Exploration Library

Typography and the Letter S

Every "S" you've ever read was built from circles and tangent lines …

Riding the Sag: How Far Does a Vinpearl …

The Vinpearl cable car crosses more than 3km of open sea between …

Modelling Catenary Curves +3

The Humber Bridge's Towers Are 36mm Further Apart …

Both towers of the Humber Bridge were built perfectly vertical — and …

Trigonometry Circle Geometry +3

Where on Earth Is Directly Below You? Finding …

Every point on Earth has an antipode — the point exactly opposite …

Trigonometry Coordinate Systems +3

How Video Games Spin the World

Every rotation, zoom and tilt on your screen is the same trick: …

Matrices Coordinate Geometry +3

Why Does My Phone Choose That Mast?

If every phone mast were identical, coverage maps would be a simple …

Modelling Coordinate Geometry +3

Why Climbers Never Let the Rope Make a …

Hang a weight from two ropes and widen the angle between them: …

Trigonometry Vectors +3

Will These Two Planes Get Too Close?

Two aircraft fly straight paths through the same airspace. From their positions …

Optimization Vectors +3

The Willy Wonka Elevator

Willy Wonka's glass elevator moves in every direction — up, down, sideways, …

Vectors 3D Geometry +3

Can a Cube Pass Through a Hole Smaller …

A cube can be cut with a hole large enough for an …

Trigonometry Geometry +3

Great Circle Routes: The Shortest Way Home

Why don't planes fly in a straight line on a map? Use …

Trigonometry Modelling +3

The Geometry of Woodwork Joints

Woodwork joints such as dovetails and mitres depend on precise angles for …

Trigonometry Geometry +3

Coordinating a Robot Army

How do you program hundreds of identical robots to move in perfect …

Vectors Matrices +3

Anamorphic Football Pitch Sponsors

Football pitch sponsor logos appear flat and perfectly proportioned on TV, but …

Geometry Matrices +3

Why Do Pitch-Side Sponsors Look Normal on TV? …

Investigating how football pitch advertisements are deliberately distorted so they appear flat …

Trigonometry Sports Mathematics +4

Penrose Unilluminable Room

Penrose Unilluminable Room is a room with mirrored walls that can't be …

Buildings That Look Straight But Aren't: Parthenon

How architects use lines to counteract optical illusions

Applied Geometry Architecture +3

The Spring-Balanced Desk Lamp

An adjustable desk lamp with springs instead of a counterweight stays balanced …

Vectors Forces +3

Car Blind Spots and A-Pillars

How car windshield pillars create dangerous blind spots for drivers

Trigonometry Angles +3

Rugby Goal Kicking

Finding the optimal angle for distance and accuracy in rugby kicks

Optimization Trigonometry +3

How Gears Work

Understanding gear systems in bicycles, cars, and machinery

Applied Mathematics Circular Motion +3

Airplane Holding Patterns

How aircraft circle while waiting to land, maintaining safe separation