Posted: 3/10/2015 9:27:39 PM EDT
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Dave Durkingston has a fence running along the perimeter of his property surrounding his house. Each fence post was precisely measured so that the fence is symmetrical along at least two axes with Dave's house positioned in the center. A Bavarian Barn Swallow named Jim, slaloms the fence posts. Jim starts on the inside of the first post, slaloms his way all the way around the property ending up on the opposite side of the fence post that marks his starting point.
What shape is Dave's fence? How do you know? |
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Who the fuck has a triangular fence? j/k...Is the fence round? Somebody with a lot on a cul-de-sac? And, I think you're right with the triangle (gonna go a bit further and say equilateral triangle) shaped lot as a solution. Hell if I'm going to write a proof, though. 
Not sure why a regular pentagon wouldn't also work; OP didn't specify any constraints on the number of sides... |
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Quoted: Somebody with a lot on a cul-de-sac? And, I think you're right with the triangle (gonna go a bit further and say equilateral triangle) shaped lot as a solution. Hell if I'm going to write a proof, though. Not sure why a regular pentagon wouldn't also work; OP didn't specify any maximum number of sides... Quoted: Quoted: Who the fuck has a triangular fence? j/k...Is the fence round? Somebody with a lot on a cul-de-sac? And, I think you're right with the triangle (gonna go a bit further and say equilateral triangle) shaped lot as a solution. Hell if I'm going to write a proof, though. Not sure why a regular pentagon wouldn't also work; OP didn't specify any maximum number of sides... I think it has to be equilateral to have two axis symmetry. |
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Quoted: Circle, equilateral triangle or Pentagon all would work Posted Via AR15.Com Mobile I was kind of being a smartass with the circle comment. Because it is a bunch of points/nodes (posts) connected by chords (sections of fence) I was thinking it had to be some kind of polygon. |
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Circle, equilateral triangle or Pentagon all would work Posted Via AR15.Com Mobile Any regular polygon with an odd number of sides works. You can't quite get a circle but you could get close. You do need enough of a space between the posts for the bird to get by. The two axes do not need to be 90 degrees apart. An axis just starts at one point and ends up at the middle of the opposite side. |
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I was kind of being a smartass with the circle comment. Because it is a bunch of points/nodes (posts) connected by chords (sections of fence) I was thinking it had to be some kind of polygon. Quoted:
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Circle, equilateral triangle or Pentagon all would work Posted Via AR15.Com Mobile I was kind of being a smartass with the circle comment. Because it is a bunch of points/nodes (posts) connected by chords (sections of fence) I was thinking it had to be some kind of polygon. Polygon with 999,999 sides Semantics at that point
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Any regular polygon with an odd number of sides works. You can't quite get a circle but you could get close. You do need enough of a space between the posts for the bird to get by. The two axes do not need to be 90 degrees apart. An axis just starts at one point and ends up at the middle of the opposite side. Quoted:
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Circle, equilateral triangle or Pentagon all would work Any regular polygon with an odd number of sides works. You can't quite get a circle but you could get close. You do need enough of a space between the posts for the bird to get by. The two axes do not need to be 90 degrees apart. An axis just starts at one point and ends up at the middle of the opposite side. So we can all agree that a regular polygon with an odd number of sides is the correct answer? OP, how about it? Posted Via AR15.Com Mobile |
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Quoted: So we can all agree that a regular polygon with an odd number of sides is the correct answer? OP, how about it? Posted Via AR15.Com Mobile Quoted: Quoted: Quoted: Circle, equilateral triangle or Pentagon all would work Any regular polygon with an odd number of sides works. You can't quite get a circle but you could get close. You do need enough of a space between the posts for the bird to get by. The two axes do not need to be 90 degrees apart. An axis just starts at one point and ends up at the middle of the opposite side. So we can all agree that a regular polygon with an odd number of sides is the correct answer? OP, how about it? Posted Via AR15.Com Mobile I'd like to see a diagram of pentagon working. |
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Legendary! |
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So we can all agree that a regular polygon with an odd number of sides is the correct answer? OP, how about it? Posted Via AR15.Com Mobile Quoted:
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Circle, equilateral triangle or Pentagon all would work Any regular polygon with an odd number of sides works. You can't quite get a circle but you could get close. You do need enough of a space between the posts for the bird to get by. The two axes do not need to be 90 degrees apart. An axis just starts at one point and ends up at the middle of the opposite side. So we can all agree that a regular polygon with an odd number of sides is the correct answer? OP, how about it? Posted Via AR15.Com Mobile Along what 2 axes would a regular polygon with an odd number of sides be symmetrical? Hint: It's only 1. |
