Geometric Cut

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Geometric Cut

What is an ideal cut diamond?

In 1919, a Belgian mathematician, Marcel Tolkowsky, who came from a family of diamond cutters, published a Masters thesis on the best proportions for round brilliant diamonds.  This work formed the basis of the defining proportions for what are now known as “Ideal cut diamonds”.  It must be noted however that different grading laboratories allocate different names to the basic Ideal cut diamond.  American Ideal Cut, Superb Ideal Cut or even Excellent Cut all refer to diamonds that match the range of acceptable geometric proportions based on Tolkowsky’s work.

So, what are these proportions?  The diameter of the diamond is considered to be 100%, so all percentages quoted are relative to the diameter (or 100%) of the diamond.

• Table diameter = 52.4 - 57.5%

• Crown angle = 33.7º - 35.8º

• Girdle thickness = 0.51 - 2.95%

• Pavilion depth = 42.2 -43.8%

• Total depth = 58.7 - 62.3%

You may be asking what difference these proportions make.  When a diamond has been cut in such a way that all proportions are correct, the diamond will reflect all of the light that enters the diamond, irrespective of the direction that the light has come from.  All this light is then reflected out through the top of the diamond, leading to the brilliant flashes of light and rainbow colours that we associate with diamonds.

Sometimes, a diamond cutter will sacrifice the proportions of a diamond to fit the diamond into a specific size (carat) category, allowing for the potential of a higher price.  If the diamond has been cut too deep, the diamond will appear black in the centre.  If the diamond has been cut too shallow, the diamond will look dull and lifeless.

When buying a round brilliant diamond, make sure that the accompanying diamond certificate contains a printed insert providing the full details of the proportions of your diamond.  This is the best way to ensure that the diamond you have purchased has been cut to acceptable, ideal proportions.

About the Author

Clare Appleyard is co-owner and the resident Technical Diamond Specialist with Katannuta, a company specializing in the manufacture of bespoke jewellery and the supply of quality diamonds and gemstones. Having completed a Masters Degree in Geology at the University of Cape Town, South Africa, Clare spent 6 years working for the world's leading diamond producer before moving to the retail diamond and jewellery market with the formation of Katannuta.

Geometric dissections with rational non-integral numbers?

I'm studying for my geometry final and a practice problem my teacher came up with is:

First, drawing a sketch of 462 little squares sounds TEDIOUS! Eek.

Here's how you do the math part of the problem, tho'.

First, find the area of the whole figure. That's (7/6)(11/4) = 77/24 square units. Don't round!

Now, if you have 77/24 square units, and you're dividing it into 462 little squares, then each square has an area of (77/24) / 462 = 77/(462 * 24) = (7 * 11) / (7 * 11 * 6 * 24) = 1 / (6 * 24) = 1/144 square units.

So, if a square has an area of 1/144 square units, how big is its side? The square root of 1/144, which is 1/12 units! (Notice that the square root of 1/144 is actually BIGGER than 1/144 itself. Cool, huh?)

So, if you're drawing a diagram, you probably want to know how many square are on the 7/6 side, and how many are on the 11/4 side. So, how many 1/12 units are there in 7/6? The answer is (7/6) / (1/12), which is 12 * 7 / 6 = 2 * 7 = 14. So there are 14 squares on the 7/6 side.

Similarly, there are (11/4) / (1/12) = 12 * 11 / 4 = 3 * 11 = 33 squares long the 11/4 side.

SANITY CHECK TIME:
So if there are 33 squares in one direction and 14 squares along the other direction, how many squares are there total? 33 * 14 = 462. Bingo!

Geometric Cut /TUTORIAL/