Interactive tutorials · built from the videos
Game Math
you can grab.
Thirteen hands-on chapters that follow the same path the videos take:
start from math you already know, add one slider at a time,
and watch it become curves, flocks, walking feet, fireworks and pixels.
Every chapter opens with a press-play lesson — a 90-second
movie that explains itself and pauses when it's your turn.
it's weighted averages all the way down
The spine — math → pixels
CHAPTER 01
Vectors & the Dot Product
Arrows are numbers. Drag two of them and watch the dot product answer
"same direction or not?" — the trick behind enemy vision cones and lighting.
a · b = |a||b| cos(θ)
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CHAPTER 02
Lerp → Bézier Curves
The midpoint formula from school, one weight slider, and suddenly you've
invented the pen tool. Named points, construction lines, the whole magic.
P = (1−t)·A + t·B
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CHAPTER 03
Matrices Move Worlds
Translate, rotate, scale — a matrix is a machine that eats every point
of a shape. See the numbers change live, and why order matters.
p′ = M · p
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CHAPTER 04
Why a GPU at all?
Race a CPU doing pixels one-by-one against a GPU doing them all at once.
Then read the real shader line every 3D game runs.
gl_Position = P·V·M·pos
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Motion & life
CHAPTER 07
Sin, Cos & Motion
One spinning point explains all of trig. Unroll it into a wave, then make
fish swim, bees bob, and moons orbit — with two lines of math.
x = r·cos(θ), y = r·sin(θ)
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CHAPTER 09
Springs & Smoothing
Why game cameras feel buttery: lerp a little bit, every frame. Then add
springiness and overshoot — the secret sauce of "game juice".
x += (target − x) · k
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CHAPTER 05
Boids — Flocks from 3 Rules
Separation, alignment, cohesion. Three tiny forces, weighted and summed,
and a hundred triangles start behaving like birds over a lake.
F = w₁Fs + w₂Fa + w₃Fc
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CHAPTER 06
Inverse Kinematics
"The foot must land here — figure out the knee." Drag a target and watch
a jointed arm solve itself, exactly like feet on uneven stairs.
angles ⇄ end effector
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CHAPTER 08
Particles & Forces
Every explosion, spark and smoke puff is the same three lines:
force → velocity → position. Build fireworks and bend them with wind.
v += F·dt; p += v·dt
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The GPU deep cut — where it all meets
CHAPTER 11
The 3D World — press W, watch a matrix
Drive a neon wireframe ship. Moving edits the Model matrix, mouse-look edits
the View, sniper-zoom edits the Projection — all three live on screen.
screen = P · V · M · point
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CHAPTER 10
Shaders — the GPU's tiny programs
color = f(x, y, time). Write pixel functions, light a sphere with the
chapter-01 dot product, and snap it into toon shading.
brightness = max(0, N·L)
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CHAPTER 12 · CAPSTONE
A tiny RTS — every chapter, deployed
Command a squad, dodge the watchtower's vision cone, watch shells arc and
health bars lerp. Six formulas composing into behavior. X-ray included.
seek + separate + arrive + spot + shoot + smooth
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CHAPTER 13 · THE ARCADE
Three tiny games, three kinds of math
A racer that IS a Bézier curve, a platformer that IS a parabola, and a
lead-the-target turret that IS a vector equation. Playable, with live formulas.
🏎 P(t) · 🐸 vy += g·dt · 🎯 pos + vel·t
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Suggested order: 01 → 02 → 03 → 04 is the math→pixels spine, then go deeper with 11 (the 3D world) and 10 (shaders); the rest are where it comes alive. Every page stands alone.