The area was measured on the map

# Self-authored for the EML case corpus (no external origin). A coverage report
# gives each region's share of the mapped land, computed from the pixels each
# region occupies on the web map. The pixel counts are real and the shares are
# correctly divided. What a pixel of the map measures is computed below.
#
# The report is careful. It counts real rendered pixels, not estimates; it covers
# every region on the map; the shares are the honest division of each count by
# the total; and the intent is exactly 'each region's share of the land'.
#
# The web map is a Mercator projection, which keeps angles by stretching area by
# the inverse square of the cosine of the latitude, so a region at 70 north is
# drawn about fourteen times larger than its land.

2166 => greenland_true_area_thousand_km2
30370 => africa_true_area_thousand_km2
30000 => greenland_area_on_the_map
30370 => africa_area_on_the_map

greenland_true_area_thousand_km2 + africa_true_area_thousand_km2 => true_total
int(greenland_true_area_thousand_km2 * 10000 / true_total) => greenland_true_share_per_myriad
greenland_area_on_the_map + africa_area_on_the_map => map_total
int(greenland_area_on_the_map * 10000 / map_total) => greenland_map_share_per_myriad
int(africa_true_area_thousand_km2 / greenland_true_area_thousand_km2) => africa_over_greenland_true
int(africa_area_on_the_map / greenland_area_on_the_map) => africa_over_greenland_on_the_map
int(greenland_map_share_per_myriad * 10 / greenland_true_share_per_myriad) => greenland_share_inflated_tenths

"Greenland, true area            : " + str(greenland_true_area_thousand_km2) + " thousand km2" ^0
"Africa, true area               : " + str(africa_true_area_thousand_km2) + " thousand km2" ^0
"Africa over Greenland, true     : " + str(africa_over_greenland_true) + " to 1" ^0
"" ^0
"Greenland, area on the map      : " + str(greenland_area_on_the_map) ^0
"Africa, area on the map         : " + str(africa_area_on_the_map) ^0
"Africa over Greenland, on map   : " + str(africa_over_greenland_on_the_map) + " to 1" ^0
"" ^0
"Greenland share, true           : " + str(greenland_true_share_per_myriad) + " per ten thousand" ^0
"Greenland share, from the map   : " + str(greenland_map_share_per_myriad) + " per ten thousand" ^0
"share inflated by               : " + str(greenland_share_inflated_tenths) + " tenths, about 7 times" ^0
"" ^0

# ---- what the report verified ----

"the coverage report" ^0
"  counts : real rendered pixels, not estimates" ^0
"  covers : every region on the map" ^0
"  shares : the honest division of each count by the total" ^0
"  intent : each region's share of the land" ^0
"  regions omitted : 0" ^0
"  verdict : GREENLAND IS HALF THE MAPPED AREA" ^0
"" ^0
"  counting real pixels over every region and dividing" ^0
"  honestly is the part done right here, and it is why the" ^0
"  shares are exact for the picture" ^0
"" ^0

# ---- what a pixel of the map measures ----

"the Mercator projection" ^0
"  what it preserves : angles, so a compass course is a" ^0
"    straight line" ^0
"  what it pays with : area, stretched by the inverse square" ^0
"    of the cosine of the latitude" ^0
"  at 70 north the cosine is about a third : area drawn" ^0
"    about nine times over; averaged over Greenland, about" ^0
"    fourteen" ^0
"  so a pixel : is a fixed piece of the picture, not a fixed" ^0
"    piece of the ground" ^0
"" ^0

# ---- what the caller got ----

"the reported shares" ^0
"  Greenland's share as reported : " + str(greenland_map_share_per_myriad) + " per ten thousand" ^0
"  Greenland's share of the land : " + str(greenland_true_share_per_myriad) + " per ten thousand" ^0
"  is the pixel count wrong : no; it is exact for the map" ^0
"  is the map the land : no; at 70 north it is drawn" ^0
"    fourteen times too large" ^0
"" ^0

# ---- null control ----

# The same regions, measured in an equal-area projection (or by geodesic area on
# the ellipsoid) instead of on the Mercator picture.
4969 => nc_greenland_share_on_mercator
665 => nc_greenland_share_equal_area
1 => nc_africa_over_greenland_on_mercator
14 => nc_africa_over_greenland_equal_area

