When I think about ideal proportions, this makes me think about the Fibonacci Sequence, where the next number is found by adding the two numbers before it. This can be seen in spirals, and has been found in the proportions of the human body as well. If you look at the theater at Epidauros and the sanctuary of Apollo at Delphi, you can kind of see this in the shape and form of the seating, how each rim of the circle is proportionally larger than the previous ones. This isn’t exactly the Fibonacci Sequence, but it is a type of proportion that is very pleasing to see.
As for the sculptures of human bodies, you can see that there is much detail placed in the anatomy assessment of the body. Pergamon is a perfect example of this, there is so much detail placed into the anatomy and detailing of the Gaul’s body, it is perfect. If we look at the mathematics of the human finger, as an example, it would look like in the image below. The sum of the two smaller bones equals the length of the next bone. This can be extended and applied to the rest of the body.
Honestly, we have seen influences of this ever since the Classical Period. Take a look at the Vitruvian man, for example. Where Leonardo Da Vinci completed an art and mathematical analysis of human anatomy. This is a study of the ideal proportions of the human body that he based on De Architectura a guide for building by the Roman architect Vitruvius between 30 and 15 BC (Richman-Abdou, 2018). The Golden Number, the ideal proportions that creates “beauty” is something that I believe we can see in everything today.
Reference
Richman-Abdou, K. “The Significance of Leonardo da Vinci’s Famous ‘Vitruvian Man’ Drawing, My Modern Met, 5 Aug 2018, https://mymodernmet.com/leonardo-da-vinci-vitruvian-man/