In 1919 a young mathematician, Marcel Tolkowsky, wrote a Masters thesis on the proportions for round brilliant cut diamonds. This became the basis for what is now known as the “Ideal Cut”.
It is said he asked passers by, in the streets of London, to select the most appealing diamond from a small group. From these casual observer opinions, together with those of the diamond cutters in his family’s Belgian business, he confirmed the proportions of the best looking diamonds. He then applied math and physics to prove why.
The proportions he chose produce a beautiful diamond. But it has taken more than 80 years for the industry to realize that his theorem predicted a range of proportions , not just the single set of parameters shown on the image; he was aware of a trade off between maximum brilliance and maximum fire that results from varying combinations of crown and pavilion angles.
You can read Tolkowsky’s book here and play with his mathematic model thanks to Mathematician Jasper Paulsen.