RE: due east photos

[R. Hooijenga]

I wonder how anyone can think that the placement of an arbritrarily chosen
coordinate net on the globe will change the actual direction from A to B.

 

Suppose there were no coordinate system, and all we had was the globe and
points A and B on it.

No doubt, all would agree on what would constitute the direction from A to
B: it would be what a piece of string would do when pulled taut between the
points. Or the way in which a car would have to be driven over the surface
when only going 'straight ahead'.

To be sure, one could take the other way round; but this would still concern
the same great circle.

 

Now, add two more points; for the sake of argument, let these be called N
and S and be opposite each other on the globe.

Draw a family of lines from N to S, spread out all around the globe. We
could call them 'meridians', if we like.

Does the existence of these meridians miraculously change the position of
the taut string, or does it make the car suddenly drive differently?

 

One may certainly construct a curve from A to B which intersects all the
meridians at equal angles. But the position of such a curve on the globe
would be entirely dependent on the chosen locations for N and S. 

 

It seems humorous to me that anyone could think that the direction to Mecca
should correspond to (the start of) such an arbitrary curve, - especially
when one considers that Mercator projection did not exist at the time this
rule was postulated.

 

Rudolf

 

Van: sundial [mailto:sundial-boun...@uni-koeln.de] Namens Brent
Verzonden: donderdag 24 september 2015 22:12
Aan: sundial@uni-koeln.de
Onderwerp: Re: due east photos

 

I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent



 

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RE: due east photos

[Jack Aubert]

Why not?  Richard Feynman argued that that a quantum mechanical particle can
take an infinite number of paths between two points to explain the wave
function.  Or something like that.  I don’t actually understand that stuff
myself. Maybe the direction to Mecca should be a wave function.  

 

https://www.quora.com/What-is-Richard-Feynmans-sum-over-paths-approach-to-qu
antum-mechanics

 

Jack

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: Thursday, September 24, 2015 5:58 PM
To: Bill Gottesman
Cc: Sundials List
Subject: Re: due east photos

 

"an infinite number of compass directions to Mecca"

allahu akbar!



.

On 9/24/2015 2:39 PM, Bill Gottesman wrote:

Well, if you are going to allow compass directions, then that opens the door
to all loxodromes.  There are an infnite number of loxodromes that connect
two points on a sphere, if you allow loxodrome paths that travel more than
once around the globe!  This gives an infinite number of compass directions
to Mecca. 

 

-Bill

 

On Thu, Sep 24, 2015 at 4:11 PM, Brent  wrote:

I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent 

 



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Re: due east photos

[Brent]

"an infinite number of compass directions to Mecca"

allahu akbar!



.

On 9/24/2015 2:39 PM, Bill Gottesman wrote:
Well, if you are going to allow compass directions, then that opens 
the door to all loxodromes.  There are an infnite number of loxodromes 
that connect two points on a sphere, if you allow loxodrome paths that 
travel more than once around the globe!  This gives an infinite number 
of compass directions to Mecca.


-Bill

On Thu, Sep 24, 2015 at 4:11 PM, Brent > wrote:


I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent



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Re: due east photos

[Bill Gottesman]

Well, if you are going to allow compass directions, then that opens the
door to all loxodromes.  There are an infnite number of loxodromes that
connect two points on a sphere, if you allow loxodrome paths that travel
more than once around the globe!  This gives an infinite number of compass
directions to Mecca.

-Bill

On Thu, Sep 24, 2015 at 4:11 PM, Brent  wrote:

> I think you can face Mecca from 4 directions:
>
> 1. along great circle shortest direction
> 2. along great circle longest direction
> 3. along constant compass method shortest direction
> 4. along constant compass method longest direction
>
> I wonder if it says in Koran to face Mecca in shortest direction?
>
> brent
>
>
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Re: due east photos

[Brent]

I think you can face Mecca from 4 directions:

1. along great circle shortest direction
2. along great circle longest direction
3. along constant compass method shortest direction
4. along constant compass method longest direction

I wonder if it says in Koran to face Mecca in shortest direction?

brent


On 9/24/2015 12:20 PM, Brent wrote:
Apparently Muslims have a similar problem when determining which way 
to pray towards Mecca (Qibla).

This non-scientific website gives  a choice of 2 different directions:

https://threesixty360.wordpress.com/2008/09/01/which-direction-is-mecca/

There is more confusion found in the comments at the bottom of that 
website.


brent



On 9/17/2015 2:05 AM, Richard Mallett wrote:

On 17/09/2015 09:31, Fabio nonvedolora wrote:

well said Jack,
flat Earth and similar are unlikely :-)
globe
Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Ita
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)


The comedian Michael Bentine used to have a show called 'It's a 
Square World' on BBC TV when I was young :-)


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Eaton Bray, Dunstable
South Beds. UK


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Re: due east photos

[Brent]

Apparently Muslims have a similar problem when determining which way to 
pray towards Mecca (Qibla).

