# Poll on *Really* Wide Angle Lenses

Discussion in 'Digital Photography' started by BC, Aug 5, 2005.

1. ### NostrobinoGuest

Yes, but if tangents were drawn at those points *they* would be parallel,
which seems a reasonable basis for calling the points parallel.

N.

Nostrobino, Aug 22, 2005

2. ### David LittlewoodGuest

Plagiarise, plagiarise, plagiarise!
You can't have a "moon" in a Rieman 2-space. The universe consists only
of the spherical surface, nothing else exists.
See above. I guess parallel lines in this world are only parallel at one
(or two) points, though I've never gone into it in detail.

David

David Littlewood, Aug 22, 2005

3. ### David LittlewoodGuest

Only if you accept that "parallelism" is a concept which can be applied
to non-straight lines, which it can't, at least in the world of
mathematics.

David

David Littlewood, Aug 22, 2005
4. ### David LittlewoodGuest

At least in part, I think. It's all so far back I've almost lost the
will to live.

David

David Littlewood, Aug 22, 2005
5. ### NostrobinoGuest

It may have been related to Chris's idea (if I understood him correctly)
that the rules of spherical projection must strictly apply to the retina,
since that is (approximately) hemispherical. That is what I question, since
we don't know (or at least I don't) how accurately the lens of the eye
manages spherical projection. It does not appear to be, and doesn't need to
be, very accurately at all as soon as you move away from the axis.

Yes, definitely.

N.

Nostrobino, Aug 22, 2005
6. ### NostrobinoGuest

Well, he said, "Because you are receiving light reflected from four times as
much wall
area." I wouldn't take that to mean "from the whole wall," only that any
point on the negative receives light from four times as many points on the
wall (as it did at half the distance). In fact, if "the whole wall" were
meant that would be wrong, unless the wall filled the frame vertically as
well as horizontally of course. I doubt he meant that.

N.

Nostrobino, Aug 22, 2005
7. ### Neil EllwoodGuest

Points cannot be either diverging or converging.

Neil Ellwood, Aug 22, 2005
8. ### NostrobinoGuest

Rectilinear, not necessarily wide angle (doesn't matter), wall and film
parallel, lens axis perpendicular to both. On- or near-axis part of the wall
should be presumed, I think, since otherwise moving back from it would
change everything.

N.

Nostrobino, Aug 22, 2005
9. ### PrometheusGuest

I remember my calculus (just, it was a long time ago), hence my comment
about the function. But does knowing what happens when d -> 0 let you
distinguish Euclid, Rieman and Lobachevsky space? Of course the point
of the rail in contact with the wheel can be said to be parallel
(ignoring deformities) or it can be said to be a tangent; neither view
is incorrect but which is more useful depends on rather more. Of course
the rim of the wheel is NOT parallel as can be shown if you consider
more than one point (not the diametrically opposed point), more work for
your calculus, whereas the set of points defining two non-crossing
Euclidean lines can be shown to be parallel for any closest pair.
Actually thinking about it I am not sure that the points where the wheel
touches the rail can be said to be parallel since they reduce to one
point.

Prometheus, Aug 22, 2005
10. ### PrometheusGuest

Nor can they be parallel, but a series of points can be diverging or
converging.

Prometheus, Aug 22, 2005
11. ### ASAARGuest

I was well aware of the "real world" problem cause by deformities,
since I first started to describe the concept using a car's tire on
a road. Even steel is elastic, but I hoped that it would allow the
question of deformities (which don't change what the concept I was
trying to illustrate) to be sidestepped.

That's correct, points have no direction. But a purely
mathematical wheel (unlike a steel, or any other real wheel) would
touch at only one point. And as one looks at a vanishingly small
section of the rim containing the single point that touches the
rail, one would see what appears to be an increasingly straight line
which does have a direction, and which would be parallel to the
rail. Those that don't see this (not referring to you) probably
have non-mathematical reasons for their lack of vision.

ASAAR, Aug 22, 2005
12. ### ASAARGuest

My friend's 10 inch disc was the first one I came across, but my
own copies were all standard 12" LPs. I may have an old 10" Benny
Goodman record from my father's collection buried away somewhere.
There are only a few performances that I can say that I recall
precisely where I was when I first heard them. One was hearing Tom
Lerher's record. Another was Stravinsky's "Rites of Spring", heard
heard live.

ASAAR, Aug 22, 2005
13. ### ASAARGuest

A moon isn't necessary. Would a spherical, infinitesimally thin
shell be acceptable in Rieman's 2-space? Real world objects are
only used to try to make it easier to visualize concepts. I also
thought of describing an orange, cut into slices (the cuts being
great circles) but remaining intact.

ASAAR, Aug 22, 2005
14. ### ASAARGuest

I never said or implied that the entire line or curve was
parallel. Just that a vanishingly small part of it could be
considered to be parallel. That's always been a part of the
mathematics I was taught. But as someone else mentioned here,
tangent surfaces are usually described instead.

ASAAR, Aug 22, 2005
15. ### ASAARGuest

Hang in there David Littlewill. We'd miss your points if you
vanished.

ASAAR, Aug 22, 2005
16. ### David LittlewoodGuest

Indeed, tangents (which are by definition straight lines) can be
parallel.

David

David Littlewood, Aug 22, 2005
17. ### David LittlewoodGuest

Yes; it would of course be a point....

David Littlewood, Aug 22, 2005
18. ### NostrobinoGuest

Though I haven't listened to that Lehrer record for many years (in fact,
don't know where it is now and haven't even owned a turntable to play it on
for many years), I can still clearly recall the tunes and that inimitable
voice of his in at least some of the songs. That Lobachevsky piece for one,
The Boy Scouts' Marching Song, The Old Dope Peddler, and odd fragments of

N.

Nostrobino, Aug 22, 2005
19. ### NostrobinoGuest

<guffaw!>
I know what you mean! Glad I'm not the only one.

N.

Nostrobino, Aug 22, 2005
20. ### David LittlewoodGuest

Sorry, I think I misunderstood; I read as infinitesimal rather than
infinitesimally thin. What you say is in fact a description of the space
itself. Another such space adjacent to it makes as much sense as a
parallel 3D universe lying alongside ours but not touching it.

David Littlewood, Aug 23, 2005