What is the symbol for “coincident” in geometry?
$begingroup$
I am looking for a symbol to say that one geometrical figure coincides with another without writing the phrase "is coincident with." For example, the altitude $a$ of an equilateral triangle coincides with a median $m$ of the triangle. Each point of one figure is in the same place as some point of the other figure.
The idea is not just that one figure is congruent with another, since congruent figures can be in different places.
Also, the idea is not just that a figure with one name is identical to itself under a different name, as if a point is used in one figure, two figures, a 1000 figures, or no figures, and the differences among those names are insignificant. We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
In set notation, we would say $A=B$, if $A$ is the set of all points in one figure and $B$ is the set of all points in the other figure, but I prefer to avoid set theory.
I have not seen any symbol used in print or online. The following is a list of symbols that I think mathematicians might use:
- Geometrically equivalent to ≎
- Geometrically equal to ≈
- Geometrically equal to ≑
- Equivalent to ≍
- Equivalent to ⇌
- Equivalent to ⟷
- Equivalent to ⇔
- Equivalent to ⟺
- Equivalent to ≡
- Equal to =
geometry equivalence-relations
asked Dec 16 '15 at 18:25
JonesJones
162
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add a comment |
$begingroup$
I am looking for a symbol to say that one geometrical figure coincides with another without writing the phrase "is coincident with." For example, the altitude $a$ of an equilateral triangle coincides with a median $m$ of the triangle. Each point of one figure is in the same place as some point of the other figure.
The idea is not just that one figure is congruent with another, since congruent figures can be in different places.
Also, the idea is not just that a figure with one name is identical to itself under a different name, as if a point is used in one figure, two figures, a 1000 figures, or no figures, and the differences among those names are insignificant. We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
In set notation, we would say $A=B$, if $A$ is the set of all points in one figure and $B$ is the set of all points in the other figure, but I prefer to avoid set theory.
I have not seen any symbol used in print or online. The following is a list of symbols that I think mathematicians might use:
- Geometrically equivalent to ≎
- Geometrically equal to ≈
- Geometrically equal to ≑
- Equivalent to ≍
- Equivalent to ⇌
- Equivalent to ⟷
- Equivalent to ⇔
- Equivalent to ⟺
- Equivalent to ≡
- Equal to =
geometry equivalence-relations
asked Dec 16 '15 at 18:25
JonesJones
162
$endgroup$
$begingroup$
You can feel free to avoid set theory and still use the $=$ sign.
$endgroup$
– Lee Mosher
Dec 16 '15 at 18:27
$begingroup$
Note that the meaning of "$AB=CD$" depends on whether "$XY$" indicates "segment $XY$" or "the length of segment $XY$", both of which are in fairly common use. So long as your segment-vs-length notation is unambiguous ---say, "$overline{XY}$" for the geometric object and "$|overline{XY}|$" for the numeric one--- potential confusion can be minimized.
$endgroup$
– Blue
Dec 16 '15 at 18:46
add a comment |
$begingroup$
I am looking for a symbol to say that one geometrical figure coincides with another without writing the phrase "is coincident with." For example, the altitude $a$ of an equilateral triangle coincides with a median $m$ of the triangle. Each point of one figure is in the same place as some point of the other figure.
The idea is not just that one figure is congruent with another, since congruent figures can be in different places.
Also, the idea is not just that a figure with one name is identical to itself under a different name, as if a point is used in one figure, two figures, a 1000 figures, or no figures, and the differences among those names are insignificant. We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
In set notation, we would say $A=B$, if $A$ is the set of all points in one figure and $B$ is the set of all points in the other figure, but I prefer to avoid set theory.
I have not seen any symbol used in print or online. The following is a list of symbols that I think mathematicians might use:
- Geometrically equivalent to ≎
- Geometrically equal to ≈
- Geometrically equal to ≑
- Equivalent to ≍
- Equivalent to ⇌
- Equivalent to ⟷
- Equivalent to ⇔
- Equivalent to ⟺
- Equivalent to ≡
- Equal to =
geometry equivalence-relations
asked Dec 16 '15 at 18:25
JonesJones
162
$endgroup$
I am looking for a symbol to say that one geometrical figure coincides with another without writing the phrase "is coincident with." For example, the altitude $a$ of an equilateral triangle coincides with a median $m$ of the triangle. Each point of one figure is in the same place as some point of the other figure.
The idea is not just that one figure is congruent with another, since congruent figures can be in different places.
Also, the idea is not just that a figure with one name is identical to itself under a different name, as if a point is used in one figure, two figures, a 1000 figures, or no figures, and the differences among those names are insignificant. We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
In set notation, we would say $A=B$, if $A$ is the set of all points in one figure and $B$ is the set of all points in the other figure, but I prefer to avoid set theory.
