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Roads that are also inportnant latitudes or longitudes
"Dick Boyd" wrote in message oups.com... The legals are flat earth representations of a curved surface. North-south lines on the surface of the earth converge. Longitude lines get closer and closer until they all meet in one place at the poles. So north-south roads laid out on legals, really don't run true north-south. To compensate, north-south section line roads are offset to correct for the convergence of meridians of longitude. Fascinating; I never thought much of meridians from a global perspective! So let's say you're standing on the North Pole and took a few steps south. If one was to then walk to the east (or west), each step would be onto a different meridian. Likewise, one would have to traverse long distances between meridians at the equator. With that in mind, the distance between the meridian is relative to where one is between the equator and one of the earth's pole. If you're lucky enough, maybe you'd get to stand directly on the poles and never take a step--however that's a privilege most don't have! With that in mind, all meridians converge at one of the earth's poles. This solves a riddle an algebra teacher gave me nine years ago, which was, "When do parallel lines touch each other? Hint: Think of the earth's curvature." ....Here's an off-shoot to the discussion. In theory, let's say that our ancestors created poles at two points on what we have been considering (for centuries) the equator. Thus, the north and south poles would have never received any polar nomenclature. Also, to remove confusion in this discussion, what we know in reality as "west" and "east" is mentioned as "x" and "y", respectively, while "north" and "south" is mentioned as "w" and "z", respectively. The x pole would have lines which would spread and re-converge at the y pole. Meanwhile "w" and "z" would consist of lines running parallel to to the x and y poles. Here are a couple questions that arise for this scenario: Would it be appropriate to call those lines converging in and from the x and y poles "meridians"? Would it be appropriate to label "lines of latitude" as those lines which span out in w and z directions? The objective for this question is to determine whether the terms "meridian" or "line-of-latitude" are relative to our ancestors' perception & assignment of the North and South Poles, or if the terms are relative to the poles' location as assigned by the person(s) studying a spherical object. Cheers, Carl Rogers ----------------- Calrog.com, Pictures of Highway Shields: http://hwy-shields.calrog.com Calrog.com, Personal and Interpersonal Psychology page: http://psychology.calrog.com Highway Shield & Travel Literatu http://www.lulu.com/calrog-bookstore |
#2
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Roads that are also inportnant latitudes or longitudes
"Carl Rogers" wrote...
...Here's an off-shoot to the discussion. In theory, let's say that our ancestors created poles at two points on what we have been considering (for centuries) the equator. Thus, the north and south poles would have never received any polar nomenclature. Also, to remove confusion in this discussion, what we know in reality as "west" and "east" is mentioned as "x" and "y", respectively, while "north" and "south" is mentioned as "w" and "z", respectively. The x pole would have lines which would spread and re-converge at the y pole. Meanwhile "w" and "z" would consist of lines running parallel to to the x and y poles. Here are a couple questions that arise for this scenario: Would it be appropriate to call those lines converging in and from the x and y poles "meridians"? Would it be appropriate to label "lines of latitude" as those lines which span out in w and z directions? The objective for this question is to determine whether the terms "meridian" or "line-of-latitude" are relative to our ancestors' perception & assignment of the North and South Poles, or if the terms are relative to the poles' location as assigned by the person(s) studying a spherical object. Chances are, if such a polar system had been developed, the name 'meridian of longitude' would not have been used as the word 'meridian' comes from the latin root 'meridies', meaning 'midday' (the sun is at its highest at the same time [midday] along a meridian of longitude). On the other hand, the name 'parallel of latitude' would be quite appropriate as long as the 'x' and 'y' poles are at opposite points on the planet, since the planes through the planet along parallels of latitude would still be parallel to each other. Cheers, Carl Rogers --Andy -------------------------------------------------- Andrew G. Tompkins Software Engineer Beaverton, OR http://home.comcast.net/~andytom/Highways -------------------------------------------------- |
#3
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Roads that are also inportnant latitudes or longitudes
Carl Rogers wrote: "Dick Boyd" wrote in message oups.com... The legals are flat earth representations of a curved surface. North-south lines on the surface of the earth converge. Longitude lines get closer and closer until they all meet in one place at the poles. So north-south roads laid out on legals, really don't run true north-south. To compensate, north-south section line roads are offset to correct for the convergence of meridians of longitude. Fascinating; I never thought much of meridians from a global perspective! So let's say you're standing on the North Pole and took a few steps south. If one was to then walk to the east (or west), each step would be onto a different meridian. Likewise, one would have to traverse long distances between meridians at the equator. With that in mind, the distance between the meridian is relative to where one is between the equator and one of the earth's pole. If you're lucky enough, maybe you'd get to stand directly on the poles and never take a step--however that's a privilege most don't have! With that in mind, all meridians converge at one of the earth's poles. This solves a riddle an algebra teacher gave me nine years ago, which was, "When do parallel lines touch each other? Hint: Think of the earth's curvature." ...Here's an off-shoot to the discussion. In theory, let's say that our ancestors created poles at two points on what we have been considering (for centuries) the equator. Thus, the north and south poles would have never received any polar nomenclature. Also, to remove confusion in this discussion, what we know in reality as "west" and "east" is mentioned as "x" and "y", respectively, while "north" and "south" is mentioned as "w" and "z", respectively. The x pole would have lines which would spread and re-converge at the y pole. Meanwhile "w" and "z" would consist of lines running parallel to to the x and y poles. Here are a couple questions that arise for this scenario: Would it be appropriate to call those lines converging in and from the x and y poles "meridians"? Would it be appropriate to label "lines of latitude" as those lines which span out in w and z directions? The objective for this question is to determine whether the terms "meridian" or "line-of-latitude" are relative to our ancestors' perception & assignment of the North and South Poles, or if the terms are relative to the poles' location as assigned by the person(s) studying a spherical object. Cheers, Carl Rogers ----------------- Calrog.com, Pictures of Highway Shields: http://hwy-shields.calrog.com Calrog.com, Personal and Interpersonal Psychology page: http://psychology.calrog.com Highway Shield & Travel Literatu http://www.lulu.com/calrog-bookstore I think it was Robin in Winnie the Pooh who searched for the East Pole. Or was it the West Pole? In navigating over the poles, aircraft resort to "grid navigation". The navigators invent a grid for the specific flight and use gyro compasses to align to that grid. The equator and meridians are great circles on the surface of a sphere. At the poles, the meridians converge. The shorter arc of a great circle is the shortest distance between two points on the surface of a sphere. For long flights, the navigator plots the shorter arc of the great circle. Except for going east or west along the equator, or directly north or south, the desired arc of a great circle will intersect latitudes and longitudes of earth coordinates at changing angles. Think of flying from New York to London. On a flat map with mercator projection, the route is pretty much east. (Rhumb line) On a sphere the flight starts out to the northeast, at mid point of the flight is flying east and as it approaches London is flying south east. Another factor with legals is the "closure". In surveying around a circuit, the circuit must "close". Go around clockwise or counterclockwise, the surveyor should arrive at the strating point. On a flat surface, the angles of a triangle add to 180 degrees. Not so with spherical triangles. to "close" the triangle, the surveyor adds or subtracts corrections. For example, if the angles of his triangle added to 183 degrees and the legs were all about the same length, he would subtract one degree from each angle. Surveying errors would accumulate and then be corrected out at the border with a new datum. I think all the dog legs in roads in flat lands due to closure errors have been corrected by now. There is a riddle about walking one mile south, one mile east and one mile north and coming back to the same place. You see a bear, what color is the bear? What is the other place on the surface of the earth that you could be and not see any animals? Measuring angles gets even trickier in three dimensions. Trying to get elevated highways to line up, for instance. |
#4
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Roads that are also inportnant latitudes or longitudes
"Dick Boyd" wrote...
Carl Rogers wrote: ...Here's an off-shoot to the discussion. In theory, let's say that our ancestors created poles at two points on what we have been considering (for centuries) the equator. Thus, the north and south poles would have never received any polar nomenclature. Also, to remove confusion in this discussion, what we know in reality as "west" and "east" is mentioned as "x" and "y", respectively, while "north" and "south" is mentioned as "w" and "z", respectively. The x pole would have lines which would spread and re-converge at the y pole. Meanwhile "w" and "z" would consist of lines running parallel to to the x and y poles. Here are a couple questions that arise for this scenario: Would it be appropriate to call those lines converging in and from the x and y poles "meridians"? Would it be appropriate to label "lines of latitude" as those lines which span out in w and z directions? The objective for this question is to determine whether the terms "meridian" or "line-of-latitude" are relative to our ancestors' perception & assignment of the North and South Poles, or if the terms are relative to the poles' location as assigned by the person(s) studying a spherical object. Carl Rogers I think it was Robin in Winnie the Pooh who searched for the East Pole. Or was it the West Pole? In navigating over the poles, aircraft resort to "grid navigation". The navigators invent a grid for the specific flight and use gyro compasses to align to that grid. The equator and meridians are great circles on the surface of a sphere. At the poles, the meridians converge. I was going to mention this myself, having flown grid on a number of occasions, in my last post but decided against it as I felt that it was far enough off the asked question. Actually, there is usually a pre-printed standard grid printed on aviation charts (usually the JNC and GNC series charts) that allows you to convert from polar to grid headings using a multiplication factor on the longitude. Regulations specify that grid must be used north of 70N and south of 60S. I only got into that range once but we practiced on a regular basis. Getting in and out can be a real chore sometimes. The shorter arc of a great circle is the shortest distance between two points on the surface of a sphere. For long flights, the navigator plots the shorter arc of the great circle. Except for going east or west along the equator, or directly north or south, the desired arc of a great circle will intersect latitudes and longitudes of earth coordinates at changing angles. Think of flying from New York to London. On a flat map with mercator projection, the route is pretty much east. (Rhumb line) On a sphere the flight starts out to the northeast, at mid point of the flight is flying east and as it approaches London is flying south east. --Andy -------------------------------------------------- Andrew G. Tompkins Software Engineer Beaverton, OR http://home.comcast.net/~andytom/Highways -------------------------------------------------- |
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Roads that are also inportnant latitudes or longitudes
Twittering One wrote: "Andy, Beaverton ~ ! Double-A lives amongs those beavers, Too." ~ Folly "Silicon Forest dwellers we be." ~ Double-A |
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