## 2D Collisions and Unity’s 2D Physics Engine

This article describes the primitive geometric forms used in 2D collisions, with references to the features provided by the Unity’s 2D Physics engine. For a review of vector algebra, necessary to understand the topic, you can also see the article of this site.Collision management between two or more objects can be divided Read more…

## Chess and Mathematics: Rooks, Queens and Rook Polynomials

In this article we propose some combinatorial problems related to the chessboard and the game of chess, which have a scope of application in other sectors of Mathematics as well. Exercise 1 We number an $$8 \times 8$$ chessboard with the numbers from $$1$$ to $$64$$. Arrange $$8$$ Read more…

## Number of Rectangles in a Square Lattice

Problem 1 Let a square lattice of dimensions $$n \times n$$ be given.Calculate the number $$R$$ of different rectangles which can be drawn, with the vertices in the lattice points.Two rectangles are considered different if they have different sizes or are in different positions. SolutionLet us first consider the case Read more…

## Steiner’s Division of Plane and Space

Problem 1 Calculate the maximum number of parts in which a plane can be divided by $$n$$ lines. Solution 1.1A necessary condition is that the $$n$$ lines must intersect two by two and no three lines intersect at the same point. We can proceed by induction: once we draw $$k$$ lines, Read more…