how is the following curve not simple curve? [closed]
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if we start from just above point and go up and end at just below point how is the curve not simple curve. ncert class 6 chapter 4 pg 72 says it is not http://ncert.nic.in/textbook/textbook.htm?femh1=4-14 please help
I am a student and trying to understand things it is a 8 like figure this question is not off topic as it is a maths question. don't gang up on me pls. I am not up at your level also I cant understand your big terms I don't understand why people reporting me I also need help .pls no teacher is answering me properly .Pls help .
geometry curves
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
$endgroup$
closed as off-topic by José Carlos Santos, Saad, Shailesh, Did, Moishe Kohan Jan 3 at 13:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shailesh, Did, Moishe Kohan
If this question can be reworded to fit the rules in the help center, please edit the question.
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show 3 more comments
$begingroup$
if we start from just above point and go up and end at just below point how is the curve not simple curve. ncert class 6 chapter 4 pg 72 says it is not http://ncert.nic.in/textbook/textbook.htm?femh1=4-14 please help
I am a student and trying to understand things it is a 8 like figure this question is not off topic as it is a maths question. don't gang up on me pls. I am not up at your level also I cant understand your big terms I don't understand why people reporting me I also need help .pls no teacher is answering me properly .Pls help .
geometry curves
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
$endgroup$
closed as off-topic by José Carlos Santos, Saad, Shailesh, Did, Moishe Kohan Jan 3 at 13:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shailesh, Did, Moishe Kohan
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
What does "just above" mean?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:34
$begingroup$
I don't understand what your picture is trying to say ... How is the squiggly loop defined?
$endgroup$
– Matti P.
Jan 3 at 7:40
$begingroup$
Is your curve something like $gammacolon(0,2pi)toBbb R^2$, $tmapsto(sin t,sin 2t)$?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:44
$begingroup$
a point just above that middle point on the curve .
$endgroup$
– Anirudh Gulati
Jan 3 at 8:04
$begingroup$
I am school kid learning geometry it basic 8 like shape this is the first chapter where they teach about curves
$endgroup$
– Anirudh Gulati
Jan 3 at 8:06
|
show 3 more comments
$begingroup$
if we start from just above point and go up and end at just below point how is the curve not simple curve. ncert class 6 chapter 4 pg 72 says it is not http://ncert.nic.in/textbook/textbook.htm?femh1=4-14 please help
I am a student and trying to understand things it is a 8 like figure this question is not off topic as it is a maths question. don't gang up on me pls. I am not up at your level also I cant understand your big terms I don't understand why people reporting me I also need help .pls no teacher is answering me properly .Pls help .
geometry curves
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
$endgroup$
if we start from just above point and go up and end at just below point how is the curve not simple curve. ncert class 6 chapter 4 pg 72 says it is not http://ncert.nic.in/textbook/textbook.htm?femh1=4-14 please help
I am a student and trying to understand things it is a 8 like figure this question is not off topic as it is a maths question. don't gang up on me pls. I am not up at your level also I cant understand your big terms I don't understand why people reporting me I also need help .pls no teacher is answering me properly .Pls help .
geometry curves
geometry curves
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
edited Jan 3 at 14:03
Anirudh Gulati
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
asked Jan 3 at 7:24
Anirudh GulatiAnirudh Gulati
12
12
closed as off-topic by José Carlos Santos, Saad, Shailesh, Did, Moishe Kohan Jan 3 at 13:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shailesh, Did, Moishe Kohan
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, Saad, Shailesh, Did, Moishe Kohan Jan 3 at 13:17
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shailesh, Did, Moishe Kohan
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
What does "just above" mean?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:34
$begingroup$
I don't understand what your picture is trying to say ... How is the squiggly loop defined?
$endgroup$
– Matti P.
Jan 3 at 7:40
$begingroup$
Is your curve something like $gammacolon(0,2pi)toBbb R^2$, $tmapsto(sin t,sin 2t)$?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:44
$begingroup$
a point just above that middle point on the curve .
