What are ideal diamond proportions?

Single example of Tolkowsky’s Theorem's predicted proportions.

Proportions determine a diamond's brilliance (the amount of light reflected back to your eye), fire (the flashes of colour due to prismatic separation into the colours of the rainbow) and scintillation (sparkling movement of light as you move the diamond).   If ideal proportions are used in the creation of diamonds, their overall excellence can be optimised.

In 1919 Marcel Tolkowsky was responsible for discovering the basis of what is now regarded as the “Ideal Cut” diamond.  The Mathematician formed a Masters thesis on the proportions for round brilliant cut diamonds.

Supposedly, he conducted his research by asking Londoners to select the most appealing diamond from a small group. He combined these observations with those of his family’s Belgian diamond cutter business and then applied maths and physics to confirm why certain proportions produced the best looking diamonds.

The image shows a single example; in fact Tolkowsky’s theorem predicted a range of proportions with varying combinations of pavilion and crown angles that could enhance brilliance and fire.  A variation on this was the Eulitz cut, developed in 1972 and considered to be ‘mathematically perfect’.