So here is the way I do that personnally with NaturalEarth data and R (but you can do something similar i m assuming with any programming language that can deal with GIS or any GIS software):
Fist download and unzip the file:
Every equal-area map displays all countries (and other areas) in their correct relative size. Inevitably, they don't show the correct shape (unless you're looking at a globe). Personally, my favourite projections are pseudocylidrical equal-area projections, such as:
Eckert IV projection
Tobler hyperelliptical projection
You can use Generic Mapping Tools (GMT): http://gmt.soest.hawaii.edu/
It's a command line tool for (among other things) plotting maps and geographical data. Works best on Linux/Mac but also on Windows.
Here's an example. Running this code generates a map:
gmt pscoast -R0/360/-80/85 -JM20 -B20/10 -Di -Glightbrown -Slightblue -Wblack > merc.ps
And this ...
It's almost certainly a difference in the UTM zones.
In most zones, the minimum easting value is 160,000 mE and the max is 834,000 mE (at the equator). People sometimes use the 'wrong' zone (i.e. not the zone that the location is actually in) if it's more convenient to use a neighbouring zone for some reason. For instance, maybe I have coordinates for 100 ...
This is pretty straight forward. The traditional map is very good for longitude and latitude. It's pretty lousy for the shapes and sizes of the continents cause everything close to the poles is expanded.
A more accurate map has to look like a carved up sphere on a flat sheet of paper.
This one claims to be the most accurate: http://imgur.com/gallery/...
Natural Earth is a public domain, map dataset available at 1:10, 1:50,
and 1:110-million scales. Announced at the 2009 NACIS (North American
Cartographic Information Society)annual meeting in Sacramento,
California, the goal is to give cartographers an off-the shelf
solution for creating small-scale world, regional, and country maps.
It has several ...
You are correct about the maximum value, you just have the easting and northing backwards.
In your first example, the easting is 414668 m and the northing is 6812844 m. The convention is eastings first. You can think of UTM coordinates as $(x, y)$ pairs, and they are sometimes labelled as such. Here's the conversion offered by one converter:
As you say, ...
I've been searching for a map that shows all continents in their actual size that is free of projection distortion, to no avail
That's because such a thing does not exist. A projection by definition has distortion, otherwise it would not be a projection.
The only way to have a distortion free view of the planet is by having a physical globe, and looking at ...
The circumference of the Earth at the equator is ~40,075km.
Given that each UTM Zone is 6 degrees spaced in Longitude, there are then 60 UTM Zones around the globe.
Each Zone is thus 40,075/60 or ~668km at the equator (less towards the poles).
The central Easting for each Zone is 500km, therefore the max and min Easting for each Zone is 500+668/2 (834km) and ...