Mixing
![How i can reformulate Riemann hypothesis in $3D=mathbbR^3$? [on hold]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZCTB4-bb-s-32SAm6ytjzFOU06cH9o8q-a_wq_UnH6lcd8hvws23CmBWHM6g256LzTX9yK1EiCCzTC1NSgtxlNk_J9hdr9bA3tD0Nqntbl521j4bLAm_uXPANuWLBhcCKTKzns2gaUodx/s72-c/1.jpg)
Finding direction using sun
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
In this vid why does the shadow trace a straight line instead of some curve ?
Intuitively it makes sense because at morning the shadow falls to west and at evening the shadow falls to east. He is basically connecting the shadow tips at these two times and claims that is the East-West line.
What I'm not able to convince myself is why the shadow tip traces a straight line at all times between morning and evening ? Is there any way to prove this using vectors or some other means ? Thanks!
vectors locus
asked Jul 16 at 12:54
rsadhvika
1,4891026
add a comment |Â
up vote
0
down vote
favorite
In this vid why does the shadow trace a straight line instead of some curve ?
Intuitively it makes sense because at morning the shadow falls to west and at evening the shadow falls to east. He is basically connecting the shadow tips at these two times and claims that is the East-West line.
What I'm not able to convince myself is why the shadow tip traces a straight line at all times between morning and evening ? Is there any way to prove this using vectors or some other means ? Thanks!
vectors locus
asked Jul 16 at 12:54
rsadhvika
1,4891026
1
North of the tropics in summer (i.e. now), the sun rises north of east then passes to the south and sets north of west, so the tip of the shadow must start south of west then pass to the north and end south of east. This seems to require a curve to me, and therefore curves are likely in other situations too, but it may be close to a straight line near the middle of the day
– Henry
Jul 16 at 13:01
Ah do you feel it can be a circle parallel to ecliptic or perhaps latitude lines ? I'll need to think a bit more when I get access to paper and pen.. @Henry
– rsadhvika
Jul 16 at 13:07
1
I suspect it may be a hyperbola (or close to one) providing that the sun actually sets: see en.wikipedia.org/wiki/Hyperbola#Sundials
– Henry
Jul 16 at 13:27
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In this vid why does the shadow trace a straight line instead of some curve ?
Intuitively it makes sense because at morning the shadow falls to west and at evening the shadow falls to east. He is basically connecting the shadow tips at these two times and claims that is the East-West line.
What I'm not able to convince myself is why the shadow tip traces a straight line at all times between morning and evening ? Is there any way to prove this using vectors or some other means ? Thanks!
vectors locus
asked Jul 16 at 12:54
rsadhvika
1,4891026
In this vid why does the shadow trace a straight line instead of some curve ?
Intuitively it makes sense because at morning the shadow falls to west and at evening the shadow falls to east. He is basically connecting the shadow tips at these two times and claims that is the East-West line.
What I'm not able to convince myself is why the shadow tip traces a straight line at all times between morning and evening ? Is there any way to prove this using vectors or some other means ? Thanks!
vectors locus
asked Jul 16 at 12:54
rsadhvika
1,4891026
asked Jul 16 at 12:54
rsadhvika
1,4891026
asked Jul 16 at 12:54
rsadhvika
1,4891026
asked Jul 16 at 12:54
rsadhvika
1,4891026
1,4891026
1
North of the tropics in summer (i.e. now), the sun rises north of east then passes to the south and sets north of west, so the tip of the shadow must start south of west then pass to the north and end south of east. This seems to require a curve to me, and therefore curves are likely in other situations too, but it may be close to a straight line near the middle of the day
– Henry
Jul 16 at 13:01
Ah do you feel it can be a circle parallel to ecliptic or perhaps latitude lines ? I'll need to think a bit more when I get access to paper and pen.. @Henry
– rsadhvika
Jul 16 at 13:07
1
I suspect it may be a hyperbola (or close to one) providing that the sun actually sets: see en.wikipedia.org/wiki/Hyperbola#Sundials
– Henry
Jul 16 at 13:27
add a comment |Â
1
North of the tropics in summer (i.e. now), the sun rises north of east then passes to the south and sets north of west, so the tip of the shadow must start south of west then pass to the north and end south of east. This seems to require a curve to me, and therefore curves are likely in other situations too, but it may be close to a straight line near the middle of the day
– Henry
Jul 16 at 13:01
Ah do you feel it can be a circle parallel to ecliptic or perhaps latitude lines ? I'll need to think a bit more when I get access to paper and pen.. @Henry
– rsadhvika
Jul 16 at 13:07
1
I suspect it may be a hyperbola (or close to one) providing that the sun actually sets: see en.wikipedia.org/wiki/Hyperbola#Sundials
