# Angry Birds

## The Largest Mobile App Success the World Has Seen

Angry Birds developed by Rovio Mobile is praised for its successful combination of addictive gameplay, comical style, and low price.

In the game, players use a slingshot to launch birds at pigs stationed on or within various structures, with the intent of destroying all the pigs on the playing field. As players advance through the game, new birds appear, some with special abilities that can be activated by the player.

With a combined 500 million downloads across all platforms the game has been called

• one of the most mainstream games out right now,
• one of the great runaway hits of 2010
• the largest mobile app success the world has seen so far.
Rovio is now valued at more than 200 million Euro and recently secured a 40 million funding from Accel Partners founded by Niklas Zennström behind Skype. Rovio was on the cusp of bankruptcy before starting work on Angry Birds in 2009.

## The Mathematics of Angry Birds

Angry Birds uses basic 2D Newtonian mechanics
• $dx = vdt$
• $dv = F dt$
• $F = (0,-1)$

with $F$ a constant downward gravitational force and the slingshot controlled by giving initial position $x$ and velocity $v$ on the touch screen, and the parabolic trajectory of the launched bird being computed by  time-stepping. In the update Angry Birds Space the force $F$ is generalized to gravitational pull from point masses which allows more intricate shots.

Angry Birds also includes rigid body mechanics for simulation of the effect on the structures of successful shots, augmented by sound effects as an important part of the game experience.

## Angry Birds as Educational Tool

Construction from scratch of a simple version of Angry Birds as Angry Math Birds can be used to learn

• basic Newtonian mechanics:
• motion under various forces
• influence of initial values of position and velocity
• mathematics:
• mathematical modeling by Newton’s equations of motion
• solution of equations of motion by time-stepping
• different time-stepping methods and choice of time-step
• programming:
• computation of trajectory
• user interface for input-output interaction of game aspects.

## Angry Math Birds

Let us now make our own simple version of Angry Birds using the tools we have:

• upcoming demo.

## Angry Birds Space

Angry Birds Space was launched in March 2012 with an extension to gravitational forces and corresonding more complicated trajectories and game.

## Angry Math Birds Space

The gravitational force $F(x)$ (per unit mass) at the point $x=(x_1,x_2)$  from a unit point mass at the origin has the form

• $F(x)= - G\frac{x}{\vert x\vert^3}$ with $\vert x\vert =\sqrt{x_1^2+x_2^2}$

with $G$ a gravitational constant.

Newton’s equations $dx=vdt$ and $dv=F(x)dt$ are solved by time-stepping with Smart Euler rather than Forward or Backward Euler. The game teaches the art of controlling a space ship subject to gravitational forces including how to enter into a stable orbit around a planet:

More generally, making your own version Angry Birds Space will open your mind to understanding the dynamics of our planetary systems and how to get around if you feel you want to take a trip.

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