This non-scientific website gives  a choice of 2 different directions:

https://threesixty360.wordpress.com/2008/09/01/which-direction-is-mecca/

There is more confusion found in the comments at the bottom of that website.

brent



On 9/17/2015 2:05 AM, Richard Mallett wrote:

On 17/09/2015 09:31, Fabio nonvedolora wrote:

well said Jack,
flat Earth and similar are unlikely :-)
globe
Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Ita
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)


The comedian Michael Bentine used to have a show called 'It's a Square 
World' on BBC TV when I was young :-)


--
--
Richard Mallett
Eaton Bray, Dunstable
South Beds. UK


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Re: due east photos

[Richard Mallett]

On 17/09/2015 09:31, Fabio nonvedolora wrote:

well said Jack,
flat Earth and similar are unlikely :-)
globe
Fabio
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Ita
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)


The comedian Michael Bentine used to have a show called 'It's a Square 
World' on BBC TV when I was young :-)


--
--
Richard Mallett
Eaton Bray, Dunstable
South Beds. UK

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Re: due east photos

[Fabio nonvedolora]

well said Jack,

flat Earth and similar are unlikely :-)



Fabio

Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Italy
45° 34' 10'' N, 9° 10' 9'' E, GMT+1 (DST +2)

From: Jack Aubert 
Sent: Thursday, September 17, 2015 12:21 AM
To: 'Brent' ; 'sundial' 
Subject: RE: due east photos

Maybe it helps to bear in mind that while all triangles on a plane surfaces 
contain 180 degrees, this is not true on a sphere.  You cannot make a triangle 
on a plane surface that has two 90 degree angles because the sides will never 
meet.

 

On a sphere, however, a triangle can easily have two 90 degree angles.  If one 
side is congruent with the equator then the two sides will meet at the pole.  
The angle a the pole depends on the length of the equatorial side.  A triangle 
with three 90 degree angles will take up one eighth of the sphere’s surface.

 

East, west, north and south are spherical directions, not straight line on a 
plane surface. 

 

Jack Aubert

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: Tuesday, September 15, 2015 9:47 PM
To: sundial
Subject: due east photos

 

I am having an off list discussion with Dave but I have a photo that you may 
find informative.

I resized them for the list so I hope you can see the latitude lines.

what you are seeing is my globe oriented on north south axis and correct angle 
for latitude.

I have a ruler close to my location with the zero on a latitude line

I am pointing the ruler due east, where the sun will rise on the equinox as it 
peaks over my horizon.

As we look straight down you see a deviation from the latitude line of about 1" 
at 4" on the ruler.

Just rough scale 4" = 4,000 miles so 1" equals 1,000 miles = 25% deviation.

My horizon is about 50 miles from here so when I look at the sunrise on the 
equinox my latitude is 
actually about 12.5 miles north of that point on the horizon.

So it's not an insignificant difference.

brent

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RE: due east photos

[Jack Aubert]

Maybe it helps to bear in mind that while all triangles on a plane surfaces 
contain 180 degrees, this is not true on a sphere.  You cannot make a triangle 
on a plane surface that has two 90 degree angles because the sides will never 
meet.

 

On a sphere, however, a triangle can easily have two 90 degree angles.  If one 
side is congruent with the equator then the two sides will meet at the pole.  
The angle a the pole depends on the length of the equatorial side.  A triangle 
with three 90 degree angles will take up one eighth of the sphere’s surface.

 

East, west, north and south are spherical directions, not straight line on a 
plane surface. 

 

Jack Aubert

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Brent
Sent: Tuesday, September 15, 2015 9:47 PM
To: sundial
Subject: due east photos

 

I am having an off list discussion with Dave but I have a photo that you may 
find informative.

I resized them for the list so I hope you can see the latitude lines.

what you are seeing is my globe oriented on north south axis and correct angle 
for latitude.

I have a ruler close to my location with the zero on a latitude line

I am pointing the ruler due east, where the sun will rise on the equinox as it 
peaks over my horizon.

As we look straight down you see a deviation from the latitude line of about 1" 
at 4" on the ruler.

Just rough scale 4" = 4,000 miles so 1" equals 1,000 miles = 25% deviation.

My horizon is about 50 miles from here so when I look at the sunrise on the 
equinox my latitude is 
actually about 12.5 miles north of that point on the horizon.

So it's not an insignificant difference.

brent

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Re: due east photos

[koolish]

At any point on the earth, there is one great circle that
is tangent to your latitude circle. That means that at that
infinitesimally small point, both circles point in the same
direction, i.e due east, but only at that point.

Also note that the plane that cuts the earth at any
latitude is perpendicular to the north-south axis of
the sphere but is not perpendicular to the surface.
The plane that cuts a great circle is perpendicular
to the surface. So if you walk along a latitude circle,
you are not standing in the plane of the circle but
are tilted by the angle of your latitude.




> I am having an off list discussion with Dave but I have a photo that you
> may find informative.
>
> I resized them for the list so I hope you can see the latitude lines.
>
> what you are seeing is my globe oriented on north south axis and correct
> angle for latitude.
>
> I have a ruler close to my location with the zero on a latitude line
>
> I am pointing the ruler due east, where the sun will rise on the equinox
> as it peaks over my horizon.
>
> As we look straight down you see a deviation from the latitude line of
> about 1" at 4" on the ruler.
>
> Just rough scale 4" = 4,000 miles so 1" equals 1,000 miles = 25%
> deviation.
>
> My horizon is about 50 miles from here so when I look at the sunrise on
> the equinox my latitude is
> actually about 12.5 miles north of that point on the horizon.
>
> So it's not an insignificant difference.
>
> brent
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> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>


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