## Vector Algebra and Game Programming

Video game programming requires extensive use of mathematics and physics. Some typical examples are the following: controlling the motion of objects in space, drawing geometric shapes on the scene, computing the effects after a collision of objects in accordance with Newton’s laws of classical mechanics, etc.Geometry plays a fundamental role. The classic Read more…

## Gauss’s Modular Arithmetic and Fermat’s Little Theorem

1) Gauss’s Modular Arithmetic Given a positive integer $$m$$, we say that two integers $$a$$ and $$b$$ are congruent modulo $$m$$ if they give the same remainder when divided by $$m$$. We use the following notation introduced by the German mathematician Gauss: \[ a \equiv b Read more…

## The Divisors of an Integer, Perfect Numbers and Fermat Numbers

The study of integers and their properties is the fundamental object of Number Theory. The properties of prime numbers and divisors of an integer were first studied extensively during the period of ancient Greece (Pythagoras, Euclid, etc.); the study resumed again in the seventeenth century, in particular thanks to the Read more…

## The Game Loop

A game engine contains several components that provide various functions: 2D/3D graphics rendering scene-graph audio and music management simulation of the laws of physics collision management between objects animation artificial intelligence I/O device management networking resource management scripting The game engine must provide its services to a plurality of application Read more…