Talk:3177: Chessboard Alignment - Revision history

SammyChips at 16:38, 10 December 2025

2025-12-10T16:38:58Z

78.144.255.82 at 21:25, 9 December 2025

2025-12-09T21:25:06Z

SammyChips at 21:16, 9 December 2025

2025-12-09T21:16:58Z

Dosbears: Definition of 'level'

2025-12-09T20:39:05Z

Definition of 'level'

SammyChips at 19:38, 9 December 2025

2025-12-09T19:38:26Z

82.132.236.87 at 18:22, 9 December 2025

2025-12-09T18:22:11Z

SammyChips at 17:38, 9 December 2025

2025-12-09T17:38:57Z

SammyChips at 17:36, 9 December 2025

2025-12-09T17:36:09Z

SammyChips at 17:34, 9 December 2025

2025-12-09T17:34:56Z

SammyChips at 17:33, 9 December 2025

2025-12-09T17:33:52Z

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 ::One Problem I see with following a circular route against the gravitational isoclines is that if the boards are not tilted to be aligned with the gravitational gradient then hopefully there would be enough friction to keep the pieces from sliding off, and if they are tilted then the vertical misalignment might not be small enough to be within the tolerance. [[User:SammyChips|SammyChips]] ([[User talk:SammyChips|talk]]) 21:16, 9 December 2025 (UTC)
 :::{{w|Chess set#Pocket and travel sets}}..? [[Special:Contributions/78.144.255.82|78.144.255.82]] 21:25, 9 December 2025 (UTC)
 Level doesn't mean "parallel to the surface of the Earth", it means perpendicular to the Earth's gravitational force.[[User:Dosbears|Dosbears]] ([[User talk:Dosbears|talk]])

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 ::Are we creating a {{w|Dyson swarm}} out of chess boards now? :D [[User:SammyChips|SammyChips]] ([[User talk:SammyChips|talk]]) 19:38, 9 December 2025 (UTC)
 ::One Problem I see with following a circular route against the gravitational isoclines is that if the boards are not tilted to be aligned with the gravitational gradient then hopefully there would be enough friction to keep the pieces from sliding off, and if they are tilted then the vertical misalignment might not be small enough to be within the tolerance. [[User:SammyChips|SammyChips]] ([[User talk:SammyChips|talk]]) 21:16, 9 December 2025 (UTC)
 Level doesn't mean "parallel to the surface of the Earth", it means perpendicular to the Earth's gravitational force.[[User:Dosbears|Dosbears]] ([[User talk:Dosbears|talk]])

@@ Line 55: / Line 55: @@
 :Aside from raising/lowering source and (where necessary) target boards to be level ''and'' realign to be square-accurate (divide the current mismatch, beyond the minor tolerance allowance, by 2.pi and shift the board(s) up or down by that amount... Perhaps move further to invoke resonance of all axes of distance, especially if on an ellipsoid, by choosing overlapping resonances in their near-integer multiples of the respective distances), one need not have to conform to the geoidal multi-term hybrid elliposodal shape, but merely take radius-from-the-core as the (identical) altitude, irrespective of local Mean Sea Level or other gravitic isoline contouring. This may involve towers/blimps and mineshafts/submersibles to match up everything, despite actual local geodic variation, but if you're measuring round-the-world distances to micrometer-accuracy then it's just a matter of applying that same accuracy to the obvious solution. [[Special:Contributions/82.132.236.87|82.132.236.87]] 18:22, 9 December 2025 (UTC)
 ::Are we creating a {{w|Dyson swarm}} out of chess boards now? :D [[User:SammyChips|SammyChips]] ([[User talk:SammyChips|talk]]) 19:38, 9 December 2025 (UTC)
 Level doesn't mean "parallel to the surface of the Earth", it means perpendicular to the Earth's gravitational force.[[User:Dosbears|Dosbears]] ([[User talk:Dosbears|talk]])