"null control - measure in an equal-area projection" ^0
"  Greenland share, Mercator : " + str(nc_greenland_share_on_mercator) + " per ten thousand" ^0
"  Greenland share, equal-area : " + str(nc_greenland_share_equal_area) + " per ten thousand" ^0
"  Africa over Greenland, on Mercator : " + str(nc_africa_over_greenland_on_mercator) + " to 1" ^0
"  Africa over Greenland, equal-area : " + str(nc_africa_over_greenland_equal_area) + " to 1" ^0
"  no region and no pixel count changed; the pixels stopped" ^0
"  standing for equal pieces of ground" ^0
"" ^0

# ---- the rule ----

"what a pixel-share report guarantees" ^0
"  each region's share of the picture is correct : exactly," ^0
"    real pixels, every region, honest division" ^0
"  each region's share of the land is correct : not" ^0
"    addressed; Mercator stretches area by the inverse square" ^0
"    of the cosine of the latitude, so Greenland at " + str(greenland_true_share_per_myriad) + " per" ^0
"    ten thousand of the land is " + str(greenland_map_share_per_myriad) + " of the map" ^0
"" ^0

"a projection is a bargain, and Mercator buys straight compass lines with area;" ^0
"what a pixel covers on the ground grows without bound toward the poles, so a" ^0
"count of pixels is a count of picture, and the picture is not to scale" ^0
"" ^0

"It counts real pixels over every region and divides honestly - the shares are" ^0
"exact for the picture. But the picture is Mercator, which draws Greenland about" ^0
"fourteen times its land, so a region that is " + str(greenland_true_share_per_myriad) + " per ten thousand of the" ^0
"ground reports as " + str(greenland_map_share_per_myriad) + ", until the area is measured on an equal-area projection." ^0

greenland_true_area_thousand_km2 = 2166
africa_true_area_thousand_km2 = 30370
greenland_area_on_the_map = 30000
africa_area_on_the_map = 30370
true_total = greenland_true_area_thousand_km2 + africa_true_area_thousand_km2
greenland_true_share_per_myriad = int(greenland_true_area_thousand_km2 * 10000 / true_total)
map_total = greenland_area_on_the_map + africa_area_on_the_map
greenland_map_share_per_myriad = int(greenland_area_on_the_map * 10000 / map_total)
africa_over_greenland_true = int(africa_true_area_thousand_km2 / greenland_true_area_thousand_km2)
africa_over_greenland_on_the_map = int(africa_area_on_the_map / greenland_area_on_the_map)
greenland_share_inflated_tenths = int(greenland_map_share_per_myriad * 10 / greenland_true_share_per_myriad)
print("Greenland, true area            : " + str(greenland_true_area_thousand_km2) + " thousand km2")
print("Africa, true area               : " + str(africa_true_area_thousand_km2) + " thousand km2")
print("Africa over Greenland, true     : " + str(africa_over_greenland_true) + " to 1")
print("")
print("Greenland, area on the map      : " + str(greenland_area_on_the_map))
print("Africa, area on the map         : " + str(africa_area_on_the_map))
print("Africa over Greenland, on map   : " + str(africa_over_greenland_on_the_map) + " to 1")
print("")
print("Greenland share, true           : " + str(greenland_true_share_per_myriad) + " per ten thousand")
print("Greenland share, from the map   : " + str(greenland_map_share_per_myriad) + " per ten thousand")
print("share inflated by               : " + str(greenland_share_inflated_tenths) + " tenths, about 7 times")
print("")
print("the coverage report")
print("  counts : real rendered pixels, not estimates")
print("  covers : every region on the map")
print("  shares : the honest division of each count by the total")
print("  intent : each region's share of the land")
print("  regions omitted : 0")
print("  verdict : GREENLAND IS HALF THE MAPPED AREA")
print("")
print("  counting real pixels over every region and dividing")
print("  honestly is the part done right here, and it is why the")
print("  shares are exact for the picture")
print("")
print("the Mercator projection")
print("  what it preserves : angles, so a compass course is a")
print("    straight line")
print("  what it pays with : area, stretched by the inverse square")
print("    of the cosine of the latitude")
print("  at 70 north the cosine is about a third : area drawn")
print("    about nine times over; averaged over Greenland, about")
print("    fourteen")
print("  so a pixel : is a fixed piece of the picture, not a fixed")
print("    piece of the ground")
print("")
print("the reported shares")
print("  Greenland's share as reported : " + str(greenland_map_share_per_myriad) + " per ten thousand")
print("  Greenland's share of the land : " + str(greenland_true_share_per_myriad) + " per ten thousand")
print("  is the pixel count wrong : no; it is exact for the map")
print("  is the map the land : no; at 70 north it is drawn")
print("    fourteen times too large")
print("")
nc_greenland_share_on_mercator = 4969
nc_greenland_share_equal_area = 665
nc_africa_over_greenland_on_mercator = 1
nc_africa_over_greenland_equal_area = 14
print("null control - measure in an equal-area projection")
print("  Greenland share, Mercator : " + str(nc_greenland_share_on_mercator) + " per ten thousand")
print("  Greenland share, equal-area : " + str(nc_greenland_share_equal_area) + " per ten thousand")
print("  Africa over Greenland, on Mercator : " + str(nc_africa_over_greenland_on_mercator) + " to 1")
print("  Africa over Greenland, equal-area : " + str(nc_africa_over_greenland_equal_area) + " to 1")
print("  no region and no pixel count changed; the pixels stopped")
print("  standing for equal pieces of ground")
print("")
print("what a pixel-share report guarantees")
print("  each region's share of the picture is correct : exactly,")
print("    real pixels, every region, honest division")
print("  each region's share of the land is correct : not")
print("    addressed; Mercator stretches area by the inverse square")
print("    of the cosine of the latitude, so Greenland at " + str(greenland_true_share_per_myriad) + " per")
print("    ten thousand of the land is " + str(greenland_map_share_per_myriad) + " of the map")
print("")
print("a projection is a bargain, and Mercator buys straight compass lines with area;")
print("what a pixel covers on the ground grows without bound toward the poles, so a")
print("count of pixels is a count of picture, and the picture is not to scale")
print("")
print("It counts real pixels over every region and divides honestly - the shares are")
print("exact for the picture. But the picture is Mercator, which draws Greenland about")
print("fourteen times its land, so a region that is " + str(greenland_true_share_per_myriad) + " per ten thousand of the")
print("ground reports as " + str(greenland_map_share_per_myriad) + ", until the area is measured on an equal-area projection.")

