Creating accurate world maps is mathematically impossible.
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Maps are flat representations of our spherical planet. Johnny Harris cut open a plastic globe to understand what it takes to turn a sphere into something flat.

His efforts to turn the plastic globe into a flat map represent a challenge that cartographers have faced for centuries: it is mathematically impossible to transfer the surface of a sphere to a plane without some form of distortion.

To solve this problem, mathematicians and cartographers have developed a huge library of representations of the globe, each of which distorts a particular feature and preserves others.

For example, the Mercator projection preserves the shape of countries while distorting their size, especially near the North and South Poles.

For a more accurate representation of land area, use the Gall-Peters projection, which preserves the area but distorts the shape.

Ultimately, there is no /"right/" map projection. Each has its advantages and disadvantages, and cartographers make decisions about projection based on the task at hand. However, if you are interested in an accurate representation of the planet, your best bet is to stick with a globe.

Interact with projections: http://metrocosm.com/compare-map-projections.html
Mercator tool: http://thetruesize.com/
Mike Bostock map transitions: http://bl.ocks.org/mbostock/3711652
Mercator Puzzle: http://hive.sewanee.edu/ldale/maps/10/06-LOCAL.html

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