# Human Proportion II.3

## The geometry and algebra of the child 3

### Applying the mathematical formula for child proportion

Here is Velázquez's portrait of the Infanta Margarita Teresa, a princess in the Spanish royal family. I wish to make a copy of this painting, and first, I shall apply the formula derived in the previous page.

Nude proportions of Velázquez's Margarita Teresa

Following classical procedure, I first wish to represent the nude figure before clothing it. The painting has to carry the conviction that there is a real body inhabiting the cloth.

Everyone has seen poor paintings and sculptures where the clothing hides the inability of the artist to depict limbs. To know where the body is in the present case is particularly important, because the poor little girl is almost taken over by her extraordinary costume.

In order to draw a plausible figure, I estimated where the soles of her feet would be (a short way back from the edge of the dress). Click here to go back to the picture, and then click on the picture to toggle back and forth between Velázquez's original and my guess as to how her limbs are disposed under her burden of rich cloth.

Let the height of Margarita Teresa's head be h1, and let her total height be h2. Let the number of heads in her height be H. I measured h1 and h2, then calculated

H = h2/h1.

I found H = 5.

Let Margarita Teresa's age be a. Applying the algebraic formula for age derived on the previous page, we have:

a = 9(H - 4)/2

which gives:

a = 9(5-4)/2 = 4.5

... in other words, her age is four and a half years at the date of this painting, 1656. Perhaps some historian can tell me if this is correct. Some leeway must be allowed, firstly for the fact that all human beings vary a little one way or the other from the average, and secondly for the fact that the painting would have been completed a little later than the original sittings and sketches. Thus by the date the painting was completed she may have been a little older.

By measuring 3/8 of the total height down from the chin (i.e. h2 x 3/8) I found a plausible location for the pubic bone, which makes the figure look in proportion for a child of about that age.

Click for the initial oil sketch for my copy of Margarita Teresa by Velázquez.

to Human Proportion I

to Child Proportion 1

to Child Proportion 2

Authorised uses: This article and images are copyright © Martin Dace 2003, 2006 (including the image on this page of Margarita Teresa desnuda). I give permission for the page to be copied provided that my authorship is acknowledged and that any copy includes this notice and this reference to my website at www.dace.co.uk. Likewise images may be copied on web sites provided a link or reference is made to my website. Please link to the page, not just to the images. The author may be contacted by email at