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Why are lengths different when an object is curved?
Determine these two angle (Isosceles triangle)area of rotated squares on top of each otherHow can the angle be found in this triangle?Martini Glass - ExtensionCan we construct a given angle again using only compass and ruler?Unknown internal angles of a quadrilateral where its area and side lengths are knownVolume of irregular piece of pieWhy are these answers different? Which one is correct? (Distance between to two 3D points)Tailoring a jacket with a $1$-inch lapel notch at a horizontally-symmetric $40^circ$ angleWhy does using different units yield different areas?
$begingroup$
In the above diagram ad is equal to bc. Likewise, ce should be equal to df (Since angle F and E are at 90 degree). My question is why when calculating length of ce and df using $2pi r$ they are different?
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same?
geometry
asked Mar 13 at 9:30
user653717user653717
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 2 more comments
$begingroup$
In the above diagram ad is equal to bc. Likewise, ce should be equal to df (Since angle F and E are at 90 degree). My question is why when calculating length of ce and df using $2pi r$ they are different?
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same?
geometry
asked Mar 13 at 9:30
user653717user653717
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Wellcome to MathSE! It would be more helpful for us to provide some more insight about your thoughts! However, as a hint, consider that two runners start at poitns $c$ and $d$ and run with the same velocity. Who will arrive first to their route's end?
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:35
$begingroup$
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same? Runner who started at c because the distance is less. What I'm not getting is why the distance is less
$endgroup$
– user653717
Mar 13 at 9:41
1
$begingroup$
It's like the fact that on a track, the inside lane is shorter around the curve. So they lag the starts for different lanes to make it fair.
$endgroup$
– coffeemath
Mar 13 at 9:41
$begingroup$
Have you tried bending a ruler like that? Isn't it difficult? That's because the material is getting stretched and compressed, because the lengths are changing. Maybe try it with something more flexible, like a rubber eraser or a piece of foam.
$endgroup$
– Rahul
Mar 13 at 9:47
$begingroup$
Try this; take some thread and try to measure the length of two circular items of different radii. You will realize that you will need a longer piece of thread to measure the one with the biggest radius (assume we have equal arcs on both shapes). Alternatively, consider that what you ahve there are two circles with the same centre, so the one with the largest radius will have a larger circumference.
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:48
|
show 2 more comments
$begingroup$
In the above diagram ad is equal to bc. Likewise, ce should be equal to df (Since angle F and E are at 90 degree). My question is why when calculating length of ce and df using $2pi r$ they are different?
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same?
geometry
asked Mar 13 at 9:30
user653717user653717
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
In the above diagram ad is equal to bc. Likewise, ce should be equal to df (Since angle F and E are at 90 degree). My question is why when calculating length of ce and df using $2pi r$ they are different?
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same?
geometry
geometry
asked Mar 13 at 9:30
user653717user653717
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 9:30
user653717user653717
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Mar 13 at 9:42
user653717
asked Mar 13 at 9:30
user653717user653717
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 13 at 9:30
user653717user653717
12
asked Mar 13 at 9:30
user653717user653717
12
12
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user653717 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Wellcome to MathSE! It would be more helpful for us to provide some more insight about your thoughts! However, as a hint, consider that two runners start at poitns $c$ and $d$ and run with the same velocity. Who will arrive first to their route's end?
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:35
$begingroup$
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same? Runner who started at c because the distance is less. What I'm not getting is why the distance is less
$endgroup$
– user653717
Mar 13 at 9:41
1
$begingroup$
It's like the fact that on a track, the inside lane is shorter around the curve. So they lag the starts for different lanes to make it fair.
$endgroup$
– coffeemath
Mar 13 at 9:41
$begingroup$
Have you tried bending a ruler like that? Isn't it difficult? That's because the material is getting stretched and compressed, because the lengths are changing. Maybe try it with something more flexible, like a rubber eraser or a piece of foam.
$endgroup$
– Rahul
Mar 13 at 9:47
$begingroup$
Try this; take some thread and try to measure the length of two circular items of different radii. You will realize that you will need a longer piece of thread to measure the one with the biggest radius (assume we have equal arcs on both shapes). Alternatively, consider that what you ahve there are two circles with the same centre, so the one with the largest radius will have a larger circumference.
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:48
|
show 2 more comments
1
$begingroup$
Wellcome to MathSE! It would be more helpful for us to provide some more insight about your thoughts! However, as a hint, consider that two runners start at poitns $c$ and $d$ and run with the same velocity. Who will arrive first to their route's end?
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:35
$begingroup$
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same? Runner who started at c because the distance is less. What I'm not getting is why the distance is less
$endgroup$
– user653717
Mar 13 at 9:41
1
$begingroup$
It's like the fact that on a track, the inside lane is shorter around the curve. So they lag the starts for different lanes to make it fair.
$endgroup$
– coffeemath
Mar 13 at 9:41
$begingroup$
Have you tried bending a ruler like that? Isn't it difficult? That's because the material is getting stretched and compressed, because the lengths are changing. Maybe try it with something more flexible, like a rubber eraser or a piece of foam.
$endgroup$
– Rahul
Mar 13 at 9:47
$begingroup$
Try this; take some thread and try to measure the length of two circular items of different radii. You will realize that you will need a longer piece of thread to measure the one with the biggest radius (assume we have equal arcs on both shapes). Alternatively, consider that what you ahve there are two circles with the same centre, so the one with the largest radius will have a larger circumference.
