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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
Height, Marriage, and What "Random" Would Predict
Height, Marriage, and What "Random" Would Predict

If height didn't matter at all when people paired up, the gap …

Typography and the Letter S
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 Cable Car Cabin Really Travel?
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 at the Top — Can You Prove It?
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 Your Antipode
Where on Earth Is Directly Below You? Finding …

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

Trigonometry Coordinate Systems +3
Reading a Wind Turbine Like a Sine Graph
Reading a Wind Turbine Like a Sine Graph

Track the height of a single turbine blade tip as it spins, …

Modelling Trigonometric Functions +3
Why Your Car Doesn't Skid on a Turn
Why Your Car Doesn't Skid on a Turn

On every corner, your car's inside and outside wheels travel different-sized circles …

Geometry Circular Motion +3
Sorting Speeds Into Bins
Sorting Speeds Into Bins

Four hundred balls bounce around inside a spinning drum, then shoot one …

Physics Normal Distribution +3
The Sprinkler's Secret Pattern
The Sprinkler's Secret Pattern

A rotating garden sprinkler throws water along a parabola — so why …

Trigonometry Modelling +3
The Airport Money Trap
The Airport Money Trap

Exchange £100 into euros and straight back, and you won't get £100. …

Financial Mathematics Consumer Mathematics +3
The Guinness Question: Is the Difference Real?
The Guinness Question: Is the Difference Real?

Run any experiment with two groups and the averages will differ — …

Data Collection Experimental Design +3
Is Anything Actually Normal?
Is Anything Actually Normal?

The bell curve appears throughout statistics textbooks. This exploration tests it against …

Data Collection Sampling +3
One Graph, Two Stories: the Power of Log Scales
One Graph, Two Stories: the Power of Log …

Plot a pandemic, a YouTube channel or world population and you get …

Data Analysis Exponential Models +3
How Video Games Spin the World
How Video Games Spin the World

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

Matrices Coordinate Geometry +3
How Many Goals on Saturday?
How Many Goals on Saturday?

Goals are rare, sudden and unpredictable — yet the number of goals …

Data Collection Probability +3
How Many Fish Are in the Lake?
How Many Fish Are in the Lake?

You can't count every fish in a lake — so ecologists tag …

Data Collection Experimental Design +3
The Freddo Index
The Freddo Index

In 2000 a Freddo cost 10p. Track what it has cost since, …

Data Collection Financial Mathematics +3
The Real Cost of Your First Car
The Real Cost of Your First Car

'Only £199 a month!' — but what does the car actually cost …

Modelling Financial Mathematics +3
Phone Contract or Buy It Outright?
Phone Contract or Buy It Outright?

A 24-month contract feels cheap because the numbers are small. Add them …

Data Collection Sequences +3
Why Does My Phone Choose That Mast?
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 Wide V
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?
Will These Two Planes Get Too Close?

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

Optimization Vectors +3
Why Won't My Phone Charge the Last 20%?
Why Won't My Phone Charge the Last 20%?

Charging races to 80% and then crawls. Collect your own phone's charging …

Data Collection Modelling +3
One Student Comes to School With Flu
One Student Comes to School With Flu

How many people catch it, and when is the worst week? Split …

Data Collection Modelling +3