The turnip we all know and love today is not the same turnip that has always been. Originally, turnips were very narrow and flat. These turnips were about a centimetre thick, and twenty centimetres in diameter. While this made it easier to plant a great number of them in rows, occasionally farmers would get the seeds the wrong way around and the turnips would grow askew when they collided underground. This started to become a real problem in the 11th Century.
Turnip-stacking wasn't possible with deformed turnips, meaning valuable storage space was taken up, and cleaning up the collapse of a stack of turnips that had a single warped turnip placed in the middle was time-consuming. Even worse, the deformed ones were not aesthetically pleasing to the aristocracy. Petty feudal lords would have farmers thrashed soundly if their turnips were not flat and easy to cut up on the plate. "Mine turnips shalle be flatte, as a bent turnippe is an abomination in thee eye of the Lord as much as in thee eye of the hungry!" was one statement from a particularly angry baron, who had several farmers executed for the crime of presenting twisted turnips.
To avoid the various cruel fates, ranging from being put in the stocks and pelted with rotting vegetables (usually deformed turnips) to execution, farmers had to spend countless extra hours carefully placing turnip seeds in the soil so that all the crops would line up. This dragged out the planting season to ridiculous length, and many farmers had to work late into the night or face the possibility of not getting enough precious turnips planted.
Seeing the plight of the poor peasants, a monk called Bertram took it upon himself to find an answer. After some careful enquiry he found that the problem was not so much that the turnips were bent, but that such a deformed vegetable was no longer symmetrical. Brother Bertram spent five long years trying to think up a more acceptable form of turnip. His notes on the matter have been preserved, and they show that he was very methodical, going through several different ideas. He started with with cubic turnips, passing through pyramids, cones, dodecahedrons, and many more shapes, before finally realising after painstaking investigations into geometry that a roughly spherical turnip might be a simpler option to actually breed.
Having come to this conclusion, he set out to find some sample turnips to start his turnip breeding with. It took another five long years trekking around Europe before he finally gathered some turnips that looked promising. The key was to find examples of the plant that were bulging outward near enough to the centre of the flat face of the turnip. After returning to his monastery, he started to breed turnips. After another twenty years, mainly involving a lot of turnip farming, he finally produced the turnip we know today: The 3D turnip.
The name comes from a description of the problem Brother Bertram faced, written in the margin of his intricate diagrams of turnip geometry: "The present turnippe hath only two dimensions of note, height and width, it's breadth being insignificante. It is my object to breed a turnip of three dimensions. For such a turnippe, havinge along with height and width, a breadth of equalle measure, shall thus satisfy this curious passione for vegetables of a symmetrical nature amongst the nobles. Thus shall the labour and livelihood of the poor folk be spared."
The new turnip was a runaway success, apart from the initial false start of certain landed people getting angry when the round turnips rolled off their plates. The speedy invention of the turnip cup, using the same principle as the egg-cup, solved that problem. Thanks to the popularity of the new and geometrically pleasing vegetable, the old flat turnip was on the fast track to extinction, and Bertram ended up being beatified some four hundred years after his death as Saint Bertram, patron saint of turnip farmers.
These days we only have the 3D turnip. Occasionally a throwback turnip seed grows into a 2D turnip, but this is rarer than a turnip growing into an obscene shape. Turnip enthusiasts do discuss bringing back the 2D turnip, and occasionally articles for magazines like Turnip Growers Monthly describe the need for the turnip community to attempt such a feat. For the rest of us, the 2D turnip remains a curious footnote in history, and most people don't even know that what they simply call a turnip is correctly called the 3D turnip.