$endgroup$
– Anirudh Gulati
Jan 3 at 8:04
$begingroup$
I am school kid learning geometry it basic 8 like shape this is the first chapter where they teach about curves
$endgroup$
– Anirudh Gulati
Jan 3 at 8:06
|
show 3 more comments
$begingroup$
What does "just above" mean?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:34
$begingroup$
I don't understand what your picture is trying to say ... How is the squiggly loop defined?
$endgroup$
– Matti P.
Jan 3 at 7:40
$begingroup$
Is your curve something like $gammacolon(0,2pi)toBbb R^2$, $tmapsto(sin t,sin 2t)$?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:44
$begingroup$
a point just above that middle point on the curve .
$endgroup$
– Anirudh Gulati
Jan 3 at 8:04
$begingroup$
I am school kid learning geometry it basic 8 like shape this is the first chapter where they teach about curves
$endgroup$
– Anirudh Gulati
Jan 3 at 8:06
$begingroup$
What does "just above" mean?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:34
$begingroup$
What does "just above" mean?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:34
$begingroup$
I don't understand what your picture is trying to say ... How is the squiggly loop defined?
$endgroup$
– Matti P.
Jan 3 at 7:40
$begingroup$
I don't understand what your picture is trying to say ... How is the squiggly loop defined?
$endgroup$
– Matti P.
Jan 3 at 7:40
$begingroup$
Is your curve something like $gammacolon(0,2pi)toBbb R^2$, $tmapsto(sin t,sin 2t)$?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:44
$begingroup$
Is your curve something like $gammacolon(0,2pi)toBbb R^2$, $tmapsto(sin t,sin 2t)$?
$endgroup$
– Hagen von Eitzen
Jan 3 at 7:44
$begingroup$
a point just above that middle point on the curve .
$endgroup$
– Anirudh Gulati
Jan 3 at 8:04
$begingroup$
a point just above that middle point on the curve .
$endgroup$
– Anirudh Gulati
Jan 3 at 8:04
$begingroup$
I am school kid learning geometry it basic 8 like shape this is the first chapter where they teach about curves
$endgroup$
– Anirudh Gulati
Jan 3 at 8:06
$begingroup$
I am school kid learning geometry it basic 8 like shape this is the first chapter where they teach about curves
$endgroup$
– Anirudh Gulati
Jan 3 at 8:06
|
show 3 more comments
1 Answer
1
active
oldest
votes
$begingroup$
Consider this:
The blue curve on the right is a simple closed curve, also called a Jordan curve.
The red curve on the left is a closed curve, but is is not simple, because it intersects (crosses) itself. It does not matter where it crosses itself.
You can think of it this way: When you draw the curve, and you need to cross or overlap the already drawn part of the curve (except at the very end or start), it cannot be a simple curve. The only place where a closed simple curve overlaps, is at the starting and ending point.
If you make the mistake of starting drawing the curve exactly where it starts, the above thought model is a bit broken. You do not get to cheat that way; such curves are still not simple. Consider the above way of thinking about it only valid, if you start the curve at a point that is not close to an intersection.
You can draw it as large as you need, with as sharp pen or pencil as you need, to check if some parts are just very close, or really intersect/cross/overlap. Only a real intersection/crossing/overlapping matters: you can think of having a very, very sharp pen/pencil and a huge area to draw on.
A simple curve does not need to be closed, it can be open as well. (Simple open curves are also called Jordan arcs.) Such curves do not cross themselves, nor do they end where they staryed. For example, $alpha$ is not a simple curve, because it crosses itself; but $nu$ is simple.
Furthermore, $rho$ is not a simple curve, because it starts (or ends, depending on which way you draw it) at the middle of itself; it does cross/intersect itself.
The proper mathematical term for when a curve crosses itself is "self-intersecting". Thus, every curve is either "simple" or "self-intersecting".
