Parametrisation of a curve notation
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If I have some curve $C$ and the parameterisation is the bijective map $P:[a,b] rightarrow C$ What do $a$ and $b$ represent? I though that they would be the coordinates of the start and end of the curve but in some solutions to answers they are given as single numbers e.g. $p:[0,1] rightarrow C$.
calculus notation parametrization
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$begingroup$
If I have some curve $C$ and the parameterisation is the bijective map $P:[a,b] rightarrow C$ What do $a$ and $b$ represent? I though that they would be the coordinates of the start and end of the curve but in some solutions to answers they are given as single numbers e.g. $p:[0,1] rightarrow C$.
calculus notation parametrization
$endgroup$
add a comment |
$begingroup$
If I have some curve $C$ and the parameterisation is the bijective map $P:[a,b] rightarrow C$ What do $a$ and $b$ represent? I though that they would be the coordinates of the start and end of the curve but in some solutions to answers they are given as single numbers e.g. $p:[0,1] rightarrow C$.
calculus notation parametrization
$endgroup$
If I have some curve $C$ and the parameterisation is the bijective map $P:[a,b] rightarrow C$ What do $a$ and $b$ represent? I though that they would be the coordinates of the start and end of the curve but in some solutions to answers they are given as single numbers e.g. $p:[0,1] rightarrow C$.
calculus notation parametrization
calculus notation parametrization
asked Dec 15 '18 at 13:45
user571032
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p(a) is where the curve starts and p(b) is where it ends. You have a continuous function from the interval [a,b]. So C is a connected set. Think of the interval as a timer that goes from t=0 to t=1. At time t, you are at the point p(t) on C.
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
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1 Answer
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1 Answer
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active
oldest
votes
active
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active
oldest
votes
$begingroup$
p(a) is where the curve starts and p(b) is where it ends. You have a continuous function from the interval [a,b]. So C is a connected set. Think of the interval as a timer that goes from t=0 to t=1. At time t, you are at the point p(t) on C.
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
$endgroup$
add a comment |
$begingroup$
p(a) is where the curve starts and p(b) is where it ends. You have a continuous function from the interval [a,b]. So C is a connected set. Think of the interval as a timer that goes from t=0 to t=1. At time t, you are at the point p(t) on C.
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
$endgroup$
add a comment |
$begingroup$
p(a) is where the curve starts and p(b) is where it ends. You have a continuous function from the interval [a,b]. So C is a connected set. Think of the interval as a timer that goes from t=0 to t=1. At time t, you are at the point p(t) on C.
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
$endgroup$
p(a) is where the curve starts and p(b) is where it ends. You have a continuous function from the interval [a,b]. So C is a connected set. Think of the interval as a timer that goes from t=0 to t=1. At time t, you are at the point p(t) on C.
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
answered Dec 15 '18 at 13:59
Joel PereiraJoel Pereira
75719
75719
add a comment |
add a comment |
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