The Geometry of Globes

Hockney & Falco propose that the accuracy of the geometry in this globe support the idea that Holbein must have projected the image of a real globe to achieve this accuracy.

Visually, however, one can tell that there is something wrong with the handle. At the surface of the globe, the ellipse seems to be too oblique, whereas at the top of the handle the ellipses seem too flattened and too circular, suggesting that Holbein had not used optical projection for this feature.

Did Holbein trace the globe using a lens? If he did, the lines on the globe should be accurate. If he drew it, the lines might not be. Let us examine several tests of a true globe:

• Is the outline a circle? A sphere or globe, will always have a perfect circular perimeter, viewed from any angle. In the picture, it does.
   
• Are all the lines bounded by the outer circle? The longitude and latitude lines are perfect circles, encircling the globe, but viewed from an angle, they are ovals. In reality, the ovals must be fully contained within the outer circle. Moreover, the longitude lines must project as ellipses touching the perimeter, twice. We trace Holbein's lines, and they are consistent.
   
• Are the latitude lines in the right place? On Holbein's globe, the equator is the thick red line going through the middle of Africa. The Tropic of Cancer is at 23.5° North, and the Arctic Circle is at 66.5° North. The angles of these great circle was known in the 16th century. If we reconstruct a globe, with the North Pole matching Holbein's picture, the Arctic circle matches closely, but the Tropic of Cancer and the Arctic Circle do not.
   
• Are the longitude lines in the right place? On Holbein's globe, the longitude lines appear to be spaced every 30° East to West. If we closely match the longitude lines though Egypt Asia, and Greenland match; but the lines though Europe and the Atlantic do not.