Note that a closed curve must start and end at exactly the same point. It is not enough for the curve to look closed. For example,
is indeed an open simple curve. However, you cannot close it but keep it simple it by moving the endpoints closer to the vertical part. No matter how close you put the endpoints, the two points will be separate (distinct), unless you cross the vertical part. If you cross the vertical part, the curve is no longer simple.
Here is how we can classify any single curve we might encounter, properly:
If the curve starts and ends at the exact same point, the curve is closed. Otherwise the curve is open. (Arcs are another term used for open curves.)
If the curve does not intersect itself, the curve is simple. Otherwise, it is self-intersecting.
A closed simple curve is one where the start and end points are the same, but no other part of the curve passes through that point, and there are no (other) intersections.
The start and end point being the same is a special case for simple curves. Because it is such a tiny detail in the mathematical definition (closed interval vs. open interval), it is often missed or forgotten; it is crucial, however: because it makes the curve closed, it does not count as an intersection, as long as no other part of the curve passes through that point.
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
$endgroup$
$begingroup$
you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
$endgroup$
– Anirudh Gulati
Jan 3 at 13:55
$begingroup$
@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
$endgroup$
– Nominal Animal
Jan 3 at 14:39
$begingroup$
@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
$endgroup$
– Nominal Animal
Jan 3 at 14:42
$begingroup$
I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
$endgroup$
– Anirudh Gulati
Jan 3 at 14:58
$begingroup$
same way I ended at just below point
$endgroup$
– Anirudh Gulati
Jan 3 at 15:05
|
show 17 more comments
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Consider this:
The blue curve on the right is a simple closed curve, also called a Jordan curve.
The red curve on the left is a closed curve, but is is not simple, because it intersects (crosses) itself. It does not matter where it crosses itself.
You can think of it this way: When you draw the curve, and you need to cross or overlap the already drawn part of the curve (except at the very end or start), it cannot be a simple curve. The only place where a closed simple curve overlaps, is at the starting and ending point.
If you make the mistake of starting drawing the curve exactly where it starts, the above thought model is a bit broken. You do not get to cheat that way; such curves are still not simple. Consider the above way of thinking about it only valid, if you start the curve at a point that is not close to an intersection.
You can draw it as large as you need, with as sharp pen or pencil as you need, to check if some parts are just very close, or really intersect/cross/overlap. Only a real intersection/crossing/overlapping matters: you can think of having a very, very sharp pen/pencil and a huge area to draw on.
A simple curve does not need to be closed, it can be open as well. (Simple open curves are also called Jordan arcs.) Such curves do not cross themselves, nor do they end where they staryed. For example, $alpha$ is not a simple curve, because it crosses itself; but $nu$ is simple.
Furthermore, $rho$ is not a simple curve, because it starts (or ends, depending on which way you draw it) at the middle of itself; it does cross/intersect itself.
The proper mathematical term for when a curve crosses itself is "self-intersecting". Thus, every curve is either "simple" or "self-intersecting".
Note that a closed curve must start and end at exactly the same point. It is not enough for the curve to look closed. For example,
is indeed an open simple curve. However, you cannot close it but keep it simple it by moving the endpoints closer to the vertical part. No matter how close you put the endpoints, the two points will be separate (distinct), unless you cross the vertical part. If you cross the vertical part, the curve is no longer simple.
Here is how we can classify any single curve we might encounter, properly:
If the curve starts and ends at the exact same point, the curve is closed. Otherwise the curve is open. (Arcs are another term used for open curves.)
If the curve does not intersect itself, the curve is simple. Otherwise, it is self-intersecting.
A closed simple curve is one where the start and end points are the same, but no other part of the curve passes through that point, and there are no (other) intersections.
The start and end point being the same is a special case for simple curves. Because it is such a tiny detail in the mathematical definition (closed interval vs. open interval), it is often missed or forgotten; it is crucial, however: because it makes the curve closed, it does not count as an intersection, as long as no other part of the curve passes through that point.
