-Krish Veera-
Parabolas. The graphs that dominate secondary mathematics and are the crux of quadratic graphing. These beautiful curves are the result of the plotting of coordinates obtained by quadratic equations. This crucial tool of mathematics is used in a lot of different aspects of real life, but, in my opinion, the most fun experience of analyzing parabolas is choosing the best trajectory in the Editor’s Choice game with over 100 million downloads:
The relation of parabolas to the game is:
Here, the catapult is considered as the origin of a Cartesian plane, and ‘Red’, like every other bird, has a trajectory that it follows. The objects in its path are the obstacles that it has to breach through to reach the shrewd pigs that it has to destroy. So, while you, as the player actually aims for the pig, what you are essentially doing is, you are making that particular pig a coordinate in Red’s parabolic trajectory.
Now, I’m specifically mentioning Red here because, unlike Red, the other birds have certain special skills that explore different aspects of coordinate graphing. For example, Chuck, the yellow bird, has the ability to go super fast in a linear path at any point in the original parabolic path that it takes. Thus, Chuck introduces tangential motion into the picture.
Consider the red path shown in the previous diagram. Now if the player activates chuck’s ability at coordinates (16,2), chuck would accelerate tangentially. The tangent below shows the new path that chuck takes.
The player has to take into account that, mid-way, when Chuck is pointed directly at where a hit has to be made, his skill to accelerate linearly has to be activated.
On the other hand, The Blues, i.e. the little blue bird that separates into three little birds when the skill is activated provides two additional trajectories for giving a wider range to destroy things. However, the only con is that those birds are pretty small and weak so the damage that they do is pretty minimal.
Now that is an aspect to consider. Where the accuracy and correct aim of the trajectories is important in the game, it’s the size and strength of the bird that matters too. Frankly speaking, Terrence, i.e. the big red bird is simply an older and bigger Red, but it’s the sheer size of it that makes it different. The colossal damage it can cause identifies its individuality.
Pivoter, the green bird, can traverse back its initial trajectory. At any point in the original path, you can suddenly command it to boomerang back. Matilda, the white bird, has the ability to jump the trajectory. So right when the original trajectory is going to end she can shoot an egg which allows her to enter a new trajectory, with the point when she dropped the egg being the origin of the same. Bomb, the black explosive bird, doesn’t really have mathematically inclined skills but its explosive ability makes it unique and as for the Mighty Eagle, well, he is just the ultimate destroyer, a final measure, per se.
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It is games like these that ignite interest in me because we tend to make precisely calculated judgments without even knowing that we are doing the same. It gives me a sense of how much we overlook the math in simple things that we do in our daily life and how elegant they can truly be.
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