← Older revision		Revision as of 20:39, 9 December 2025
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	:Aside from raising/lowering source and (where necessary) target boards to be level ''and'' realign to be square-accurate (divide the current mismatch, beyond the minor tolerance allowance, by 2.pi and shift the board(s) up or down by that amount... Perhaps move further to invoke resonance of all axes of distance, especially if on an ellipsoid, by choosing overlapping resonances in their near-integer multiples of the respective distances), one need not have to conform to the geoidal multi-term hybrid elliposodal shape, but merely take radius-from-the-core as the (identical) altitude, irrespective of local Mean Sea Level or other gravitic isoline contouring. This may involve towers/blimps and mineshafts/submersibles to match up everything, despite actual local geodic variation, but if you're measuring round-the-world distances to micrometer-accuracy then it's just a matter of applying that same accuracy to the obvious solution. [[Special:Contributions/82.132.236.87\|82.132.236.87]] 18:22, 9 December 2025 (UTC)		:Aside from raising/lowering source and (where necessary) target boards to be level ''and'' realign to be square-accurate (divide the current mismatch, beyond the minor tolerance allowance, by 2.pi and shift the board(s) up or down by that amount... Perhaps move further to invoke resonance of all axes of distance, especially if on an ellipsoid, by choosing overlapping resonances in their near-integer multiples of the respective distances), one need not have to conform to the geoidal multi-term hybrid elliposodal shape, but merely take radius-from-the-core as the (identical) altitude, irrespective of local Mean Sea Level or other gravitic isoline contouring. This may involve towers/blimps and mineshafts/submersibles to match up everything, despite actual local geodic variation, but if you're measuring round-the-world distances to micrometer-accuracy then it's just a matter of applying that same accuracy to the obvious solution. [[Special:Contributions/82.132.236.87\|82.132.236.87]] 18:22, 9 December 2025 (UTC)
	::Are we creating a {{w\|Dyson swarm}} out of chess boards now? :D [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 19:38, 9 December 2025 (UTC)		::Are we creating a {{w\|Dyson swarm}} out of chess boards now? :D [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 19:38, 9 December 2025 (UTC)
		+
		+	Level doesn't mean "parallel to the surface of the Earth", it means perpendicular to the Earth's gravitational force.[[User:Dosbears\|Dosbears]] ([[User talk:Dosbears\|talk]])

← Older revision		Revision as of 19:38, 9 December 2025
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	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid is always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge {{citation needed}}. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)		{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid is always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge {{citation needed}}. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)
	:Aside from raising/lowering source and (where necessary) target boards to be level ''and'' realign to be square-accurate (divide the current mismatch, beyond the minor tolerance allowance, by 2.pi and shift the board(s) up or down by that amount... Perhaps move further to invoke resonance of all axes of distance, especially if on an ellipsoid, by choosing overlapping resonances in their near-integer multiples of the respective distances), one need not have to conform to the geoidal multi-term hybrid elliposodal shape, but merely take radius-from-the-core as the (identical) altitude, irrespective of local Mean Sea Level or other gravitic isoline contouring. This may involve towers/blimps and mineshafts/submersibles to match up everything, despite actual local geodic variation, but if you're measuring round-the-world distances to micrometer-accuracy then it's just a matter of applying that same accuracy to the obvious solution. [[Special:Contributions/82.132.236.87\|82.132.236.87]] 18:22, 9 December 2025 (UTC)		:Aside from raising/lowering source and (where necessary) target boards to be level ''and'' realign to be square-accurate (divide the current mismatch, beyond the minor tolerance allowance, by 2.pi and shift the board(s) up or down by that amount... Perhaps move further to invoke resonance of all axes of distance, especially if on an ellipsoid, by choosing overlapping resonances in their near-integer multiples of the respective distances), one need not have to conform to the geoidal multi-term hybrid elliposodal shape, but merely take radius-from-the-core as the (identical) altitude, irrespective of local Mean Sea Level or other gravitic isoline contouring. This may involve towers/blimps and mineshafts/submersibles to match up everything, despite actual local geodic variation, but if you're measuring round-the-world distances to micrometer-accuracy then it's just a matter of applying that same accuracy to the obvious solution. [[Special:Contributions/82.132.236.87\|82.132.236.87]] 18:22, 9 December 2025 (UTC)
		+	::Are we creating a {{w\|Dyson swarm}} out of chess boards now? :D [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 19:38, 9 December 2025 (UTC)

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 {{w|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal).  The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles.  The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point.  However, because the ellipsoid in always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge [citation needed]. [[User:SammyChips|SammyChips]] ([[User talk:SammyChips|talk]]) 17:33, 9 December 2025 (UTC)
 Do you have to consider other boards to avoid castling through check? [[Special:Contributions/2600:100C:B29E:1DBD:C9D:1FF3:39A0:FC2E|2600:100C:B29E:1DBD:C9D:1FF3:39A0:FC2E]] 20:19, 6 December 2025 (UTC)
 I think a funnier title text would've been: Bfi8(!!!) [[User:Fephisto|Fephisto]] ([[User talk:Fephisto|talk]]) 06:22, 6 December 2025 (UTC)
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 {{w|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal).  The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles.  The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point.  However, because the ellipsoid is always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge {{citation needed}}. [[User:SammyChips|SammyChips]] ([[User talk:SammyChips|talk]]) 17:34, 9 December 2025 (UTC)

