I feel the need to add context to the contents of my previous article about the architecture of the royal Castle of Chambord, probably one of the most beautiful castles in France. It's commonly accepted that the castle was built based on a grid layout, and the french version of Wikipedia has some details about that design:

Architecture of Chambord
Plan illustrant le concept initial du Château - Monsieur W, CC0

Unfortunately, this theory is really partial since it does not explain many, too many choices:

  • on the grid above, the dungeons seems carefully aligned with the grid, and the center of the towers should then be perfectly aligned with the sides of the main body of the castle. It is very clear from the map and de visu that it's not the case. The main body of the castle eats lets than a fourth of each tower and, again, it's extremely visible if you pay a real-life visit to the castle: the two angles between a tower's walls and the main body are less than 90°.
  • this does not explain how the size of the main body of the castle was chosen
  • the grid above works only if the center column and row are slightly larger than the other ones
  • it does not explain the obvious ratios between the castle itself and its enclosure
  • with my Standards freak's eye, there are too many things left unspecified

So I think the way the castle was designed is different and I think the WHOLE basis for it is the diameter of the towers/enclosure towers. Once that value is specified, the whole castle can be entirely derived from very basic operations that are so simple a rule and a compass are enough to draw the whole thing.

Before diving into the architecture of the main body of the castle itself, we must see that the enclosure of the castle (without towers) is very precisely a scale(3, 2) of the main body of the castle (without towers). So if we can show that the main body of the castle itself is determined solely from the diameter of the towers, it will imply the whole architecture, from enclosure to main body will rely on a single length only !

Let's do that here...

If you take the result of that experiment and overlay it over the map of the main body of the castle, it's a perfect and precise match. Since the enclosure is trivial to determine from here, the whole plan relies, as expected, on a single value : the diameter of the towers.

Chambord is a mathematical construct, with the computation of a square enclosing a pavement of 5 circles, a placement of 4 of the same circles around the square and then a trivial scaling of that construct to build the enclosure. I'm pretty sure we could also find a scale ratio between the height of the enclosure and the height of the main body of the castle.

All in all, the grid system quoted above seems to me approximative, and most probably mistaken.