The 50km route from Amboise to Chambord is scenic, the air in early April still chilly. Visibility is greater from lack of foliage early in Spring. The entrance is grand, the château looks iconic from afar. Not just being a sight from a distance, Chambord revels in opulence at close range. The roofline’s ornate complexity, for instance, is best seen. But the centerpiece of this near-perfect example of the French Renaissance is a quintessential double-helix spiral staircase.

Double helix stair in Chateau de Chambord

While believed is the current stance on who actually conceived or designed it, circumstantial evidence suggests that this could have been conceived by Leonardo da Vinci: François I, a man of grand plans, invites Leonardo in 1516 to the Loire valley. Leonardo dies in 1519 at Clos Lucé, the same year François begins the construction of the château. It is also the same year incidentally the prime architect of Chambord, mysteriously unknown, dies. (No one knows for certain if Leonardo did indeed conceive the whole plan of Chambord.) The latter fact about the architect’s death in effect implies that before the construction began, plans of the château were ready for the work to begin. The other evidence is that the double helix spiral staircase is found in one of Leonardo’s sketches — the Paris Manuscript B, 1488-1490.

Following is an illustration of a double-helix staircase that I sketched-up for my daughter. Notice how each flight of stairs runs diametrically opposite to each other, ensuring that they never meet.

Double helix staircase sketch

Interesting thing here is that unlike other structures, Chambord’s centerpiece is quite literally the staircase itself. Not just in position, but in its geometric proportions too. For instance, the plan is four times the 9m diameter in both length and width. (Chambord’s inner structure is a square.)

Searching for more led me to this very interesting article [pdf], in which the author, Dr. Philip Pells, mentions about such a double helix staircase in the 10th century in the unlikeliest of places: Ghur province, Afghanistan. (This story by Rory Stewart in the New York Times Magazine (Aug 2002) is just as fascinating to read, which I found via a citation in the former article.) In Dr. Pells’s words:

This search has taken me from the entry vestibule of the Vatican Museum into the chateaus of the Loire Valley and down a 15th Century well in Orvieto. It ended in the most unexpected place, in a Qantas aeroplane, 35,000 ft above the Simpson Desert, when I saw a single picture of a structure in the badlands of Afghanistan, a structure so remarkable that if it is not the world’s first double helix it deserves to be.

Double helix staircase inside the Minaret of Jam, Afghanistan

He goes further in hypothesizing that Omar Khayyám, the Persian poet and mathematician, perhaps conceived The minaret of Jam:

The minaret of Jam is covered with geometric and floral brickwork and turquoise-glazed epigraphic bands. One of the many peculiarities of the minaret is its almost exclusive dependence on varieties of angular script at a time when cursive had been in common use for hundreds of years for monumental inscriptions in that region. The sole use of cursive is for the architect’s name, or signature, one Ali ibn Ibrahim al-Nisaburi. This suggests that Ali, or his family, was from the eastern Iranian city of Nishapur. Now this is where it gets very interesting.

Apart from its mines being the world’s source of turquoise (copper aluminium phosphate) for almost 2,000 years, and hence the turquoise ceranuis on the minaret, Nishapur was the home of Omar Khayyam. He lived from 1048CE to 1131CE, about 100 years before the minaret of Jam was built, and whilst most of the westerners know of him as a poet, he was a brilliant mathematician. Given that he cracked the difficult problem of solving cubic equations, by a geometrical method of intersecting a circle with a parabola, I think he would have determined the elegance of a double helix, and worked out its simple geometry, whilst eating his cornflakes.

Each staircase — the one in Chambord and the other in The Minaret of Jam — I suppose is simply catering function to its form. Chambord’s is easy, feels almost effortless with low rise, wider treads; whereas the one in the minaret appears intensely steep. And the reason for this is simply because for a typical double-helix staircase to work, it needs adequate diametric width to cross the meeting point with good headroom to spare. If the plan diameter is limited, then it is imperative that the rise needs to become steeper.

I digress here.

Chambord and its surrounding is so vast that it is taxing for people going around on foot. With two children in tow, we didn’t bother venturing into the gardens around it anyway. Even the rooms, 440 in all, are just too many to cover every one of them. The fact that Chambord is sparsely furnished made it somewhat easier to skip most. Instead we chose to head upstairs for a closer look at the complex roof, and the towering terrace above the open staircase column.

It is ironic that the chateau so magnificent had more than its share of neglect, and destruction by the luddites of the revolution, besides bearing the eternally unfinished tag for a long time. Four centuries in fact makes you look at it in disbelief. The thing that I took home that evening was the king’s quote — displayed via the audio-visual prelude at the start of the tour:

If one is worried about finishing, then one would never start anything.

Being in Amboise, Clos Lucé was hard to miss. For a chateau, once home to François’s sister Marguerite de Navarre, Clos Lucé is unremarkable. Sans few embellishments on its façade, it could easily be mistaken for a contemporary French country house. And it certainly does not look like it could once have been home to Leonardo da Vinci. Nevertheless, it was here between 1516 and 1519 that the renaissance artist lived and worked for the king.

Clos Lucé is now a museum with things on display that were once part of the everyday life of Leonardo. But the exhibits of curiosity lie in its basement. They are part of a growing collection of scaled models — based on Leonardo’s sketches — built and donated by individuals, organizations or institutions from around the world.

The fundamental consistency in these models is awe-inspiring. He seems to have understood mechanics of motion early on, which is clearly visible from the implementation of gears across his machines. It is obvious however from sketches that his gears weren’t yet considered for long-term wear and tear. And this is apparent in the way the sketches show the teeth of a typical gear. I couldn’t help notice the lack of finesse in gear geometry — the addendum and the dedendum for instance. Also notice the location of gears in wheels; they’re at the outer circumferential end than near the axle for power transmission.

The exhibit of my fascination however was a rather subtle one — the cross section of a double hulled battleship. Besides introducing a layer of structural redundancy to ramming — the primary mode of naval warfare of time, I wonder if Leonardo also considered the other benefit such configuration offered: the reduced waterplane area as a consequence of reduced metacentric height that would help battleships move and maneuver swifter than the conventional single hulled ships.1

  1. The gap between hulls increases the ship’s buoyancy, thereby reducing its draft.