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Dave Durkingston has a fence running along the perimeter of his property surrounding his house. Each fence post was precisely measured so that the fence is symmetrical along at least two axes with Dave's house positioned in the center. A Bavarian Barn Swallow named Jim, slaloms the fence posts. Jim starts on the inside of the first post, slaloms his way all the way around the property ending up on the opposite side of the fence post that marks his starting point. What shape is Dave's fence? How do you know? Were either Dave or Jim, at anytime on a treadmill ? |
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An axis is a line that bisects a figure. Were you referring specifically to right angled axes? X and Y (or maybe Z)? Quoted:
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Since when does "axis" mean "any line in the R^2 plane"? An axis is a line that bisects a figure. Were you referring specifically to right angled axes? X and Y (or maybe Z)? No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. |
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Quoted: No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. Quoted: Quoted: Quoted: Since when does "axis" mean "any line in the R^2 plane"? An axis is a line that bisects a figure. Were you referring specifically to right angled axes? X and Y (or maybe Z)? No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. A Cartesian plane has perpendicular x and y axes. Not all axes are perpendicular though and an axis of symmetry (not the x and y axis in a Cartesian plane but a generic axis) is a line about which a figure is drawn so it's the same on either side. |
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A Cartesian plane has perpendicular x and y axes. Not all axes are perpendicular though and in gemetry an axis (not the x and y axis in a Cartesian plane but a generic axis) is a line about which a figure is drawn. Quoted:
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Since when does "axis" mean "any line in the R^2 plane"? An axis is a line that bisects a figure. Were you referring specifically to right angled axes? X and Y (or maybe Z)? No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. A Cartesian plane has perpendicular x and y axes. Not all axes are perpendicular though and in gemetry an axis (not the x and y axis in a Cartesian plane but a generic axis) is a line about which a figure is drawn. That is the not the definition of an axis. At least not in Euclidean, Lobachevskian, Differential, Analytic, Algebraic, Archimedean, Absolute or Projective Geometry. You're wrong. |
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Quoted: That is the not the definition of an axis. At least not in Euclidean, Lobachevskian, Differential, Analytic, Algebraic, Archimedean, Absolute or Projective Geometry. You're wrong. Quoted: Quoted: Quoted: Quoted: Quoted: Since when does "axis" mean "any line in the R^2 plane"? An axis is a line that bisects a figure. Were you referring specifically to right angled axes? X and Y (or maybe Z)? No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. A Cartesian plane has perpendicular x and y axes. Not all axes are perpendicular though and in gemetry an axis (not the x and y axis in a Cartesian plane but a generic axis) is a line about which a figure is drawn. That is the not the definition of an axis. At least not in Euclidean, Lobachevskian, Differential, Analytic, Algebraic, Archimedean, Absolute or Projective Geometry. You're wrong. Why don't you check to see if, in addition to the popular x and y axes everyone knows and loves, there are non-perpendicular axes? Just in case. Because there are some references out there even for someone doing a casual check that mention it. This one actually talks about both. The Cartesian plane usage as well as the "line about which a figure is drawn" usage. http://www.icoachmath.com/math_dictionary/axis.html An Axis is a line about which a figure is drawn, measured, rotated, etc. The horizontal line and the vertical line on a coordinate plane are known as the X-axis and the Y-axis respectively. It's here too. 2. Mathematics.
See, I know what you're saying and I agree with some of it. Because I work with coordinate systems professionally every day. And often the systems I work with have perpendicular axes. But the term is used for other things that it sounds like you are not yet familiar with. Not all axes are perpendicular and not all axes are the ones we are most familiar with, x,y, and z. There are an infinite number of axes that don't get a special name and are used when describing shapes and figures. Just because you aren't aware of it does not mean it is not true and in use. |
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No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. Quoted:
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Since when does "axis" mean "any line in the R^2 plane"? An axis is a line that bisects a figure. Were you referring specifically to right angled axes? X and Y (or maybe Z)? No, a line is a line that bisects a figure. An axis exists relative to a coordinate system, not a figure in the coordinate system. It has been that way since 300 BC. You didn't specify any particular coordinate system; you said 'axis'. Axes don't have to be orthogonal. |
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Why don't you check to see if, in addition to the popular x and y axes everyone knows and loves, there are non-perpendicular axes? Just in case. Because there are some references out there even for someone doing a casual check that mention it. This one actually talks about both. The Cartesian plane usage as well as the "line about which a figure is drawn" usage. http://www.icoachmath.com/math_dictionary/axis.html An Axis is a line about which a figure is drawn, measured, rotated, etc. The horizontal line and the vertical line on a coordinate plane are known as the X-axis and the Y-axis respectively. It's here too. http://dictionary.reference.com/browse/axis 2.Mathematics.
