[math-fun] __agramma Mirificum
(__agramma is neuter?) I just learned of this. Choose a point on a 2-sphere and traverse 90º of a great circle. Hang a 90º left turn. Traverse another 90º arc. Turn. Iterate. When, if ever, do you return to your starting point? —rwg
Why not start at the north pole, go south to equator, east on equator for 90 degrees, then north back to north pole. What am I missing?? On Sat, Oct 27, 2018 at 8:05 AM Bill Gosper <billgosper@gmail.com> wrote:
(__agramma is neuter?) I just learned of this. Choose a point on a 2-sphere and traverse 90º of a great circle. Hang a 90º left turn. Traverse another 90º arc. Turn. Iterate. When, if ever, do you return to your starting point? —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Apologies to those who cannot read Unicode, but, indeed, τὸ <https://en.wiktionary.org/wiki/%CF%84%E1%BD%B8#Ancient_Greek> *γρᾰ́μμᾰ* is neuter. All the -ma nouns that are derived from verbal stems are neuter, and take -ta as the plural suffix. Apparently the original Indoeuropean suffix (something like -mn-) was also neuter, and since we can't reconstruct further back, there isn't any way to say why. On Sat, Oct 27, 2018 at 9:28 AM James Buddenhagen <jbuddenh@gmail.com> wrote:
Why not start at the north pole, go south to equator, east on equator for 90 degrees, then north back to north pole. What am I missing??
On Sat, Oct 27, 2018 at 8:05 AM Bill Gosper <billgosper@gmail.com> wrote:
(__agramma is neuter?) I just learned of this. Choose a point on a 2-sphere and traverse 90º of a great circle. Hang a 90º left turn. Traverse another 90º arc. Turn. Iterate. When, if ever, do you return to your starting point? —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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GACK—As Rudy Rucker points out, this is just a 90-90-90 spherical triangle! Stay tuned for a correction. —rwg On Sat, Oct 27, 2018 at 6:04 AM Bill Gosper <billgosper@gmail.com> wrote:
(__agramma is neuter?) I just learned of this. Choose a point on a 2-sphere and traverse 90º of a great circle. Hang a 90º left turn. Traverse another 90º arc. Turn. Iterate. When, if ever, do you return to your starting point? —rwg
To make the pentagram with all right angles and edges equal pieces of great circles on the surface of a sphere the central angle of each edge is t, where cos(t) = (1-sqrt(5))/2 = -0.618... , about 128.17 degrees. On Sat, Oct 27, 2018 at 8:05 AM Bill Gosper <billgosper@gmail.com> wrote:
(__agramma is neuter?) I just learned of this. Choose a point on a 2-sphere and traverse 90º of a great circle. Hang a 90º left turn. Traverse another 90º arc. Turn. Iterate. When, if ever, do you return to your starting point? —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Suppose you have a spherical square whose external angles equal its sides. What is that angle? On Sat, Oct 27, 2018 at 5:40 PM James Buddenhagen <jbuddenh@gmail.com> wrote:
To make the pentagram with all right angles and edges equal pieces of great circles on the surface of a sphere the central angle of each edge is t, where cos(t) = (1-sqrt(5))/2 = -0.618... , about 128.17 degrees.
On Sat, Oct 27, 2018 at 8:05 AM Bill Gosper <billgosper@gmail.com> wrote:
(__agramma is neuter?) I just learned of this. Choose a point on a 2-sphere and traverse 90º of a great circle. Hang a 90º left turn. Traverse another 90º arc. Turn. Iterate. When, if ever, do you return to your starting point? —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (3)
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Allan Wechsler -
Bill Gosper -
James Buddenhagen