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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
Solar Analemma
Solar Analemma

Photograph the sun at the same clock time every day for a …

Trigonometry Astronomy +2
Spirals and Polygons
Spirals and Polygons

Join every k-th of n equally spaced points around a circle instead …

Geometric Patterns Nature +2
Is a Snail Shell Archimedean or Logarithmic?
Is a Snail Shell Archimedean or Logarithmic?

Snail shells, hurricanes and galaxies all spiral, but not all spirals are …

Geometric Patterns Nature +2
Suspension Dock
Suspension Dock

Explore the shape of the cables and the design of this dock.

Forces Catenary Curves +2
Measuring Volumes with LASERs
Measuring Volumes with LASERs

Turn a grid of laser-measured heights into a volume estimate, the method …

3D Geometry Measurement +2
Theatre Acoustics
Theatre Acoustics

Calculate direct and reflected sound path lengths in a theatre to find …

Geometry Physics +2
Satellite Dishes
Satellite Dishes

Fit a parabola to a real satellite dish's profile and check whether …

Geometry Physics +2
Laser Light Shows
Laser Light Shows

Work out the mirror angles and beam paths that let a single …

Trigonometry Distance Measurement +2
SpiderCam
SpiderCam

Work out the cable lengths that place a stadium SpiderCam at any …

Geometry Vectors +2
Conic Sections
Conic Sections

Tilt a torch or lamp against a flat surface and the edge …

Geometry Architecture +2
In an Emergency, Where Will You Land Your Aircraft?
In an Emergency, Where Will You Land Your …

If an aircraft loses all engine power mid-flight, how far can it …

Aviation Great Circle Routes +2
Which Country is the Closest when you are in the USA
Which Country is the Closest when you are …

Which foreign country is closest to the geographic centre of the continental …

Optimization Geometry +2
Voronoi Diagrams
Voronoi Diagrams

Which school, defibrillator, fire station or kebab shop is closest to any …

Optimization Perpendicular Bisectors +6
Point Nemo
Point Nemo

Point Nemo is the point in the ocean furthest from any land. …

Optimization Geography +2
Flying by Vectors: The 3D Geometry of a Flight Path
Flying by Vectors: The 3D Geometry of a …

Turn two airport coordinates into 3D vectors from the centre of the …

Aviation Great Circle Routes +2
VAR
VAR

VAR offside lines look pixel-precise on screen. Model the real margin of …

Decision Making Sports +2
Tunnel Segments
Tunnel Segments

Crossrail tunnel segments stockpiled in preparation for digging

Geometry Circular Segments +2
Horse Riding
Horse Riding

Model the geometry of a horse's circular exercise track (or any circular …

Optimization Geometry +2
Lénart Spheres
Lénart Spheres

What is the shortest distance between two points on a sphere?

Education Non-Euclidean Geometry +2
Why Cracks and Cells Meet at 120 Degrees
Why Cracks and Cells Meet at 120 Degrees

Dried mud, cooling basalt columns and a giraffe's coat pattern all split …

Geometry Patterns +2
Modelling a Bridge Construction
Modelling a Bridge Construction

Model the changing shape of an arch bridge as it is built …

Bridge Engineering Catenary +2
Expanding a Football Stadium: The Geometry of More Seats
Expanding a Football Stadium: The Geometry of More …

Arsenal have discussed a major expansion of the Emirates Stadium that could …

Optimization Geometry +2
A Shadow Compass
A Shadow Compass

How to create a shadow compass in the Northern Hemisphere.

Trigonometry Navigation +2
Ordnance Survey
Ordnance Survey

The height of every point on a British map is measured relative …

Trigonometry Geometry +2