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
$endgroup$
$begingroup$
you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
$endgroup$
– Anirudh Gulati
Jan 3 at 13:55
$begingroup$
@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
$endgroup$
– Nominal Animal
Jan 3 at 14:39
$begingroup$
@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
$endgroup$
– Nominal Animal
Jan 3 at 14:42
$begingroup$
I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
$endgroup$
– Anirudh Gulati
Jan 3 at 14:58
$begingroup$
same way I ended at just below point
$endgroup$
– Anirudh Gulati
Jan 3 at 15:05
|
show 17 more comments
$begingroup$
Consider this:
The blue curve on the right is a simple closed curve, also called a Jordan curve.
The red curve on the left is a closed curve, but is is not simple, because it intersects (crosses) itself. It does not matter where it crosses itself.
You can think of it this way: When you draw the curve, and you need to cross or overlap the already drawn part of the curve (except at the very end or start), it cannot be a simple curve. The only place where a closed simple curve overlaps, is at the starting and ending point.
If you make the mistake of starting drawing the curve exactly where it starts, the above thought model is a bit broken. You do not get to cheat that way; such curves are still not simple. Consider the above way of thinking about it only valid, if you start the curve at a point that is not close to an intersection.
You can draw it as large as you need, with as sharp pen or pencil as you need, to check if some parts are just very close, or really intersect/cross/overlap. Only a real intersection/crossing/overlapping matters: you can think of having a very, very sharp pen/pencil and a huge area to draw on.
A simple curve does not need to be closed, it can be open as well. (Simple open curves are also called Jordan arcs.) Such curves do not cross themselves, nor do they end where they staryed. For example, $alpha$ is not a simple curve, because it crosses itself; but $nu$ is simple.
Furthermore, $rho$ is not a simple curve, because it starts (or ends, depending on which way you draw it) at the middle of itself; it does cross/intersect itself.
The proper mathematical term for when a curve crosses itself is "self-intersecting". Thus, every curve is either "simple" or "self-intersecting".
Note that a closed curve must start and end at exactly the same point. It is not enough for the curve to look closed. For example,
is indeed an open simple curve. However, you cannot close it but keep it simple it by moving the endpoints closer to the vertical part. No matter how close you put the endpoints, the two points will be separate (distinct), unless you cross the vertical part. If you cross the vertical part, the curve is no longer simple.
Here is how we can classify any single curve we might encounter, properly:
If the curve starts and ends at the exact same point, the curve is closed. Otherwise the curve is open. (Arcs are another term used for open curves.)
If the curve does not intersect itself, the curve is simple. Otherwise, it is self-intersecting.
A closed simple curve is one where the start and end points are the same, but no other part of the curve passes through that point, and there are no (other) intersections.
The start and end point being the same is a special case for simple curves. Because it is such a tiny detail in the mathematical definition (closed interval vs. open interval), it is often missed or forgotten; it is crucial, however: because it makes the curve closed, it does not count as an intersection, as long as no other part of the curve passes through that point.
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
$endgroup$
$begingroup$
you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
$endgroup$
– Anirudh Gulati
Jan 3 at 13:55
$begingroup$
@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
$endgroup$
– Nominal Animal
Jan 3 at 14:39
$begingroup$
@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
$endgroup$
– Nominal Animal
Jan 3 at 14:42
$begingroup$
I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
$endgroup$
– Anirudh Gulati
Jan 3 at 14:58
$begingroup$
same way I ended at just below point
$endgroup$
– Anirudh Gulati
Jan 3 at 15:05
|
show 17 more comments
$begingroup$
Consider this:
The blue curve on the right is a simple closed curve, also called a Jordan curve.
The red curve on the left is a closed curve, but is is not simple, because it intersects (crosses) itself. It does not matter where it crosses itself.
