The Mathematics of Angry Birds The Physics of Angry Birds

2. PRODIP GHOSH

3. The Mathematics
of
Angry Birds

4. 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.

5. 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.

6. 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.

7. Angry Birds
They’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.

8. 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.

9. 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.

10. 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.

11. The Mathematics of Angry Birds
How 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.

12. The Mathematics of Angry Birds
Mathematically, 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.

13. The Mathematics of Angry Birds

14. 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

15. The Mathematics of Angry Birds

16. The Mathematics of Angry Birds

17. The Mathematics of Angry Birds

18. The Mathematics of Angry Birds

19. The Mathematics of Angry Birds

20. 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.

21. TRAJECTORY IN ANGRY BIRD

22. Trajectory In Angry Bird

23. TRAJECTORY IN ANGRY BIRD

24. 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.

25. Projectile Motion In Angry Birds

26. 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