to you – I do believe the third problem is significantly harder than the first two, and solving it instantly is quite remarkable.

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