– Henry
Jul 16 at 13:27
1
1
North of the tropics in summer (i.e. now), the sun rises north of east then passes to the south and sets north of west, so the tip of the shadow must start south of west then pass to the north and end south of east. This seems to require a curve to me, and therefore curves are likely in other situations too, but it may be close to a straight line near the middle of the day
– Henry
Jul 16 at 13:01
North of the tropics in summer (i.e. now), the sun rises north of east then passes to the south and sets north of west, so the tip of the shadow must start south of west then pass to the north and end south of east. This seems to require a curve to me, and therefore curves are likely in other situations too, but it may be close to a straight line near the middle of the day
– Henry
Jul 16 at 13:01
Ah do you feel it can be a circle parallel to ecliptic or perhaps latitude lines ? I'll need to think a bit more when I get access to paper and pen.. @Henry
– rsadhvika
Jul 16 at 13:07
Ah do you feel it can be a circle parallel to ecliptic or perhaps latitude lines ? I'll need to think a bit more when I get access to paper and pen.. @Henry
– rsadhvika
Jul 16 at 13:07
1
1
I suspect it may be a hyperbola (or close to one) providing that the sun actually sets: see en.wikipedia.org/wiki/Hyperbola#Sundials
– Henry
Jul 16 at 13:27
I suspect it may be a hyperbola (or close to one) providing that the sun actually sets: see en.wikipedia.org/wiki/Hyperbola#Sundials
– Henry
Jul 16 at 13:27
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
(This is mostly just an amplification of @Henry's comment, which I didbn't read carefully until after I'd written it...sigh.)
The shadow tip does not trace a straight line. But at a local scale, it probably comes close enough to work for the purpose shown.
Here's the proof that it doesn't: move north of the arctic circle during midsummer, where the sun's above the horizon all day long, and appears, over the course of a day, to trace a circle around the whole horizon (rising and falling a bit as it does so). The arc traced out by the shadow-tip must then be a simple closed curve, hence not a line.
Now maybe you think "Well, that's a special case...if you're south of the arctic circle, you're OK. If you move a little bit south of the arctic circle, then things are fine." But the shape of the shadow-tip-trace must varies "continuously" as a function of latitude (**), so if you move just south of the arctic circle, you get an almost closed curve, hence it's once again not a straight line.
(**) I grant that this assertion needs proof, but not a lot: the displacement of the location of the shadow-tip from the stick-base, at a particular moment in the day, pretty clearly varies continuously as a function of the stick-base location (at least when there actually is a shadow at that hour); from that, and a bit of a compactness argument, you can make a pretty good case that the tip-trace can't jump from being a closed curve to being a straight line as you cross some particular latitude.
answered Jul 16 at 13:48
John Hughes
59.4k23785
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
(This is mostly just an amplification of @Henry's comment, which I didbn't read carefully until after I'd written it...sigh.)
The shadow tip does not trace a straight line. But at a local scale, it probably comes close enough to work for the purpose shown.
Here's the proof that it doesn't: move north of the arctic circle during midsummer, where the sun's above the horizon all day long, and appears, over the course of a day, to trace a circle around the whole horizon (rising and falling a bit as it does so). The arc traced out by the shadow-tip must then be a simple closed curve, hence not a line.
Now maybe you think "Well, that's a special case...if you're south of the arctic circle, you're OK. If you move a little bit south of the arctic circle, then things are fine." But the shape of the shadow-tip-trace must varies "continuously" as a function of latitude (**), so if you move just south of the arctic circle, you get an almost closed curve, hence it's once again not a straight line.
(**) I grant that this assertion needs proof, but not a lot: the displacement of the location of the shadow-tip from the stick-base, at a particular moment in the day, pretty clearly varies continuously as a function of the stick-base location (at least when there actually is a shadow at that hour); from that, and a bit of a compactness argument, you can make a pretty good case that the tip-trace can't jump from being a closed curve to being a straight line as you cross some particular latitude.
answered Jul 16 at 13:48
John Hughes
59.4k23785
add a comment |Â
up vote
2
down vote
(This is mostly just an amplification of @Henry's comment, which I didbn't read carefully until after I'd written it...sigh.)
The shadow tip does not trace a straight line. But at a local scale, it probably comes close enough to work for the purpose shown.