See, I know what you're saying and I agree with some of it. Because I work with coordinate systems professionally every day. And often the systems I work with have perpendicular axes. But the term is used for other things that it sounds like you are not yet familiar with. Not all axes are perpendicular and not all axes are the ones we are most familiar with, x,y, and z. There are an infinite number of axes that don't get a special name and are used when describing shapes and figures. Just because you aren't aware of it does not mean it is not true and in use. Oh, you work with coordinate systems? You have know idea how little that impresses me.  As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19.
Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com |
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Quoted: Oh, you work with coordinate systems? You have know idea how little that impresses me. As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19. Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com Quoted: Quoted: Why don't you check to see if, in addition to the popular x and y axes everyone knows and loves, there are non-perpendicular axes? Just in case. Because there are some references out there even for someone doing a casual check that mention it. This one actually talks about both. The Cartesian plane usage as well as the "line about which a figure is drawn" usage. http://www.icoachmath.com/math_dictionary/axis.html An Axis is a line about which a figure is drawn, measured, rotated, etc. The horizontal line and the vertical line on a coordinate plane are known as the X-axis and the Y-axis respectively. It's here too. http://dictionary.reference.com/browse/axis 2.Mathematics.
See, I know what you're saying and I agree with some of it. Because I work with coordinate systems professionally every day. And often the systems I work with have perpendicular axes. But the term is used for other things that it sounds like you are not yet familiar with. Not all axes are perpendicular and not all axes are the ones we are most familiar with, x,y, and z. There are an infinite number of axes that don't get a special name and are used when describing shapes and figures. Just because you aren't aware of it does not mean it is not true and in use. Oh, you work with coordinate systems? You have know idea how little that impresses me. As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19. Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com I wasn't trying to impress you, just let you know that I am not a random drunk poster and actually work with coordinate systems for a living. That's all I meant. I referenced dictionary because I figured it would be appropriate for anyone who didn't realize how the term axis was used. Are you saying that none of your math books mention axes in the context I'm describing? If that's so would you mind mentioning the titles? I'm sure they're very prestigious and complicated but I somehow doubt they contradict geometry/math fundamentals almost everyone knows. |
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I wasn't trying to impress you, just let you know that I am not a random drunk poster and actually work with this for a living. That's all I meant. I referenced dictionary because I figured it would be appropriate for anyone who didn't realize how the term axis was used. Are you saying that none of your math books mention an axes in the context I'm describing? If that's so would you mind mentioning the titles? Quoted:
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Why don't you check to see if, in addition to the popular x and y axes everyone knows and loves, there are non-perpendicular axes? Just in case. Because there are some references out there even for someone doing a casual check that mention it. This one actually talks about both. The Cartesian plane usage as well as the "line about which a figure is drawn" usage. http://www.icoachmath.com/math_dictionary/axis.html An Axis is a line about which a figure is drawn, measured, rotated, etc. The horizontal line and the vertical line on a coordinate plane are known as the X-axis and the Y-axis respectively. It's here too. http://dictionary.reference.com/browse/axis 2.Mathematics.
See, I know what you're saying and I agree with some of it. Because I work with coordinate systems professionally every day. And often the systems I work with have perpendicular axes. But the term is used for other things that it sounds like you are not yet familiar with. Not all axes are perpendicular and not all axes are the ones we are most familiar with, x,y, and z. There are an infinite number of axes that don't get a special name and are used when describing shapes and figures. Just because you aren't aware of it does not mean it is not true and in use. Oh, you work with coordinate systems? You have know idea how little that impresses me. As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19.
Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com I wasn't trying to impress you, just let you know that I am not a random drunk poster and actually work with this for a living. That's all I meant. I referenced dictionary because I figured it would be appropriate for anyone who didn't realize how the term axis was used. Are you saying that none of your math books mention an axes in the context I'm describing? If that's so would you mind mentioning the titles? Manifolds and Differential Geometry Geometry - A comprehensive course Foundations of Euclidean and Non-Euclidean Geometry Principles of Algebraic Geometry Hodge Theory and Complex Algebraic Geometry Perspectives of Projective Geometry |
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Quoted: Manifolds and Differential Geometry Geometry - A comprehensive course Foundations of Euclidean and Non-Euclidean Geometry Principles of Algebraic Geometry Hodge Theory and Complex Algebraic Geometry Perspectives of Projective Geometry Quoted: Quoted: Quoted: Oh, you work with coordinate systems? You have know idea how little that impresses me. As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19. Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com I wasn't trying to impress you, just let you know that I am not a random drunk poster and actually work with this for a living. That's all I meant. I referenced dictionary because I figured it would be appropriate for anyone who didn't realize how the term axis was used. Are you saying that none of your math books mention an axes in the context I'm describing? If that's so would you mind mentioning the titles? Manifolds and Differential Geometry Geometry - A comprehensive course Foundations of Euclidean and Non-Euclidean Geometry Principles of Algebraic Geometry Hodge Theory and Complex Algebraic Geometry Perspectives of Projective Geometry Wow, that sounds pretty hardcore...what do you do for work? And is there something in these books that specifies axis is not used in the way the links I posted describes or is it just not mentioned in that context? |
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Wow, that sounds pretty hardcore...what do you do for work? And is there something in these books that specifies axis is not used in the way the links I posted describes or is it just not mentioned in that context? Quoted:
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Oh, you work with coordinate systems? You have know idea how little that impresses me. As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19.
Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com I wasn't trying to impress you, just let you know that I am not a random drunk poster and actually work with this for a living. That's all I meant. I referenced dictionary because I figured it would be appropriate for anyone who didn't realize how the term axis was used. Are you saying that none of your math books mention an axes in the context I'm describing? If that's so would you mind mentioning the titles? Manifolds and Differential Geometry Geometry - A comprehensive course Foundations of Euclidean and Non-Euclidean Geometry Principles of Algebraic Geometry Hodge Theory and Complex Algebraic Geometry Perspectives of Projective Geometry Wow, that sounds pretty hardcore...what do you do for work? And is there something in these books that specifies axis is not used in the way the links I posted describes or is it just not mentioned in that context? What is it with you and asking what people do for a living? |
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Quoted: What is it with you and asking what people do for a living? Quoted: Quoted: Quoted: Quoted: Quoted: Oh, you work with coordinate systems? You have know idea how little that impresses me. As long as we're share thing about ourselves, I published my first paper on absolute geometry when I was 19. Your knowledge of mathematics is elementary and you don't know what you are talking about. From where I sit I can see 5 graduate level geometry texts. You quote dictionary.com I wasn't trying to impress you, just let you know that I am not a random drunk poster and actually work with this for a living. That's all I meant. I referenced dictionary because I figured it would be appropriate for anyone who didn't realize how the term axis was used. Are you saying that none of your math books mention an axes in the context I'm describing? If that's so would you mind mentioning the titles? Manifolds and Differential Geometry Geometry - A comprehensive course Foundations of Euclidean and Non-Euclidean Geometry Principles of Algebraic Geometry Hodge Theory and Complex Algebraic Geometry Perspectives of Projective Geometry Wow, that sounds pretty hardcore...what do you do for work? And is there something in these books that specifies axis is not used in the way the links I posted describes or is it just not mentioned in that context? What is it with you and asking what people do for a living? I don't know, it only just came up in this one instance. I just figured based on those books it was something cool and didn't think it would be a sore spot. Forget it. Anyway, is there one of those books that specifically refutes the notion of axis not associated with a Cartesian coordinate system that almost everyone learned in geometry and was referenced in the links I posted? Or does it just not show up in those book so you consider that to be proof that the concept does not exist? |
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Dave Durkingston has a fence running along the perimeter of his property surrounding his house. Each fence post was precisely measured so that the fence is symmetrical along at least two axes with Dave's house positioned in the center. A Bavarian Barn Swallow named Jim, slaloms the fence posts. Jim starts on the inside of the first post, slaloms his way all the way around the property ending up on the opposite side of the fence post that marks his starting point. What shape is Dave's fence? How do you know? 
Edit: Awe sorry California_Kid, you nailed it first! |