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:48
1
1
$begingroup$
Wellcome to MathSE! It would be more helpful for us to provide some more insight about your thoughts! However, as a hint, consider that two runners start at poitns $c$ and $d$ and run with the same velocity. Who will arrive first to their route's end?
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:35
$begingroup$
Wellcome to MathSE! It would be more helpful for us to provide some more insight about your thoughts! However, as a hint, consider that two runners start at poitns $c$ and $d$ and run with the same velocity. Who will arrive first to their route's end?
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:35
$begingroup$
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same? Runner who started at c because the distance is less. What I'm not getting is why the distance is less
$endgroup$
– user653717
Mar 13 at 9:41
$begingroup$
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same? Runner who started at c because the distance is less. What I'm not getting is why the distance is less
$endgroup$
– user653717
Mar 13 at 9:41
1
1
$begingroup$
It's like the fact that on a track, the inside lane is shorter around the curve. So they lag the starts for different lanes to make it fair.
$endgroup$
– coffeemath
Mar 13 at 9:41
$begingroup$
It's like the fact that on a track, the inside lane is shorter around the curve. So they lag the starts for different lanes to make it fair.
$endgroup$
– coffeemath
Mar 13 at 9:41
$begingroup$
Have you tried bending a ruler like that? Isn't it difficult? That's because the material is getting stretched and compressed, because the lengths are changing. Maybe try it with something more flexible, like a rubber eraser or a piece of foam.
$endgroup$
– Rahul
Mar 13 at 9:47
$begingroup$
Have you tried bending a ruler like that? Isn't it difficult? That's because the material is getting stretched and compressed, because the lengths are changing. Maybe try it with something more flexible, like a rubber eraser or a piece of foam.
$endgroup$
– Rahul
Mar 13 at 9:47
$begingroup$
Try this; take some thread and try to measure the length of two circular items of different radii. You will realize that you will need a longer piece of thread to measure the one with the biggest radius (assume we have equal arcs on both shapes). Alternatively, consider that what you ahve there are two circles with the same centre, so the one with the largest radius will have a larger circumference.
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:48
$begingroup$
Try this; take some thread and try to measure the length of two circular items of different radii. You will realize that you will need a longer piece of thread to measure the one with the biggest radius (assume we have equal arcs on both shapes). Alternatively, consider that what you ahve there are two circles with the same centre, so the one with the largest radius will have a larger circumference.
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:48
|
show 2 more comments
1 Answer
1
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votes
$begingroup$
imagine that df is a part of a circle, and ce is a part of another circle
is the circumference of the first circle equal to the circumference of the second one
or less ?
i think it's clear now.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
add a comment |
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1 Answer
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$begingroup$
imagine that df is a part of a circle, and ce is a part of another circle
is the circumference of the first circle equal to the circumference of the second one
or less ?
i think it's clear now.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
add a comment |
$begingroup$
imagine that df is a part of a circle, and ce is a part of another circle
is the circumference of the first circle equal to the circumference of the second one
or less ?
i think it's clear now.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
add a comment |
$begingroup$
imagine that df is a part of a circle, and ce is a part of another circle
is the circumference of the first circle equal to the circumference of the second one
or less ?
i think it's clear now.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
imagine that df is a part of a circle, and ce is a part of another circle
is the circumference of the first circle equal to the circumference of the second one
or less ?
i think it's clear now.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
answered Mar 13 at 9:41
Tamer GhareebTamer Ghareeb
61
61
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Tamer Ghareeb is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
add a comment |
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
$begingroup$
Could you refer to the ruler example I've just added
$endgroup$
– user653717
Mar 13 at 9:44
add a comment |
user653717 is a new contributor. Be nice, and check out our Code of Conduct.
user653717 is a new contributor. Be nice, and check out our Code of Conduct.
user653717 is a new contributor. Be nice, and check out our Code of Conduct.
user653717 is a new contributor. Be nice, and check out our Code of Conduct.
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1
$begingroup$
Wellcome to MathSE! It would be more helpful for us to provide some more insight about your thoughts! However, as a hint, consider that two runners start at poitns $c$ and $d$ and run with the same velocity. Who will arrive first to their route's end?
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:35
$begingroup$
If I was holding a ruler so it is vertical and then bent it a bit at the bottom. Wouldn't the length be the same? Runner who started at c because the distance is less. What I'm not getting is why the distance is less
$endgroup$
– user653717
Mar 13 at 9:41
1
$begingroup$
It's like the fact that on a track, the inside lane is shorter around the curve. So they lag the starts for different lanes to make it fair.
$endgroup$
– coffeemath
Mar 13 at 9:41
$begingroup$
Have you tried bending a ruler like that? Isn't it difficult? That's because the material is getting stretched and compressed, because the lengths are changing. Maybe try it with something more flexible, like a rubber eraser or a piece of foam.
$endgroup$
– Rahul
Mar 13 at 9:47
$begingroup$
Try this; take some thread and try to measure the length of two circular items of different radii. You will realize that you will need a longer piece of thread to measure the one with the biggest radius (assume we have equal arcs on both shapes). Alternatively, consider that what you ahve there are two circles with the same centre, so the one with the largest radius will have a larger circumference.
$endgroup$
– Βασίλης Μάρκος
Mar 13 at 9:48