Here's the proof that it doesn't: move north of the arctic circle during midsummer, where the sun's above the horizon all day long, and appears, over the course of a day, to trace a circle around the whole horizon (rising and falling a bit as it does so). The arc traced out by the shadow-tip must then be a simple closed curve, hence not a line.
Now maybe you think "Well, that's a special case...if you're south of the arctic circle, you're OK. If you move a little bit south of the arctic circle, then things are fine." But the shape of the shadow-tip-trace must varies "continuously" as a function of latitude (**), so if you move just south of the arctic circle, you get an almost closed curve, hence it's once again not a straight line.
(**) I grant that this assertion needs proof, but not a lot: the displacement of the location of the shadow-tip from the stick-base, at a particular moment in the day, pretty clearly varies continuously as a function of the stick-base location (at least when there actually is a shadow at that hour); from that, and a bit of a compactness argument, you can make a pretty good case that the tip-trace can't jump from being a closed curve to being a straight line as you cross some particular latitude.
answered Jul 16 at 13:48
John Hughes
59.4k23785
add a comment |Â
up vote
2
down vote
up vote
2
down vote
(This is mostly just an amplification of @Henry's comment, which I didbn't read carefully until after I'd written it...sigh.)
The shadow tip does not trace a straight line. But at a local scale, it probably comes close enough to work for the purpose shown.
Here's the proof that it doesn't: move north of the arctic circle during midsummer, where the sun's above the horizon all day long, and appears, over the course of a day, to trace a circle around the whole horizon (rising and falling a bit as it does so). The arc traced out by the shadow-tip must then be a simple closed curve, hence not a line.
Now maybe you think "Well, that's a special case...if you're south of the arctic circle, you're OK. If you move a little bit south of the arctic circle, then things are fine." But the shape of the shadow-tip-trace must varies "continuously" as a function of latitude (**), so if you move just south of the arctic circle, you get an almost closed curve, hence it's once again not a straight line.
(**) I grant that this assertion needs proof, but not a lot: the displacement of the location of the shadow-tip from the stick-base, at a particular moment in the day, pretty clearly varies continuously as a function of the stick-base location (at least when there actually is a shadow at that hour); from that, and a bit of a compactness argument, you can make a pretty good case that the tip-trace can't jump from being a closed curve to being a straight line as you cross some particular latitude.
answered Jul 16 at 13:48
John Hughes
59.4k23785
(This is mostly just an amplification of @Henry's comment, which I didbn't read carefully until after I'd written it...sigh.)
The shadow tip does not trace a straight line. But at a local scale, it probably comes close enough to work for the purpose shown.
Here's the proof that it doesn't: move north of the arctic circle during midsummer, where the sun's above the horizon all day long, and appears, over the course of a day, to trace a circle around the whole horizon (rising and falling a bit as it does so). The arc traced out by the shadow-tip must then be a simple closed curve, hence not a line.
Now maybe you think "Well, that's a special case...if you're south of the arctic circle, you're OK. If you move a little bit south of the arctic circle, then things are fine." But the shape of the shadow-tip-trace must varies "continuously" as a function of latitude (**), so if you move just south of the arctic circle, you get an almost closed curve, hence it's once again not a straight line.
(**) I grant that this assertion needs proof, but not a lot: the displacement of the location of the shadow-tip from the stick-base, at a particular moment in the day, pretty clearly varies continuously as a function of the stick-base location (at least when there actually is a shadow at that hour); from that, and a bit of a compactness argument, you can make a pretty good case that the tip-trace can't jump from being a closed curve to being a straight line as you cross some particular latitude.
answered Jul 16 at 13:48
John Hughes
59.4k23785
edited Jul 16 at 15:50
answered Jul 16 at 13:48
John Hughes
59.4k23785
answered Jul 16 at 13:48
John Hughes
59.4k23785
answered Jul 16 at 13:48
John Hughes
59.4k23785
59.4k23785
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2853377%2ffinding-direction-using-sun%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
North of the tropics in summer (i.e. now), the sun rises north of east then passes to the south and sets north of west, so the tip of the shadow must start south of west then pass to the north and end south of east. This seems to require a curve to me, and therefore curves are likely in other situations too, but it may be close to a straight line near the middle of the day
– Henry
Jul 16 at 13:01
Ah do you feel it can be a circle parallel to ecliptic or perhaps latitude lines ? I'll need to think a bit more when I get access to paper and pen.. @Henry
– rsadhvika
Jul 16 at 13:07
1
I suspect it may be a hyperbola (or close to one) providing that the sun actually sets: see en.wikipedia.org/wiki/Hyperbola#Sundials
– Henry
Jul 16 at 13:27