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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) 184 ideas
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
The House Always Wins
The House Always Wins

Investigate common casino games.

Probability Statistics +2
Spinner Games
Spinner Games

Make your own and investigate fair games.

Probability Statistics +2
Skyjo
Skyjo

A game about scoring the lowest score with negatives

Randomness Game Theory +2
Efron's Dice
Efron's Dice

The idea for non-transitive dice has been around since the early 1970s

Randomness Game Theory +2
Sicherman Dice
Sicherman Dice

Sicherman dice, invented by Colonel George Sicherman in 1978, are a non-standard …

Randomness Game Theory +2
How Much Stone?
How Much Stone?

How would you model this? - Explore the mathematical principles and create …

Applied Calculus Bridge Engineering +2
How Much Carbon Is Stored in a Tree?
How Much Carbon Is Stored in a Tree?

A growing tree locks carbon into its wood. Model the trunk as …

3D Geometry Measurement +2
How Much Steel?
How Much Steel?

What if you varied the angle? - Explore the mathematical principles and …

Applied Calculus Bridge Engineering +2
Conic Sections
Conic Sections

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

Geometry Architecture +2
Population Density
Population Density

A claim compares population densities between places. Test it against real numbers, …

Demographics Growth Models +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
Distance Covered by Athletes
Distance Covered by Athletes

What are the mathematics of tracking athletes? - Explore the mathematical principles …

Data Analysis Sports Mathematics +2
Voronoi Diagrams
Voronoi Diagrams

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

Optimization Perpendicular Bisectors +6
Profit and Loss Optimisation
Profit and Loss Optimisation

Develop cost functions and explore the profits.

Optimization Business Mathematics +2
The Lifeguard Problem
The Lifeguard Problem

A classic problem with many personal takes - Explore the mathematical principles …

Optimization Physics +2
Explore More Interesting Area Calculations
Explore More Interesting Area Calculations

How would you approach this? - Explore the mathematical principles and create …

Geometry Area Calculation +2
Minimum-Cost Packaging
Minimum-Cost Packaging

A box needs a fixed volume, but the material for the lid …

Optimization Calculus +2
Optimisation
Optimisation

A soda can or a classic problem from 2014 Exams - Explore …

Optimization Calculus +2
Zipf's Law
Zipf's Law

Zipf's law describes a striking pattern in the frequency of words in …

Linguistics Power Laws +2
Sinusoidal Functions and Temperature
Sinusoidal Functions and Temperature

Look beyond the seasonal differences.

Data Analysis Climate Science +2