[math-fun] Origamics
I recently acquired an e-copy of this Kazuo Haga monograph, which explores (at considerable and oriental length) geometrical constructions achievable via paper-folding. In particular, he claims to have constructed all prime length ratios up to 31:1 , prompting the following question. Given a square of paper --- assumed accurately foldable to superpose two existing points such as corners, or a point upon an existing line such as an edge --- are all rational ratios constructible? Fred Lunnon
I thought all cubic numbers were constructable with origami, including the rational numbers as a subset. Charles Greathouse Analyst/Programmer Case Western Reserve University On Wed, Jul 24, 2013 at 9:30 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
I recently acquired an e-copy of this Kazuo Haga monograph, which explores (at considerable and oriental length) geometrical constructions achievable via paper-folding. In particular, he claims to have constructed all prime length ratios up to 31:1 , prompting the following question.
Given a square of paper --- assumed accurately foldable to superpose two existing points such as corners, or a point upon an existing line such as an edge --- are all rational ratios constructible?
Fred Lunnon
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Plenty of relevant hits on the web, once I thought to search for them! Including http://buzzard.ups.edu/courses/2012spring/projects/engle-origami-ups-434-201... which says that rationals, square roots and cube roots(!) are possible. Not quite the same thing as roots of cubic equations --- unless the paper is complex? --- but near enough. WFL On 7/24/13, Charles Greathouse <charles.greathouse@case.edu> wrote:
I thought all cubic numbers were constructable with origami, including the rational numbers as a subset.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Wed, Jul 24, 2013 at 9:30 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
I recently acquired an e-copy of this Kazuo Haga monograph, which explores (at considerable and oriental length) geometrical constructions achievable via paper-folding. In particular, he claims to have constructed all prime length ratios up to 31:1 , prompting the following question.
Given a square of paper --- assumed accurately foldable to superpose two existing points such as corners, or a point upon an existing line such as an edge --- are all rational ratios constructible?
Fred Lunnon
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Fred lunnon