← Older revision		Revision as of 17:38, 9 December 2025
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	The text currently says, "A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere ... would form a great circle", which isn't quite right because a line of chessboards has some width to it and therefore isn't a line. You could align chessboards to form a great circle out of their left edges, or their right edges, or any one inter-square line. Not sure how to fix this. [[User:DKMell\|DKMell]] ([[User talk:DKMell\|talk]]) 18:04, 8 December 2025 (UTC)		The text currently says, "A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere ... would form a great circle", which isn't quite right because a line of chessboards has some width to it and therefore isn't a line. You could align chessboards to form a great circle out of their left edges, or their right edges, or any one inter-square line. Not sure how to fix this. [[User:DKMell\|DKMell]] ([[User talk:DKMell\|talk]]) 18:04, 8 December 2025 (UTC)

−	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid is always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge [citation needed]. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)	+	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid is always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge {{citation needed}}. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)

← Older revision		Revision as of 17:36, 9 December 2025
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	The text currently says, "A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere ... would form a great circle", which isn't quite right because a line of chessboards has some width to it and therefore isn't a line. You could align chessboards to form a great circle out of their left edges, or their right edges, or any one inter-square line. Not sure how to fix this. [[User:DKMell\|DKMell]] ([[User talk:DKMell\|talk]]) 18:04, 8 December 2025 (UTC)		The text currently says, "A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere ... would form a great circle", which isn't quite right because a line of chessboards has some width to it and therefore isn't a line. You could align chessboards to form a great circle out of their left edges, or their right edges, or any one inter-square line. Not sure how to fix this. [[User:DKMell\|DKMell]] ([[User talk:DKMell\|talk]]) 18:04, 8 December 2025 (UTC)

−	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid in always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge [citation needed]. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)	+	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid is always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge [citation needed]. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)

← Older revision		Revision as of 17:34, 9 December 2025
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	The text currently says, "A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere ... would form a great circle", which isn't quite right because a line of chessboards has some width to it and therefore isn't a line. You could align chessboards to form a great circle out of their left edges, or their right edges, or any one inter-square line. Not sure how to fix this. [[User:DKMell\|DKMell]] ([[User talk:DKMell\|talk]]) 18:04, 8 December 2025 (UTC)		The text currently says, "A perfect line of chessboards placed end-to-end on the surface of an Earth-sized sphere ... would form a great circle", which isn't quite right because a line of chessboards has some width to it and therefore isn't a line. You could align chessboards to form a great circle out of their left edges, or their right edges, or any one inter-square line. Not sure how to fix this. [[User:DKMell\|DKMell]] ([[User talk:DKMell\|talk]]) 18:04, 8 December 2025 (UTC)
		+
		+	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid in always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge [citation needed]. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:34, 9 December 2025 (UTC)

← Older revision		Revision as of 17:33, 9 December 2025
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	Did the math for 'aiming' at geostatinary satellite from while being level. https://www.wolframalpha.com/input?i=arccos%286371%2Fsqrt%2842%2C164%5E2%2B6371%5E2%29%29 . If anybody wants to check my math please do so.--[[User:Trimutius\|Trimutius]] ([[User talk:Trimutius\|talk]]) 19:06, 6 December 2025 (UTC)		Did the math for 'aiming' at geostatinary satellite from while being level. https://www.wolframalpha.com/input?i=arccos%286371%2Fsqrt%2842%2C164%5E2%2B6371%5E2%29%29 . If anybody wants to check my math please do so.--[[User:Trimutius\|Trimutius]] ([[User talk:Trimutius\|talk]]) 19:06, 6 December 2025 (UTC)

		+	{{w\|Geodesics on an ellipsoid}} are a bit more complicated than those for a sphere (and Earth isn't really even purely ellipsoidal). The geodesics aren't actually great circles, nor even closed curves except for those tilted at specific angles. The curve could cover an extremely large distance before visiting a position within a specific displacement from its starting point. However, because the ellipsoid in always convex, even though the radius of curvature is different depending on location and direction, two geodesics that start parallel should always converge [citation needed]. [[User:SammyChips\|SammyChips]] ([[User talk:SammyChips\|talk]]) 17:33, 9 December 2025 (UTC)
	Do you have to consider other boards to avoid castling through check? [[Special:Contributions/2600:100C:B29E:1DBD:C9D:1FF3:39A0:FC2E\|2600:100C:B29E:1DBD:C9D:1FF3:39A0:FC2E]] 20:19, 6 December 2025 (UTC)		Do you have to consider other boards to avoid castling through check? [[Special:Contributions/2600:100C:B29E:1DBD:C9D:1FF3:39A0:FC2E\|2600:100C:B29E:1DBD:C9D:1FF3:39A0:FC2E]] 20:19, 6 December 2025 (UTC)