Math for Game Development: Building a 2D Shooter with High School Math

Overview

This video introduces the math used in game development, with a 2D shooting game as the running example. Everything on screen, from player movement and enemy aiming to hit detection, enemy vision, the HP bar and boss behavior, is built from just six ideas covered in school, and calculus never comes up.

The computer does the arithmetic, so there is no need to calculate quickly. What you decide is which calculation produces the movement you want.

Key Points

• Distance from the Pythagorean theorem handles proximity checks and circle-based hit detection, and comparing squared distances skips the costly square root.
• Vectors describe position and velocity. Multiplying velocity by the frame time dt keeps speed independent of the frame rate, normalizing input fixes the classic bug where diagonal movement is about 1.41 times faster, and subtracting positions gives a homing direction.
• Trigonometry converts between angles and directions: atan2 aims a shot at the player, adding 15° steps creates a spread shot, and a sine wave over time makes items float.
• The dot product of two unit vectors is the cosine of the angle between them, a cheap way to tell front from back or to check a 60° field of view.
• Lerp smooths the HP bar and damage flash, with smoothstep for easing, while Boolean logic and a state machine keep the boss’s behavior organized.

Chapters

• 0:00 Introduction
• 0:09 The task: building a 2D shooter
• 0:23 Only six kinds of math
• 0:38 No calculus needed
• 1:03 1. Distance (Pythagorean theorem)
• 7:47 2. Vectors
• 11:13 3. Angles and trigonometry
• 14:36 4. Dot product
• 16:54 5. Lerp (linear interpolation)
• 18:57 6. Boolean logic and state machines
• 20:57 Summary