[math-fun] Rectangle-to-Square
Square-to-Rectangle construction problem is trivial. But what about Rectangle-to-Square construction problem? There are some trivial cases, e.g., if a<b are side lengths such that a*b is a square: (a,b)=(6, 24), (a,b)=(6, 54), etc. But what about general case of any rectangle? zak
If you mean construct-with-compass-and-straightedge, see for instance http://planetmath.org/compassandstraightedgeconstructionofgeometricmean Jim Propp On Saturday, July 30, 2016, Zak Seidov <math-fun@mailman.xmission.com> wrote:
Square-to-Rectangle construction problem is trivial. But what about Rectangle-to-Square construction problem? There are some trivial cases, e.g., if a<b are side lengths such that a*b is a square: (a,b)=(6, 24), (a,b)=(6, 54), etc. But what about general case of any rectangle? zak
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Yes, "construction of geometric mean". Thx a lot! I used to know it some 60 yrs ago, but couldn't recall now:) zak Суббота, 30 июля 2016, 19:04 +03:00 от James Propp <jamespropp@gmail.com>:
If you mean construct-with-compass-and-straightedge, see for instance
http://planetmath.org/compassandstraightedgeconstructionofgeometricmean
Jim Propp
On Saturday, July 30, 2016, Zak Seidov < math-fun@mailman.xmission.com > wrote:
Square-to-Rectangle construction problem is trivial. But what about Rectangle-to-Square construction problem? There are some trivial cases, e.g., if a<b are side lengths such that a*b is a square: (a,b)=(6, 24), (a,b)=(6, 54), etc. But what about general case of any rectangle? zak
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Now I recall: "In RAT, HOH is GM of 2POH" = In right-angle triangle, height on hypotenuse is geometrc mean of 2 parts of hypotenuse:) zak
Суббота, 30 июля 2016, 20:13 +03:00 от Zak Seidov via math-fun <math-fun@mailman.xmission.com>:
Yes, "construction of geometric mean". Thx a lot! I used to know it some 60 yrs ago, but couldn't recall now:) zak Суббота, 30 июля 2016, 19:04 +03:00 от James Propp < jamespropp@gmail.com >:
If you mean construct-with-compass-and-straightedge, see for instance
http://planetmath.org/compassandstraightedgeconstructionofgeometricmean
Jim Propp
On Saturday, July 30, 2016, Zak Seidov < math-fun@mailman.xmission.com > wrote:
Square-to-Rectangle construction problem is trivial. But what about Rectangle-to-Square construction problem? There are some trivial cases, e.g., if a<b are side lengths such that a*b is a square: (a,b)=(6, 24), (a,b)=(6, 54), etc. But what about general case of any rectangle? zak
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