You can think of it this way: When you draw the curve, and you need to cross or overlap the already drawn part of the curve (except at the very end or start), it cannot be a simple curve. The only place where a closed simple curve overlaps, is at the starting and ending point.
If you make the mistake of starting drawing the curve exactly where it starts, the above thought model is a bit broken. You do not get to cheat that way; such curves are still not simple. Consider the above way of thinking about it only valid, if you start the curve at a point that is not close to an intersection.
You can draw it as large as you need, with as sharp pen or pencil as you need, to check if some parts are just very close, or really intersect/cross/overlap. Only a real intersection/crossing/overlapping matters: you can think of having a very, very sharp pen/pencil and a huge area to draw on.
A simple curve does not need to be closed, it can be open as well. (Simple open curves are also called Jordan arcs.) Such curves do not cross themselves, nor do they end where they staryed. For example, $alpha$ is not a simple curve, because it crosses itself; but $nu$ is simple.
Furthermore, $rho$ is not a simple curve, because it starts (or ends, depending on which way you draw it) at the middle of itself; it does cross/intersect itself.
The proper mathematical term for when a curve crosses itself is "self-intersecting". Thus, every curve is either "simple" or "self-intersecting".
Note that a closed curve must start and end at exactly the same point. It is not enough for the curve to look closed. For example,
is indeed an open simple curve. However, you cannot close it but keep it simple it by moving the endpoints closer to the vertical part. No matter how close you put the endpoints, the two points will be separate (distinct), unless you cross the vertical part. If you cross the vertical part, the curve is no longer simple.
Here is how we can classify any single curve we might encounter, properly:
If the curve starts and ends at the exact same point, the curve is closed. Otherwise the curve is open. (Arcs are another term used for open curves.)
If the curve does not intersect itself, the curve is simple. Otherwise, it is self-intersecting.
A closed simple curve is one where the start and end points are the same, but no other part of the curve passes through that point, and there are no (other) intersections.
The start and end point being the same is a special case for simple curves. Because it is such a tiny detail in the mathematical definition (closed interval vs. open interval), it is often missed or forgotten; it is crucial, however: because it makes the curve closed, it does not count as an intersection, as long as no other part of the curve passes through that point.
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
$endgroup$
Consider this:
The blue curve on the right is a simple closed curve, also called a Jordan curve.
The red curve on the left is a closed curve, but is is not simple, because it intersects (crosses) itself. It does not matter where it crosses itself.
You can think of it this way: When you draw the curve, and you need to cross or overlap the already drawn part of the curve (except at the very end or start), it cannot be a simple curve. The only place where a closed simple curve overlaps, is at the starting and ending point.
If you make the mistake of starting drawing the curve exactly where it starts, the above thought model is a bit broken. You do not get to cheat that way; such curves are still not simple. Consider the above way of thinking about it only valid, if you start the curve at a point that is not close to an intersection.
You can draw it as large as you need, with as sharp pen or pencil as you need, to check if some parts are just very close, or really intersect/cross/overlap. Only a real intersection/crossing/overlapping matters: you can think of having a very, very sharp pen/pencil and a huge area to draw on.
A simple curve does not need to be closed, it can be open as well. (Simple open curves are also called Jordan arcs.) Such curves do not cross themselves, nor do they end where they staryed. For example, $alpha$ is not a simple curve, because it crosses itself; but $nu$ is simple.
Furthermore, $rho$ is not a simple curve, because it starts (or ends, depending on which way you draw it) at the middle of itself; it does cross/intersect itself.
The proper mathematical term for when a curve crosses itself is "self-intersecting". Thus, every curve is either "simple" or "self-intersecting".
Note that a closed curve must start and end at exactly the same point. It is not enough for the curve to look closed. For example,
is indeed an open simple curve. However, you cannot close it but keep it simple it by moving the endpoints closer to the vertical part. No matter how close you put the endpoints, the two points will be separate (distinct), unless you cross the vertical part. If you cross the vertical part, the curve is no longer simple.
