# Math

Although the study of gemology requires no formal prior training, a highschool diploma would make it easier to understand basic math. Especially knowledge of trigonometry might serve you well.

Below are some basic calculations that you may want to understand.

## Sinus, cosinus and tangent

The sinus, cosinus and tangent are used to calculate angles.

### Sinus

Sinus is usually abbreviated as *sin*.

## Degrees, minutes and seconds

When we think of degrees we usually associate it with temperature and we consider minutes and seconds as attributes of time. However in trigonometry they are used to describe angles of a circle (we name them the *radian* values).

A full circle has 360 degrees, or 360°.

Every degree can be divided into 60 minutes (like in a clock) instead of the 10 decimal subdivisions.

Minutes are notated with a ', as in 26'.

The individual minutes are further divided into 60 seconds and they are described with '', as in 23''.

This may look odd at first, but it's not very hard to understand.

If you have an angle of 24°26'23'' (24 degrees, 26 minutes and 23 seconds), this means that the decimal value is:

- 24°
- 26 divided by 60 or 26/60 = 0.433°
- 23/(60 * 60) or 23/360 = 0.063°

This totals in 24 + 0.433 + 0.063 = 24.439° in the decimal value (which is the decimal value of the critical angle of Diamond).

When you want to calculate the *radian* value of 24.439°, you do the following:

- the 24 stays 24 (because that doesn't change)
- you try to find how many times 0.439 times 60 fits in the degree by: 60 times 0.439 = 26.34, so that is 26 full minutes (0.34 left over)
- you calculate the seconds through 60 times 0.34 = 20.4 (or 20 full seconds because we don't count lower than seconds).

This gives 24°26'20'' (24° + 26' + 20'') instead of the 24°26'23''. The 3 second difference is caused by the rounding down to 3 decimals in the prior calculation. In gemology we usually don't even mention the seconds, so it will be rounded down to ≈ 24°26'.

Even though you may not need this knowledge often, it is important that you atleast know of its excistance as you may get confused when reading articles. Sometimes values are given in decimal degrees, at other times in radian values.