# Maths - Angles in 2D

In two dimensions an angle can be a measure of direction or the difference in direction between two lines.

In everyday life we specify angles in degrees. A complete rotation is divided into 360 degrees.

In this program angles are measured in radians where a complete rotation is divided into 2π radians, where π=pi approx 3.14159. Most class libraries such as Java and C# Math libraries use radians, also standards such as VRML. An exception is OpenGL, which uses degrees for some reason.

So to convert from radians to degrees multiply by 180/π =180/3.14159.

1 radian is given when a distance equal to the radius is measured round the circumference of a circle.

## Beyond 360°

When we do a compete rotation of 360° or 2*π radians then we get back to where we started, although this does not imply that the angle jumps back to zero, the angle is continuous everywhere.

This is illustrated here, this does not imply a third dimension, but it means that we can always find a continuous area to work on (even when we are close to 0° and 360°). This idea is known as a Riemann surface.

We need to be careful about these issues when we look at trig functions and especially their inverses.

## Further Reading

You may be interested in other means to represent orientation and rotational quantities such as:

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see also:

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

Engineering Mathematics - This book has been going for a long time and it is now in its 5th edition, so it is tried and tested.

Other Math Books

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

 Dark Basic Professional Edition - It is better to get this professional edition This is a version of basic designed for building games, for example to rotate a cube you might do the following: make object cube 1,100 for x=1 to 360 rotate object 1,x,x,0 next x Game Programming with Darkbasic - book for above software

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