I have not seen any symbol used in print or online. The following is a list of symbols that I think mathematicians might use:
- Geometrically equivalent to ≎
- Geometrically equal to ≈
- Geometrically equal to ≑
- Equivalent to ≍
- Equivalent to ⇌
- Equivalent to ⟷
- Equivalent to ⇔
- Equivalent to ⟺
- Equivalent to ≡
- Equal to =
geometry equivalence-relations
geometry equivalence-relations
asked Dec 16 '15 at 18:25
JonesJones
162
asked Dec 16 '15 at 18:25
JonesJones
162
asked Dec 16 '15 at 18:25
JonesJones
162
asked Dec 16 '15 at 18:25
JonesJones
162
asked Dec 16 '15 at 18:25
JonesJones
162
162
$begingroup$
You can feel free to avoid set theory and still use the $=$ sign.
$endgroup$
– Lee Mosher
Dec 16 '15 at 18:27
$begingroup$
Note that the meaning of "$AB=CD$" depends on whether "$XY$" indicates "segment $XY$" or "the length of segment $XY$", both of which are in fairly common use. So long as your segment-vs-length notation is unambiguous ---say, "$overline{XY}$" for the geometric object and "$|overline{XY}|$" for the numeric one--- potential confusion can be minimized.
$endgroup$
– Blue
Dec 16 '15 at 18:46
add a comment |
$begingroup$
You can feel free to avoid set theory and still use the $=$ sign.
$endgroup$
– Lee Mosher
Dec 16 '15 at 18:27
$begingroup$
Note that the meaning of "$AB=CD$" depends on whether "$XY$" indicates "segment $XY$" or "the length of segment $XY$", both of which are in fairly common use. So long as your segment-vs-length notation is unambiguous ---say, "$overline{XY}$" for the geometric object and "$|overline{XY}|$" for the numeric one--- potential confusion can be minimized.
$endgroup$
– Blue
Dec 16 '15 at 18:46
$begingroup$
You can feel free to avoid set theory and still use the $=$ sign.
$endgroup$
– Lee Mosher
Dec 16 '15 at 18:27
$begingroup$
You can feel free to avoid set theory and still use the $=$ sign.
$endgroup$
– Lee Mosher
Dec 16 '15 at 18:27
$begingroup$
Note that the meaning of "$AB=CD$" depends on whether "$XY$" indicates "segment $XY$" or "the length of segment $XY$", both of which are in fairly common use. So long as your segment-vs-length notation is unambiguous ---say, "$overline{XY}$" for the geometric object and "$|overline{XY}|$" for the numeric one--- potential confusion can be minimized.
$endgroup$
– Blue
Dec 16 '15 at 18:46
$begingroup$
Note that the meaning of "$AB=CD$" depends on whether "$XY$" indicates "segment $XY$" or "the length of segment $XY$", both of which are in fairly common use. So long as your segment-vs-length notation is unambiguous ---say, "$overline{XY}$" for the geometric object and "$|overline{XY}|$" for the numeric one--- potential confusion can be minimized.
$endgroup$
– Blue
Dec 16 '15 at 18:46
add a comment |
2 Answers
2
active
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$begingroup$
I have often seen ≡ used for this purpose.
Not sure if it's a widely adopted standard though.
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
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add a comment |
$begingroup$
There is no canonical symbol, but concerning your discussion of the word and concept of "coincident" and whether it should apply...
- the most common terminological options are equal, same and coincident with the latter the best choice.
Coincident really does describe the situation you are talking about:
We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
This is what happens in the example of altitude and median. Two distinct constructions, that do not in general produce the same result, happen to have the same output in some special triangles. In an equilateral triangle, the incenter and circumcenter "coincide" or "are the same".
This is not the same as reasoning from the single object that is the output (the line or point in the equilateral triangle) and trying to say that it exists in two copies. The same object is an instantiation of two different things and that is the coincidence.
These linguistic problems tend to dissolve if you think more in terms of how the "equal" figures are mapped to each other, instead of the locus of points, and in terms of additional structure that is implicitly carried by the object (things like an orientation, an ordering or labelling of vertices, or distinguishing one of the points or lines).
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
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add a comment |
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2 Answers
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2 Answers
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$begingroup$
I have often seen ≡ used for this purpose.
Not sure if it's a widely adopted standard though.
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
$endgroup$
add a comment |
$begingroup$
I have often seen ≡ used for this purpose.
Not sure if it's a widely adopted standard though.
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
$endgroup$
add a comment |
$begingroup$
I have often seen ≡ used for this purpose.
Not sure if it's a widely adopted standard though.
