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Offline MissJ  
#16 Posted : Friday, July 12, 2019 5:05:16 PM(UTC)
Rank: Administration

Joined: 5/14/2008(UTC)
Posts: 26,813
Here's the cartoon of Donald Duck in Mathmagic Land that inspired Hoefflin to look at things in terms of aesthetic ratios (golden section/golden ratio).


His analysis has a lot of focus on 'fabrege eggs'; oval highlights to the face and also some straight forward aesthetic cannons as to facial divisions. It's not really a mathematical treatise or anything much more complex than that.

In general beautiful faces (or handsome ones) are ones where a lot of golden ratio proportions can be found. Thing is one has to know where to look for them and the math relationships to them with reference to the to the Fibonacci series.

While at MIT, I took Fine Arts courses at Harvard and got A's on aesthetic analysis papers on fine works of art, especially those where looked at composition in terms of Fibonacci and golden ratio layout of the compositions. (Again, the challenge is knowing where to look for the relationships.). Later I wrote papers for students, (ones who 'had to' take a 'Humanities' course but didn't want to) where I charged a hefty price to do so, (had to finance the tuition) usually MIT students who had a hard time or just clueless on aesthetic relationships or articulation of them.

Anyway--and not to digress any more than I have--the cartoon gives a good basic idea of the golden ratio relationships as found in the pentagram and the pentagon and shows some basic golden rectangle divisions of body and face in the Greek sculpture. Although for children, it's aim is to trigger an appreciation for the geometry of things (lay out, spacing of composition whether a work of art --usually classic works of art--, things found in nature) or the face.

Thing is that if one wants to go further in how all this plays out in facial aesthetics, IMO, it takes some inherent interest in GEOMETRY and an inclination towards the arts. Aesthetic geometry (sometimes called 'sacred geometry') is geometry which is the basis of the math of a lot of design that is 'aesthetically pleasing'. People with inherent interest in geometry will know they have it. For example if that was a subject you LOVED in grammar school/high school and also are quick to really look at things in terms of their lay out division and of course, it helps to have some background in art, ideally study that involves both 'art appreciation', drawing, painting etc. For example, we can all look at a face and say/see or otherwise deem it as 'very attractive', beautiful, handsome, whatever. The brain is HARD WIRED to recognize spacial arrangement relationships that are aesthetically pleasing when the EYE sees them. So the math behind this--in a way--is already in your brain. The secret to getting it it out and into the MIND is really astute observation and a lot of INCLINATION towards looking for angle and distance relationships. 'Litmus test' for observing spacial relationships and relative distances is being able to DRAW which really is a matter of 'projecting' a 3-D object (eg a head and the face that goes with it) on to a 2-D surface. Further litmus test is being able to draw a 'beautiful face' (which might not be anyone's in particular), in which case, on a 'higher level' there is awareness of the distance relationships. Then just a matter of looking at the geometry.

Artists often were members of 'secret societies', where they studied the geometry of (for example) 'Platonic Solids' and their application aesthetically pleasing composition. Pythagorean society being most well known. But there were others after that. Basically, there existed secret societies (or 'cults') revolving around 'sacred knowledge' where worshiping mathematical harmonies, beliefs that numbers were the underlying substance of reality (and beauty) and the 'formula'/formulae of them kept SECRET and limited to the membership.

The aesthetic relationships associated with 'beauty', aren't really 'secret' anymore. But if you really want to get into it, things like classical art, Euclid's geometry, Leonardo's observations help a lot as does just practicing daily really OBSERVING what you see and enough so you can DRAW it.

Most of this resolves to INCLINATION towards TRAINING the MIND to observe geometrical relationships and relative distance relationships.

Sorry if this was too long and I went on a tangent.
Miss J. Seeing eye companion to the aesthetically blind since 1998.

Offline Anya77  
#17 Posted : Tuesday, July 16, 2019 8:36:04 PM(UTC)
Rank: Member

Joined: 10/19/2008(UTC)
Posts: 781
Location: West Coast
Originally Posted by: MissJ Go to Quoted Post
I still have the autographed copy of the book. thanx

Oh yeah ! I totally forgot about that !
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