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##### Splines and Bézier Curves and their application in Video Games
The geometry of curves and surfaces is of fundamental importance in computer graphics and in video game programming. In this article we will describe the mathematics of interpolation curves, in particular splines and Bézier …
##### Sprite Animation in Unity 3D and Finite State Machines
Animation has an essential role in video games. Most video games try to simulate real world physics; in order to achieve this objective it is essential to be able to represent, in the most realistic …
##### Motion in a Plane and Unity’s 2D Physics Engine
This article gives a brief illustration of Newton’s laws of motion in the plane and analyzes the tools that the Unity 2D engine makes available to programmers to simulate the movement of bodies in …
##### Bertrand Hypothesis and Ramanujan Prime Numbers
The French mathematician Bertrand (1822-1900) formulated the conjecture that for every positive integer $$n$$ there is always at least one prime number $$p$$ such that $n \lt p \le 2n$ This conjecture …
##### Ordinary Generating Functions and Recurrence Equations
1) Ordinary generating functions of a variable Generating functions are an important tool for solving combinatorial problems of various types. A typical problem is the counting of the number of objects as a function of the …
##### Lambert Series, the Arithmetic Function $$r(n)$$ and Gauss’s Probability Integral
In this article we will study some properties of Lambert series. Then, using Lambert series relative to the representation of integers as sum of two squares, we will compute the value of Gauss’s classical probability …

Cover photo: Kelly Sikkema