# Mona Lisa as a cylinder

The literary works of Leonardo da Vinci clearly show his passion for mathematics. We know he worked with Luca Pacioli and even illustrated Pacioli’s famous book *De Divina Propoptione* (Pacioli, 1509). It is of interest chiefly for some theorems on the inscription of polyhedrons in polyhedrons and for the use of letters to indicate numerical quantities. From dictionaries we also know that Luca taught mathematics to Leonardo while they collaborated and lived together in Milan at the turn of the centuries 1400 and 1500. (Linehan, 1911)

The background of the Mona Lisa does not seem to be in proportion. Some have wondered why the left side seems much bigger in scale compared to the right. It almost looks like the background is made up of two separate parts. When folded into a cylinder, the two sides of the Mona Lisa find confluence. This way, the clouds and mountains are in scale and their contours continue across the edge of the painting (Image 27).

*Image 27. Mona Lisa folded into a cylinder*

In this vein, we can calculate the Radius, Diameter, Area and Volume of Mona Lisa. In mathematics we know the following formulas:

*Diameter and radius: D = 2r*

*Perimeter of a circle: p = 2πr, or p = πD*

*Area of a circle: A = πr²*

*Volume of a cylinder: V = A × h*

When we fold Mona Lisa into a cylinder, its width becomes the perimeter (p). Because we know that p = 2πr, it is now valid, that w = 2πr. The radius and diameter of the Mona Lisa circle are:

r = w / 2π = 53,4 / 2π = 8,49887… ≈ 8,5 cm.

If the radius of Mona Lisa is 8,5 cm, then the diameter is

D = 2 × 8,5 = 17 cm.

Correspondingly, the area of the bottom of the cylinder is:

A = 8,5^{2} × π = 72,25 × π = 226,9 ≈ 227 cm^{2}.

As before, also the area of the Mona Lisa circle includes familiar numbers 2 and 7. Let us still calculate the volume of the Mona Lisa cylinder:

V= 227 × 79,2 = 17978,4 ≈ 18 000 cm^{3}=18 dm^{3}=18 l

V= 227 × 79,3 = 18001,1 ≈ 18 000 cm^{3}=18 dm^{3}=18 l

V = 227 × 79,4 = 18023,8 ≈ 18 000 cm^{3}=18 dm^{3}=18 l

Here, we have calculated the volume using the different heights ranging from 79,2 cm to 79,4 cm, since the exact height of the Mona Lisa is impossible to define as noted by the Louvre Museum.

Finally, these numbers seems to be random, but of course, if we wish, there are all kind of connections to be found. Still remember the number 18, which is the number of the Circle of Life? Also Diameter is 17, and in the Ancient Egyptian Book of the Dead, it was Spell 17, where Mekhwert cow with the same symbol with Mona Lisa came forward. Even the area is made with the numbers 7 and 2, being 227cm^{2}.