# Introduction line represents 30°, the green line is

Introduction In 2009, Rovio Entertainment released a new game for Apple called Angry Birds. It was created by a man from Finland by Jaakko Iisalo and later was assisted by Markus Tuppurainen and Peter Urbanics. Once the game released, it became a phenomenon causing the Angry Bird franchise to branch out to Androids as well as making it into the movie. The company has made millions and became the most downloaded freemium game (“History of Angry Birds”). Upon initial thought, one may think that the game does not involve any math, rather the player simply catapults birds to destroy their enemy, the pigs and it may involve directly hitting them or indirectly by destroying the structure to collapse on the pigs. The straightforwardness of the game makes it fun and addicting. However, when playing the game, the player are predicting the path of the bird in hopes to knock down the structure. Once releasing the bird, it follows the path the player sets. Afterwards, the game display the path the bird took using dashed white lines; the line exhibit a parabola and the highest point the bird reaches is the vertex (as shown in figure one below). In addition, the game involves vectors. In this exploration, I will be looking at how math plays a factor in this game and could players use this to their advantage. Figure 1Parabola Parabolas can be defined by the equation: y=ax2+ bx+c. In Angry Birds, the parabolas used are flipped compared to normal parabola graphs which means it is negative, therefore transforming the equation into y=-ax2+bx+c. If the bird is shot using the perfect angle, then the structure will collapse on the pig and the objective is achieved. To refer this back to parabolas, if the player finds the correct values for a, b, and c then the objective of Angry Birds will be attained quicker rather than doing trial and error. In the game, the birds are placed upon a slingshot, making their initial position (0,1) as displayed in figure 2 below. Figure 2If the bird is shot at 30°, 45°, and 60°, then the equation would look like y = 1 + 0.577x – 0.070x² for 30° y = 1 + x – 0.106x² for 45°, and y = 1 + 1.732x – 0.211x² for 60°. It is depicted in figure 3 below, the blue line represents 30°, the green line is 45°, and the orange line portrays 60°. The illustration shows how the bird only hits the structure when it is shot at 30°. Figure 3 MATH WILL GO HERE. IT WILL BE ABOUT FINDING THE PERFECT ANGLE. Vectors Magnitude and direction define vectors. Distance, speed, or translation present magnitude. The direction of a vector is often denoted as its angular bearing from a constant direction, such as an angle of elevation. In Angry Birds, two factors results in a parabola; they are: the slingshot force and its angle and the combination of these two factors creates vectors. The direction of the vector is determined by the angle of rotation of the bird about the top of the slingshot. Using figure 4, each location of an bird, as it rotates about the slingshot, is the initial point for a vector. The coordinates of this point can be determined in either a rectangular or a polar coordinate system. The rectangular coordinates can be defined by the Angry Bird units in the horizontal and vertical distances from the origin, whereas the polar coordinates can be defined by the radius, or force from the initial point to the origin, and the angle of rotation. The polar coordinates then lend themselves to defining the vector for each trajectory. Because the pig target in the game is to the right of the Angry Birds.