**Lesson 2: Basic Proportions**

This is basic geometry, but stick with me. In simple terms, a diamond can be considered as being composed of three components which fit together—a cone, a cylinder and a frustum, i.e., part of a cone shaped solid next to the base that is formed by cutting off the top by a plane parallel to the base. These shapes correspond to the pavilion, girdle, and crown of a cut diamond. The base of the cone forming the pavilion, the base of the frustum forming the crown, and the girdle all have exactly the same diameter. Now, if one defines the diameter, the crown angle and the pavilion angle, one cannot define the size or shape of the object because the size of the girdle has been ignored. If one defines the diameter, the crown and pavilion angles, and the girdle, one still cannot define the size or shape of the object because the height of the crown has been ignored. However, if one defines the diameter, the crown and pavilion angles, the girdle, and the crown height or Total Height, the size and shape of the object is completely defined. That is why these measurements are used in cut grading to define the size and shape of the stone. In practice, one can consider the combination of all of these measurements to be unique for each cut diamond.

Over 100 years of diamond cutting has led to a consensus (except for the GIA) there are optimum values for each of these measurements, if one wishes to produce a product recognized as having the best compromise between brilliance and fire. This optimum has been termed the “Ideal Cut”. To be sure, there are “many” ideal cuts which have been proposed by others. They stress brilliance, fire, or even economics, by minor alterations to things like table size. However, no one has seriously challenged the fact the crown and pavilion angles are the key to beauty.

The GIA claims there is no single set of proportions which produces the “best” cut for round brilliants. In this, they are mistaken. Granted, one will never be able to demonstrate it, as our measuring systems are not precise enough, but all the data, including the GIA’s own monumental study demonstrate there is an optimum set of proportions. Those proportions are attained when the ratio of the crown angle:pavilion angle (C/P) has a value of 0.84.

Useful as that information is, as said earlier, defining crown and pavilion angles are not enough to define the shape and size of a stone. Every dimension has an effect, and we shall now consider them.

The most critical measurements are those of crown height and girdle thickness. If one can directly measure them, fine, do so. However there is another way to get the same information. If one examines the certificates commonly found accompanying almost all diamonds in “lower end” jewelry stores, information such as diameter and total height or depth will be found.

Again, years of diamond cutting has shown the optimum thickness of the girdle can be considered to be 3% of the diameter of the stone, and the total height or depth of the pavilion plus the height of the crown also has an optimum. That value is 57.3% of the diameter. Combining these values gives us Total Height = 57.3 + 3%. This is the other equation needed in the Hanneman Cut Grading System.

**Homework Assignment**

- Using the information gathered for the stones in Homework Assignment 1, determine the C/P ratios and Total Height values for each of your samples.
- If you do not have the data to determine C/P, don’t worry. We can make up some.