Greenland, true area            : 2166 thousand km2
Africa, true area               : 30370 thousand km2
Africa over Greenland, true     : 14 to 1

Greenland, area on the map      : 30000
Africa, area on the map         : 30370
Africa over Greenland, on map   : 1 to 1

Greenland share, true           : 665 per ten thousand
Greenland share, from the map   : 4969 per ten thousand
share inflated by               : 74 tenths, about 7 times

the coverage report
  counts : real rendered pixels, not estimates
  covers : every region on the map
  shares : the honest division of each count by the total
  intent : each region's share of the land
  regions omitted : 0
  verdict : GREENLAND IS HALF THE MAPPED AREA

  counting real pixels over every region and dividing
  honestly is the part done right here, and it is why the
  shares are exact for the picture

the Mercator projection
  what it preserves : angles, so a compass course is a
    straight line
  what it pays with : area, stretched by the inverse square
    of the cosine of the latitude
  at 70 north the cosine is about a third : area drawn
    about nine times over; averaged over Greenland, about
    fourteen
  so a pixel : is a fixed piece of the picture, not a fixed
    piece of the ground

the reported shares
  Greenland's share as reported : 4969 per ten thousand
  Greenland's share of the land : 665 per ten thousand
  is the pixel count wrong : no; it is exact for the map
  is the map the land : no; at 70 north it is drawn
    fourteen times too large

null control - measure in an equal-area projection
  Greenland share, Mercator : 4969 per ten thousand
  Greenland share, equal-area : 665 per ten thousand
  Africa over Greenland, on Mercator : 1 to 1
  Africa over Greenland, equal-area : 14 to 1
  no region and no pixel count changed; the pixels stopped
  standing for equal pieces of ground

what a pixel-share report guarantees
  each region's share of the picture is correct : exactly,
    real pixels, every region, honest division
  each region's share of the land is correct : not
    addressed; Mercator stretches area by the inverse square
    of the cosine of the latitude, so Greenland at 665 per
    ten thousand of the land is 4969 of the map

a projection is a bargain, and Mercator buys straight compass lines with area;
what a pixel covers on the ground grows without bound toward the poles, so a
count of pixels is a count of picture, and the picture is not to scale

It counts real pixels over every region and divides honestly - the shares are
exact for the picture. But the picture is Mercator, which draws Greenland about
fourteen times its land, so a region that is 665 per ten thousand of the
ground reports as 4969, until the area is measured on an equal-area projection.

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