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Archive 1 | Archive 2 | Archive 3 |
NOTE: As expected, one person is against changing anything. This draft is similar to other geometry articles posted on Wikipedia, as most readers of Wikipedia know. This article is on GEOMETRY. The text herein is about the geometry of the normal form.
The normal form of a line in is specified as the set
Geometrically, is a line tangent to a circle centered at the origin (denoted as the point ) with a given radius . Consequently, this circle is the set .
Since specifies a unit circle with center at the origin, the coefficients may be specified as and , that allows the normal form to be specified as
Since the normal form is a special case of the standard form, the geometric relationships of a line inherent in its normal form can be revealed for any line by a process called normalization. A line specified as can be specified in normal form as by dividing both sides of the equation by , such that
Geometric relationships revealed by the normal form are identical to the relationship of the line with the polar axis in polar coordinates. It is not surprising that the normal form is easily coverted to a polar equation through the standard set of transform equations. [3] 69.138.197.204 ( talk) 23:05, 2 March 2021 (UTC)
References
Please clarify. I believe the level of reader knowledge of GEOMETRY is being kept far too low, especially in light of Wikipedia's vast array of GEOMETRY articles. Besides, ALL LINES ARE SETS OF POINTS -- yes the normal to a line is a line and, consequently, A SET OF POINTS with its own SPECIFICATION. In addition, why are the terms "radius of a circle" and "perdendicular" confusing in a GEOMETRY article? (How can you not mention "perpendicular" on a article on "normal" form?) The current article lacks information to understand the normal form. Readers who look at the article are in high school math and understand those terms. (I was going to prepare a diagram -- none of the sections contains them and the article needs them.) If you open your own reference, there is a diagram that accompany's the text. The vocabulary I mentioned above is still necessary for readers to understand the geometry of the normal form. OK -- apply your criteria to the main Hesse normal form article? It would be devastating if the criteria you use here are applied to it. And what would you do to article on the Real Line?
The Wikipedia editors regard this article as START class. It clearly needs continued improvement. The editors that know mathematics know what they expect out of an article on the geometry of lines. I do give compliments to the changes made on the line in polar coordinates section. However, the narrative still avoids terms readers are encountering in textbooks and their school classes. Looking at the talk and age of talk on this page, it appears many, many editors have given up trying to help. (Editors, please don't stop!) 2601:140:8980:4B20:AC68:BB15:9BFE:C2DD ( talk) 16:23, 3 March 2021 (UTC)
We all know geometric standards are those desirable for observation by teachers who try to normalize the drawings of more moderate students but in geometric outbrakes are applied other standards like desired scientific outcomes, etc., scholarships and other -- Mathstrght ( talk) 09:45, 4 November 2022 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 |
NOTE: As expected, one person is against changing anything. This draft is similar to other geometry articles posted on Wikipedia, as most readers of Wikipedia know. This article is on GEOMETRY. The text herein is about the geometry of the normal form.
The normal form of a line in is specified as the set
Geometrically, is a line tangent to a circle centered at the origin (denoted as the point ) with a given radius . Consequently, this circle is the set .
Since specifies a unit circle with center at the origin, the coefficients may be specified as and , that allows the normal form to be specified as
Since the normal form is a special case of the standard form, the geometric relationships of a line inherent in its normal form can be revealed for any line by a process called normalization. A line specified as can be specified in normal form as by dividing both sides of the equation by , such that
Geometric relationships revealed by the normal form are identical to the relationship of the line with the polar axis in polar coordinates. It is not surprising that the normal form is easily coverted to a polar equation through the standard set of transform equations. [3] 69.138.197.204 ( talk) 23:05, 2 March 2021 (UTC)
References
Please clarify. I believe the level of reader knowledge of GEOMETRY is being kept far too low, especially in light of Wikipedia's vast array of GEOMETRY articles. Besides, ALL LINES ARE SETS OF POINTS -- yes the normal to a line is a line and, consequently, A SET OF POINTS with its own SPECIFICATION. In addition, why are the terms "radius of a circle" and "perdendicular" confusing in a GEOMETRY article? (How can you not mention "perpendicular" on a article on "normal" form?) The current article lacks information to understand the normal form. Readers who look at the article are in high school math and understand those terms. (I was going to prepare a diagram -- none of the sections contains them and the article needs them.) If you open your own reference, there is a diagram that accompany's the text. The vocabulary I mentioned above is still necessary for readers to understand the geometry of the normal form. OK -- apply your criteria to the main Hesse normal form article? It would be devastating if the criteria you use here are applied to it. And what would you do to article on the Real Line?
The Wikipedia editors regard this article as START class. It clearly needs continued improvement. The editors that know mathematics know what they expect out of an article on the geometry of lines. I do give compliments to the changes made on the line in polar coordinates section. However, the narrative still avoids terms readers are encountering in textbooks and their school classes. Looking at the talk and age of talk on this page, it appears many, many editors have given up trying to help. (Editors, please don't stop!) 2601:140:8980:4B20:AC68:BB15:9BFE:C2DD ( talk) 16:23, 3 March 2021 (UTC)
We all know geometric standards are those desirable for observation by teachers who try to normalize the drawings of more moderate students but in geometric outbrakes are applied other standards like desired scientific outcomes, etc., scholarships and other -- Mathstrght ( talk) 09:45, 4 November 2022 (UTC)