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
$endgroup$
I have often seen ≡ used for this purpose.
Not sure if it's a widely adopted standard though.
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
answered Dec 16 '15 at 18:27
peter.petrovpeter.petrov
5,441821
5,441821
add a comment |
add a comment |
$begingroup$
There is no canonical symbol, but concerning your discussion of the word and concept of "coincident" and whether it should apply...
- the most common terminological options are equal, same and coincident with the latter the best choice.
Coincident really does describe the situation you are talking about:
We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
This is what happens in the example of altitude and median. Two distinct constructions, that do not in general produce the same result, happen to have the same output in some special triangles. In an equilateral triangle, the incenter and circumcenter "coincide" or "are the same".
This is not the same as reasoning from the single object that is the output (the line or point in the equilateral triangle) and trying to say that it exists in two copies. The same object is an instantiation of two different things and that is the coincidence.
These linguistic problems tend to dissolve if you think more in terms of how the "equal" figures are mapped to each other, instead of the locus of points, and in terms of additional structure that is implicitly carried by the object (things like an orientation, an ordering or labelling of vertices, or distinguishing one of the points or lines).
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
$endgroup$
add a comment |
$begingroup$
There is no canonical symbol, but concerning your discussion of the word and concept of "coincident" and whether it should apply...
- the most common terminological options are equal, same and coincident with the latter the best choice.
Coincident really does describe the situation you are talking about:
We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
This is what happens in the example of altitude and median. Two distinct constructions, that do not in general produce the same result, happen to have the same output in some special triangles. In an equilateral triangle, the incenter and circumcenter "coincide" or "are the same".
This is not the same as reasoning from the single object that is the output (the line or point in the equilateral triangle) and trying to say that it exists in two copies. The same object is an instantiation of two different things and that is the coincidence.
These linguistic problems tend to dissolve if you think more in terms of how the "equal" figures are mapped to each other, instead of the locus of points, and in terms of additional structure that is implicitly carried by the object (things like an orientation, an ordering or labelling of vertices, or distinguishing one of the points or lines).
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
$endgroup$
add a comment |
$begingroup$
There is no canonical symbol, but concerning your discussion of the word and concept of "coincident" and whether it should apply...
- the most common terminological options are equal, same and coincident with the latter the best choice.
Coincident really does describe the situation you are talking about:
We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
This is what happens in the example of altitude and median. Two distinct constructions, that do not in general produce the same result, happen to have the same output in some special triangles. In an equilateral triangle, the incenter and circumcenter "coincide" or "are the same".
This is not the same as reasoning from the single object that is the output (the line or point in the equilateral triangle) and trying to say that it exists in two copies. The same object is an instantiation of two different things and that is the coincidence.
These linguistic problems tend to dissolve if you think more in terms of how the "equal" figures are mapped to each other, instead of the locus of points, and in terms of additional structure that is implicitly carried by the object (things like an orientation, an ordering or labelling of vertices, or distinguishing one of the points or lines).
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
$endgroup$
There is no canonical symbol, but concerning your discussion of the word and concept of "coincident" and whether it should apply...
- the most common terminological options are equal, same and coincident with the latter the best choice.
Coincident really does describe the situation you are talking about:
We say that figures are coincident when they are understood independently from one another and seem to be able to exist without each other. We are often surprised when we discover they they in fact coincide.
This is what happens in the example of altitude and median. Two distinct constructions, that do not in general produce the same result, happen to have the same output in some special triangles. In an equilateral triangle, the incenter and circumcenter "coincide" or "are the same".
This is not the same as reasoning from the single object that is the output (the line or point in the equilateral triangle) and trying to say that it exists in two copies. The same object is an instantiation of two different things and that is the coincidence.
These linguistic problems tend to dissolve if you think more in terms of how the "equal" figures are mapped to each other, instead of the locus of points, and in terms of additional structure that is implicitly carried by the object (things like an orientation, an ordering or labelling of vertices, or distinguishing one of the points or lines).
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
edited Dec 16 '15 at 19:29
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
answered Dec 16 '15 at 18:46
zyxzyx
31.6k33699
31.6k33699
add a comment |
add a comment |
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$begingroup$
You can feel free to avoid set theory and still use the $=$ sign.
$endgroup$
– Lee Mosher
Dec 16 '15 at 18:27
$begingroup$
Note that the meaning of "$AB=CD$" depends on whether "$XY$" indicates "segment $XY$" or "the length of segment $XY$", both of which are in fairly common use. So long as your segment-vs-length notation is unambiguous ---say, "$overline{XY}$" for the geometric object and "$|overline{XY}|$" for the numeric one--- potential confusion can be minimized.
$endgroup$
– Blue
Dec 16 '15 at 18:46