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Exploration Ideas

All Algebra (11) Functions & Equations (26) Geometry & Trigonometry (71) Statistics & Probability (41) Calculus (20) Mathematical Modeling (5) Applied Mathematics (1) Graph Theory (9) 71 ideas Clear filters
Taxicab Problem
Taxicab Problem

In taxicab geometry, distance is measured along a grid rather than as …

Distance Metrics Geometric Proofs +2
The Walkie-Talkie Skyscraper
The Walkie-Talkie Skyscraper

20 Fenchurch Street's curved facade focused sunlight and reportedly damaged a parked …

Geometry Architecture +2
Tennis Training Wall
Tennis Training Wall

A tennis practice wall is angled so the ball rebounds back towards …

Geometry Angles +2
Construction Cranes
Construction Cranes

A tower crane balances its load using a counterweight on the opposite …

Trigonometry Forces +2
How Long is a Piece of String?
How Long is a Piece of String?

Unroll a helix of wound string into a flat triangle and calculate …

Optimization Geometry +2
Nets and Wire Frames
Nets and Wire Frames

3D wireframe structures — geodesic domes, lampshades, sculptural frames — are built …

3D Geometry Engineering +2
Sundials
Sundials

How is the sun used to tell the time? - Explore the …

Trigonometry Solar Geometry +2
Tethered Goats
Tethered Goats

A goat is tethered by a rope to the wall of a …

Optimization Geometry +2
Cube Watermelons
Cube Watermelons

Expensive but not optimised? - Explore the mathematical principles and create your …

Optimization Geometry +2
Modelling a Truss Bridge
Modelling a Truss Bridge

A steel truss bridge carries its load through triangular frames of straight …

Bridge Engineering Catenary +2
Resolving Forces: A Cyclist on a Hill
Resolving Forces: A Cyclist on a Hill

A cyclist climbing a hill pushes down at an angle to the …

Vectors Forces +2
Cable-Stayed Bridge
Cable-Stayed Bridge

In a cable-stayed bridge, straight cables run directly from the towers to …

Geometry Forces +2
The steepest cable car in the world
The steepest cable car in the world

A 159% gradient, reported as the steepest cable car in the world: …

Trigonometry Engineering +2
Moon Caves
Moon Caves

Lunar caves (lava tubes) have been located by measuring how the surface …

Geometry Geometric Proofs +2
The Pool Table Problem
The Pool Table Problem

On a rectangular table with whole-number sides, which corner does a bounced …

Geometry Angles +2
Lagrange Points
Lagrange Points

Model the point between Earth and the Sun where gravitational pulls balance, …

Physics Astronomy +2
Tipping Point
Tipping Point

These table tennis tables cannot be stored on slopes greater than 10 …

Forces Physics +2
The Maths of Pool (Billiards)
The Maths of Pool (Billiards)

Predict where to aim a pool ball using the law of reflection, …

Geometry Angles +2
The 3D Geometry of a Hexagonal Roof
The 3D Geometry of a Hexagonal Roof

A hexagonal summerhouse roof is built from six identical triangular panels meeting …

Vectors 3D Geometry +2
Reuleaux Triangle in 3D
Reuleaux Triangle in 3D

A Reuleaux triangle has constant width: rolled between two flat plates, it …

Geometry Constant Width Curves +2
The Mercator Map and Circles
The Mercator Map and Circles

How circles of increasing radius, centred on a city such as Paris, …

Geometry Cartography +2
The Mercator Map
The Mercator Map

Africa is fourteen times larger than Greenland, but they look similar in …

Geometry Cartography +2
How fast are you moving?
How fast are you moving?

How fast is a point on Earth's surface moving, just from the …

Physics Kinematics +2