### louder and funnier

here’s the page i munged yesterday, four times bigger

(twice in each dimension, duh). one (more) plainly

sees here that points of an arbitrary hemisphere

(in the top drawing of the lower right panel)

can be identified with longitude-and-latitude pairs

.

such co-ordinates depend on “choosing

a central meridian” (this was done for

usual planetary co-ordinates by passing

the central meridian through greenwich).

on the drawing (and the planet), we’re

*given* a cutting-of-the-sphere. but

on a more abstractly-given sphere

(in some other context) we might need

to consider *how* the sphere is to be

cut into hemispheres (and *which* hemi-

sphere is to be “drawn” [or what have

you… “studied”]).

on our globe-of-the-world model, this would

amount to selecting a different “north pole”

(notice that this gives us an “equator”,

as it were, “for free”).

since the (actual) north pole has a *fixed*

position, we might consider shifting our

“point-of-view” as if we were some satellite,

far enough away to see half the surface

of the “planet” we want to co-ordinatize.

when we look down *from the north pole*,

the “equator” for this point-of-view

is then (of course) the *actual* equator

(the great circle equidistance from the

two poles).

when our satellite is over some *other*

“point” (of our beloved mother earth),

what we’ll see “looking down” is essentially

a *polar projection* of (half of) the surface.

our co-ordinate frame on this model would then

appear as (1) a collection of concentric circles

(the analogues of “latitude”… the angle measured

“up north” [on the north pole model] having been

replaced by the “distance in” [toward the new center])

and (2) a collection of radii (the “meridians”…

measuring the “angle from greenwich” on the

globe and the “angle from the top of the

camera view” (say) in the space-travel version.

all this is perfectly straightforward

& beginners pick it up in a few minutes

of lecture if they’ve got any experience

with maps-of-the-world.

the tricky bits are the reason for all the

“identification diagrams” littered about

the rest of the page. and about these,

i propose to say but little. today.

heck, very little. “identify antipodes.”

here’s a song while i fix breakfast.

ana ng at yootube. (ad-ridden, natch.)

May 5, 2015 at 7:41 pm

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