The Winkel-Tripel World Map Projection was proposed by Oswald Winkel in 1921.
The word tripel, German for triple, represents its three major qualities when compared to the Earth: correct proportions, directions and distances.
Shapes are reasonably maintained, except for the curves which are inherent to any round map.
Click on the image below to see a larger view of the Winkel-Tripel World Map Projection:
Sources -
http://www.sdgs.usd.edu/pubs/Scans/NG%20The%20World.jpg
https://tomduhamel.wordpress.com/2014/01/09/the-world-map-is-wrong/