Why are USGS maps called "quadrangles? (why not rectangles?)

James Mick

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Nov 21, 2016, 8:46:13 PM11/21/16

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Why are USGS maps called "quadrangles? (why not rectangles?)

quad·ran·gle: noun Geometry, quadrangle; plural noun: quadrangles
a. a four-sided plane figure, especially a square or rectangle.
b. a square or rectangular space or courtyard enclosed by buildings.
c. the area shown on a standard topographic map sheet of the US Geological
Survey.
synonyms: courtyard, quad, court, cloister, precinct; square, plaza, piazza

The standard USGS map is a 1:24,000 7.5-minute by 7.5-minute "rectangle".
Why do they call it a "quadrangle?"

You can download an extremely detailed example for yourself to see:
1. Go to the USGS map site https://viewer.nationalmap.gov/launch/
2. To download a quadrangle, at the top left, press "Download Maps"
3. This will show in the right pane a map of the United States.
4. Left mouse drag your desired location to the center of that map.
5. Click the + (zoom) 7 times (re-center as needed) to see quadrangles.
6. It's simplest if you zoom until you have only 1 or 2 quadrangles in view.
7. In the left sidebar, click the blue "Find Products" button.
7. In the left sidebar "US Topo Available Products" section, click on the
number of "results".
8. In the left sidebar, scroll until you see the desired quadrangle listed.
9. Once you find the desired quadrangle, right click its "Download" button.
10. Choose to "Save Link As" so as to download the ~30MB PDF quadrangle
file.

Why are the USGS PDF maps called "quadrangles? (why not rectangles?)

Osmium

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Nov 21, 2016, 9:13:13 PM11/21/16

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"James Mick" wrote:

> Why are USGS maps called "quadrangles? (why not rectangles?)
>
> quad·ran·gle: noun Geometry, quadrangle; plural noun: quadrangles
> a. a four-sided plane figure, especially a square or rectangle.

Just a guess. Note the word *especially*. One degree of latitude is
shorter on the north boundary than it is on the south boundary. (In the USA
for example.) I would call it a trapezoid (which seems wrong, too), but I
don't have a real big vocabulary for plane geometry words. Maybe quadrangle
is a better word to use.

Garrett Wollman

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Nov 21, 2016, 10:22:33 PM11/21/16

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In article <e9hntl...@mid.individual.net>,

Osmium <r124c...@comcast.net> wrote:

>Just a guess. Note the word *especially*. One degree of latitude is
>shorter on the north boundary than it is on the south boundary. (In the USA
>for example.)

The maps in question are always done in the Universal Transverse
Mercator projection (for nagivation with a compass) so they actually
are rectangular as drawn. (That's what a Mercator projection does, by
definition.)

-GAWollman

--
Garrett A. Wollman | What intellectual phenomenon can be older, or more oft
wol...@bimajority.org| repeated, than the story of a large research program
Opinions not shared by| that impaled itself upon a false central assumption
my employers. | accepted by all practitioners? - S.J. Gould, 1993

Peter T. Daniels

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Nov 21, 2016, 11:20:40 PM11/21/16

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On Monday, November 21, 2016 at 8:46:13 PM UTC-5, James Mick wrote:

> Why are USGS maps called "quadrangles? (why not rectangles?)
>
> quad·ran·gle: noun Geometry, quadrangle; plural noun: quadrangles
> a. a four-sided plane figure, especially a square or rectangle.
> b. a square or rectangular space or courtyard enclosed by buildings.
> c. the area shown on a standard topographic map sheet of the US Geological
> Survey.
> synonyms: courtyard, quad, court, cloister, precinct; square, plaza, piazza
>
> The standard USGS map is a 1:24,000 7.5-minute by 7.5-minute "rectangle".
> Why do they call it a "quadrangle?"

7.5 x 7.5 sure sounds square to me. To find out why it doesn't look like
a square, consult a globe. Or a textbook of spherical geometry.

