"I ask you, my teacher. What, pray tell, is beauty?"
Though there was no way he could interpret what I had said as anything other than randomly changing the subject, his face nevertheless took on a serious expression. Taking a deep breath, he reached his hand out towards his desk.
"If you're talking about beauty as it pertains to magecraft, then a simple example would be the golden ratio, I suppose."
As he spoke, he pulled out a set square and a compass and placed them on the top of the desk. Pulling some notepaper towards him, he used the set square to draw a square with practiced precision, and then used the compass to draw a circle over one side of it.
In fact, the skills required to do this kind of drawing were indispensable in the field of drawing Magic Circles, so powerful magi often aimed at skills that would make them excellent surveyors. The theory that old magi had been involved in the beginning of Freemasonry were not far off the mark.
Extending the length of the sides of the square, using the points at which it intersected with the circle, he created a rectangle.
"This is the golden ratio. A binomial ratio that works alongside the Fibonacci Sequence - in short, a rectangle where if the short side is measured as one, the long side is measured as 1.618. Without regard to region or era, it's a ratio that humans have always found to bring out beauty. It was discovered and put to use by the architect Phidias in his work in Ancient Greece, and even two thousand years prior to him it was used in the construction of the pyramids by the Egyptian high priest Imhotep.
"Of course, there are many examples that show a harmonic beauty outside of the golden ratio. The wings of a dragon fly, the combs of a honeybee, the shell of the nautilus or a simple tornado, and even the distribution of stars in the Milky Way show a similarly spiraling structure. I think it's obvious at this point, but stabilizing things like magic circles and Workshops without paying attention to these harmonics beyond mere numbers is impossible. 'Beauty, thy name is math,' or something like that."
Case Files II, Chapter 1, Part 1