Mathematics of Beautiful Faces

I’ve studied facial patterns, the mathematics and geometry of attractiveness in proportions. There are few scientific studies on the subject that grabbed media attention over the past few years, none unfortunately as informative or as correct as I would’ve preferred. I always double-check these days whether the claims of these studies can be validated or replicated, and so been a bit disappointed but not surprised.

This one from the University of Toronto had the claim that the perfect proportions were 46% of the face from eye to eye, and 36% from the eyes to the mouth.
www.dailymail.co.uk/sciencetec…

Then there’s the Marquart Beauty Analysis.

I can’t agree with either of them. I noticed immediately that the Marquart mask strongly emphasized masculine female faces, and rather blocky-but-short male faces. The examples given often included Tom Cruise (who I think has a nose like the bow of a ship), and Angelina Jolie (whose bee-stung lips shout of injections, hard features are more masculine than feminine under the cosmetics, and her whole look screams plastic!). That reminded me too much of the look of Hollywood cosmetic surgery, and nothing like the beautiful faces of classic film stars, or the kind of models which most people would agree were very attractive. Brad Pitt doesn’t fit the Marquart mask, but most people will agree that he’s considered handsome. Neither would many of the classic film stars in their heyday.

I decided to check the University of Toronto study claims about 46% and 36% by analysing about a hundred male and a hundred female faces. I was looking for the handsome and beautiful, not the average. Probably some of my personal biases, but I tried to avoid that by throwing in what generally was agreed upon according to the search engine results. To ensure I measured the same way, I used for comparison the common actresses cited as examples that fit, like Grace Kelly.

After all of this, my conclusions are as follows;

For attractive female faces, the most common are heart-shaped, triangular, or form a sort of half-pentagon with narrowing chin. Most often with arched eyebrows, but not always. The 46% of the face between pupil to pupil claimed by the University of Toronto study is the MINIMUM, in general it’s more likely around 50% (or a tiny little bit more). The actual distance from the eyes to the mouth should be close (99% to 100%) to the same in exact measurement (not percentage), but in percentage terms is about 38%. The exact measurement is the main guideline, since hair style can drastically reduce the area of the exposed face. Several of the Bond girls had this exactly, so did Audrey Hepburn. Grace Kelly had 36% from eye to mouth, but almost exactly same measurement in pixels/millimetres from pupil to pupil as well.

For male faces, the variety was enormous.
If you measure the eyes to mouth, then eyes to chin, the handsome hero type has more space devoted to the chin than between the mouth and the bottom of the nose (by about 2 or 3 times as much). The following is what I found for the 100 male faces.

(centre of pupil to centre of pupil)
Heroic-Handsome = 47%
Average = 45%
(centre of pupil horizontal line vertically down to tip of chin)
Heroic-Handsome = 62.5% of face to hairline
Average = 60% of face to hairline
(centre of pupil horizontal line vertically down to mouth-centre)
Heroic-Handsome = 39%
Average = 37%

I hope this stuff is useful for somebody, but verify it for yourself if you can.