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PRODIP GHOSH

The Mathematics of

Angry Birds

MATHEMATICS

Mathematics is a wide discipline and has many forms. In the various engineering fields, different forms of math may be applied to achieve a specific solution.

For instance, linear algebra is widely applied in electrical engineering to design electrical circuits. Boolean algebra is the basis of digital logic design, a key component of building computers.

Angry Birds

Angry Birds is an application for the iOS, Windows Phone, web OS, Android, Mac operating systems. It was released by Rovio Entertainment and made in Helsinki, Finland in December 11, 2009.

Objective Of Angry Birds Objective of the game is to eliminate  pigs and destroy

their buildings and structures at the same time. This is done by the birds launching themselves out of a giant slingshot and hitting the pigs' various constructs, then eliminating them. Each level allows the player a certain number of birds, which must be used in the order provided.

Angry BirdsThey’re a phenomenon! They’re addictive. They’re angry…really, angry! But they’ll be happier when they see how math can help them. Yes, we’re going to use ideas often introduced in algebra, specifically polynomials, to help those Angry Birds take out their aggression on the sneaky pigs.

Angry Birds and Educational Tool

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.

The Mathematics of Angry Birds

Much of angry birds comes down to choosing the angle to sling the bird through the air! Birds initial angle out of the slingshot equals the angle between the horizontal and the stretched sling at the moment of release. The angle determines the path the bird will follow in the air.

The Mathematics of Angry Birds

Can math help us determine an angle to shoot the bird? Keep in mind, though it can be difficult to shoot exactly at, say 35 degrees vs 40 degrees.

The Mathematics of Angry BirdsHow would you launch the bird so that it lands in

front of the tower without hitting anything but the ground? Keep in mind that every time you change the launch angle for the bird, you are predicting its path.

The Mathematics of Angry BirdsMathematically, Parabolas can be written as y

= ax² + bx + c. Choosing specific values for a, b, and c defines a curve. In Angry Birds, if you find the right a, b, and c defines a curve the birds enact their revenge on the pigs and their fortresses.

The Mathematics of Angry Birds

The Mathematics of Angry Birds

Now here is a parabola that is in the form

y= a(x-h)²+k The equation for that parabola is

y= 0.6(x-12)²+14

The Mathematics of Angry Birds

The Mathematics of Angry Birds

The Mathematics of Angry Birds

The Mathematics of Angry Birds

The Mathematics of Angry Birds

Trajectory In Angry Bird

The path followed by a projectile flying or an object moving under the action of given forces.

GEOMETRY A curve or surface cutting a family of curves or surfaces at a constant

angle.

TRAJECTORY IN ANGRY BIRD

Trajectory In Angry Bird

TRAJECTORY IN ANGRY BIRD

PROJECTILE MOTION IN ANGRY BIRDS

Using Angry Birds, we can highlight many of the main points about projectile motion. Things like:

  How do you get a bird to travel the farthest ? Answer : 45-degree initial launch angle. Can you find multiple launch angles that will land on the

same spot ? Answer, there are two per spot, and they are

complementary angles.

Projectile Motion In Angry Birds

PROJECTILE MOTION IN ANGRY BIRDS

What happens when you launch birds at the same angle but change the initial velocity?

What happens when you launch birds at the same velocity but change the initial angle?

What launch angles have the longest time in flight? The shortest?

The best levels to use for teaching projectile motion meet these criteria: good open field and no high structures to get in the way of the flight

ThankYou!!!