Math and Games: A Simple Look

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Mathematics is one of the basic building blocks of making a good computer game. Without mathematics, we would not be able to create the complex characters and environments that we see on the screen. We couldn't move a simply designed point, character, or box; we couldn't make it interact with the virtual world we were creating.

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In big-budget games, the applications of mathematics are presented in much more detail. For example, mathematics is used to accurately simulate the physics and forces of a weapon, creating destructible environments and dynamic weather conditions.

It is possible to say that mathematics is also actively used in some of the following cases:

• Designing sections procedurally,
• In-game interactions, game controls (such as walking, running and jumping),
• Interaction of characters and environment,
• Interaction of artificial intelligence players (NPCs),
• Realistic water and grass animations

Unlike big-budget games with impressive graphics and higher system requirements, the simple games that most of us play involve math at a basic level. Most of the games we play from mobile phones or websites contain simple graphics, and the game mechanics can also be considered quite simple. In games of this style, he often uses trigonometry and algebra. Today, some branches of mathematics used in games are given below.

• Calculus
• Linear Algebra
• Discrete Mathematics
• Applied Mathematics

The Angry Birds

Angry Birds, which was quite in demand at the time of its release, is a good example to study the basic application of mathematics. First of all, there is no weather resistance modeled on the Angry Birds game. That is, the path that the bird takes in the air fits exactly into the parabola equation.

What is this parabola?

Mathematically expressed in the form y=ax²+bx+c, it is a mathematical expression with the following figure.

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We pointed out the differences in mathematical calculation in games large and small. Now let's look at this situation through Angry Birds.

If Angry Birds were a big-budget game, the weather resistance could be calculated, creating a more realistic game environment.

In fact, even this example can escape into much detail. Even in big-budget games, weather resistance may not be calculated, but I think we get the gist of it.

We have already said that birds follow a parabolic path. If you manage to throw the bird at a 45-degree angle while playing the game, you can reach the farthest point in the game. The movement of the bird is perhaps the clearest observable mathematical expression. But since there are also elements in the game, such as boards, stones, etc., you may not be able to clearly observe this situation.

In addition to all this, various mathematical expressions are also used in many actions in the game, such as explosions, bumps, etc.

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We would like to thank Haydar Can Coşkun for writing this text. You can check out our student's blog: https://academy.patika.dev/tr/blogs/detail/matematik-ve-oyunlar-basit-bir-bakis