Here is how we can classify any single curve we might encounter, properly:
If the curve starts and ends at the exact same point, the curve is closed. Otherwise the curve is open. (Arcs are another term used for open curves.)
If the curve does not intersect itself, the curve is simple. Otherwise, it is self-intersecting.
A closed simple curve is one where the start and end points are the same, but no other part of the curve passes through that point, and there are no (other) intersections.
The start and end point being the same is a special case for simple curves. Because it is such a tiny detail in the mathematical definition (closed interval vs. open interval), it is often missed or forgotten; it is crucial, however: because it makes the curve closed, it does not count as an intersection, as long as no other part of the curve passes through that point.
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
edited Jan 6 at 15:21
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
answered Jan 3 at 12:32
Nominal AnimalNominal Animal
7,1232617
7,1232617
$begingroup$
you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
$endgroup$
– Anirudh Gulati
Jan 3 at 13:55
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@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
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– Nominal Animal
Jan 3 at 14:39
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@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
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– Nominal Animal
Jan 3 at 14:42
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I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
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– Anirudh Gulati
Jan 3 at 14:58
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same way I ended at just below point
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– Anirudh Gulati
Jan 3 at 15:05
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show 17 more comments
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you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
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– Anirudh Gulati
Jan 3 at 13:55
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@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
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– Nominal Animal
Jan 3 at 14:39
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@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
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– Nominal Animal
Jan 3 at 14:42
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I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
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– Anirudh Gulati
Jan 3 at 14:58
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same way I ended at just below point
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– Anirudh Gulati
Jan 3 at 15:05
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you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
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– Anirudh Gulati
Jan 3 at 13:55
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you did not read what I wrote or I am mistaken if the definition says it should be plane curve on which a point object can move without need to move on already moved on points then it is a simple curve then why the curve is not a simple curve I don't understand, the definition cannot be wrong there is something missing or I am dumb
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– Anirudh Gulati
Jan 3 at 13:55
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@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
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– Nominal Animal
Jan 3 at 14:39
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@AnirudhGulati: I read what you wrote, and looked at your image. (It looks like you have an URL inside the text of your question; I did not look there, and will not look there.) The "curve on which a point object can move [along the curve] without need to move on already moved on points" definition is exactly the same as "the curve does not intersect itself".
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– Nominal Animal
Jan 3 at 14:39
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@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
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– Nominal Animal
Jan 3 at 14:42
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@AnirudhGulati: When you move along the figure eight curve, you can only move "forward" and "back", since the curve has no "thickness". When you do the first loop, and come to the intersection, you cannot "squeeze by" or "slip between the points", because every point along the curve is already "taken". So, no crossing.
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– Nominal Animal
Jan 3 at 14:42
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I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
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– Anirudh Gulati
Jan 3 at 14:58
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I didn't started at intersection I started at point just above intersection AND ON THE CURVE. that's the thing I want to ask .there is nothing about squeezing I said
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– Anirudh Gulati
Jan 3 at 14:58
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same way I ended at just below point
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– Anirudh Gulati
Jan 3 at 15:05
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same way I ended at just below point
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– Anirudh Gulati
Jan 3 at 15:05
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show 17 more comments
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What does "just above" mean?
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– Hagen von Eitzen
Jan 3 at 7:34
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I don't understand what your picture is trying to say ... How is the squiggly loop defined?
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– Matti P.
Jan 3 at 7:40
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Is your curve something like $gammacolon(0,2pi)toBbb R^2$, $tmapsto(sin t,sin 2t)$?
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– Hagen von Eitzen
Jan 3 at 7:44
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a point just above that middle point on the curve .
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– Anirudh Gulati
Jan 3 at 8:04
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I am school kid learning geometry it basic 8 like shape this is the first chapter where they teach about curves
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– Anirudh Gulati
Jan 3 at 8:06