Lewis

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Nov 22, 2016, 9:08:46 AM11/22/16

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In message <o1080v$6ac$1...@gioia.aioe.org>

James Mick <JamesM...@yahoo.com> wrote:
> Why are USGS maps called "quadrangles? (why not rectangles?)

When you put a rectangle onto a surface like a globe you do not get a
rectangle.

> The standard USGS map is a 1:24,000 7.5-minute by 7.5-minute "rectangle".
> Why do they call it a "quadrangle?"

Because its sides are curved.

--
And what rough beast, its hour come round at last,
Slouches towards Bethlehem to be born.

Richard Heathfield

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Nov 22, 2016, 9:16:13 AM11/22/16

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On 22/11/16 14:08, Lewis wrote:
> In message <o1080v$6ac$1...@gioia.aioe.org>
> James Mick <JamesM...@yahoo.com> wrote:
>> Why are USGS maps called "quadrangles? (why not rectangles?)
>
> When you put a rectangle onto a surface like a globe you do not get a
> rectangle.

Or, to say the same thing a different way, the concept of "rectangle" (a
figure with four angles, all equal) is of limited use when your frame of
reference is a sphere.

>
>> The standard USGS map is a 1:24,000 7.5-minute by 7.5-minute "rectangle".
>> Why do they call it a "quadrangle?"
>
> Because its sides are curved.

Yes, but they straighten out nicely when you map the quad onto a sphere
(because "straight" means something slightly different on a sphere).

--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

John Varela

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Nov 22, 2016, 11:06:02 AM11/22/16

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On Tue, 22 Nov 2016 01:46:08 UTC, James Mick
<JamesM...@yahoo.com> wrote:

> Why are USGS maps called "quadrangles? (why not rectangles?)
>

> quadÀranÀgle: noun Geometry, quadrangle; plural noun: quadrangles

Because they have four straight sides, as defined on a sphere.

--
John Varela

Whiskers

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Nov 22, 2016, 12:00:17 PM11/22/16

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On 2016-11-22, James Mick <JamesM...@yahoo.com> wrote:
> Why are USGS maps called "quadrangles? (why not rectangles?)
>
> quad·ran·gle: noun Geometry, quadrangle; plural noun: quadrangles
> a. a four-sided plane figure, especially a square or rectangle.
> b. a square or rectangular space or courtyard enclosed by buildings.
> c. the area shown on a standard topographic map sheet of the US Geological
> Survey.
> synonyms: courtyard, quad, court, cloister, precinct; square, plaza, piazza
>
> The standard USGS map is a 1:24,000 7.5-minute by 7.5-minute "rectangle".
> Why do they call it a "quadrangle?"

[...]

Probably because it isn't a square world. Any attempt at representing
the surface of the globe on a flat sheet will introduce distortions;
if you try to make compass bearings appear as straight lines (which is a
good start for a map used for getting from point A to point B) then some
of the distances are going to be incorrect - by how much, and
whereabouts on the map the errors are worst, is part of the art of
map-making. Compare Antarctica's appearance on different flat maps and
globes to see how extreme the distortions can be.

The USGS maps represent areas of the Earth's surface defined by their
latitude and longitude. As the USA is entirely within the northern
hemisphere, all those maps will have a northern edge that covers fewer
miles in width than the southern edge does; so the area represented
cannot be a 'rectangle' but it is a 'quadrangle' (although the maps
almost certainly are rectangles).

The UK Ordnance Survey takes a different approach (and has to deal with
a much smaller area too, which changes the challenge) and uses a grid of
1km squares onto which the lines of longitude can be projected as curves.

Both arrangements are designed to ensure that people can use compass
and map to get close enough to their destination to find it visually on
arrival, and identify their position with similar accuracy. The
distortions will be different, but tolerable within the scope of normal
use.

--
-- ^^^^^^^^^^
-- Whiskers
-- ~~~~~~~~~~