Exploration Library

AI Exploration Coach BETA

We're developing an AI mentor that provides Socratic guidance for your Mathematical Exploration. Currently in beta testing with select schools.

Triangulation and Survey Points

How surveyors use triangulation points to map terrain and measure distances

Trigonometry Applied Geometry Cosine Rule +2

Has the Elizabeth line led to a rise …

Exploring Statistics in the news

Applied Mathematics Statistics Data Analysis +1

Swiss Shooting Range Over a Wall and a …

A unique Swiss shooting range where shooters fire over a protective wall

Trigonometry Optimization Projectile Motion +2

Mathematics of Card Shuffling

How many shuffles does it take to truly randomize a deck of …

Combinatorics Permutations Probability +1

Attaching a water hose sprinkler to a speaker

A user on Reddit did this: - Explore the mathematical principles and …

Physics Cymatics Trigonometric Functions +1

Day Length

Pick two locations and compare the length of their days.

Astronomy Climate Science Seasonal Patterns +1

Daylight Hours

There are many ways to explore trigonometry in this classic problem

Astronomy Climate Science Seasonal Patterns +1

A Ferris Wheel

It's a classic example but you can put your own twist on …

Circular Motion Trigonometric Functions Engineering Applications +1

Solar Analemma

Explore the mathematics of a solar analemma.

Trigonometry Astronomy Elliptical Orbits +1

The Waterfall Swing

Make sure you calculate the correct domain! - Explore the mathematical principles …

Projectile Motion Physics Parabolas +1

Spirals and Polygons

Take the coordinates on a unit circle and put it on a …

Geometric Patterns Nature Polar Coordinates +1

Spiraling

Explore different spirals, take a look at the exploration "How long is …

Geometric Patterns Nature Polar Coordinates +1

Example Conversation

You wrote:

"I want to explore the mathematics of music because I play guitar."

AI Mentor:

"What specifically about playing guitar makes you curious about the mathematics behind it? Is it the tuning, the chord patterns, or something else?"

You wrote:

"I noticed that some chords sound good together and others don't."

AI Mentor:

"Interesting! Have you looked into the frequency ratios between notes in chords that sound harmonious vs. dissonant? What patterns might you expect to find?"

How It Helps

✓
Deepens Your Thinking
Asks questions that push you beyond surface-level ideas
✓
Never Gives Answers
Your work stays 100% authentic — the AI only guides
✓
Available 24/7
Get instant feedback as you write each section
✓
Teacher Visibility
Your teacher can see conversations to support you better

Free to start: Sign up to get 20 free AI prompts

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AI Exploration Coach BETA

Exploration Ideas

Triangulation and Survey Points

Has the Elizabeth line led to a rise …

Swiss Shooting Range Over a Wall and a …

Mathematics of Card Shuffling

Attaching a water hose sprinkler to a speaker

Day Length

Daylight Hours

A Ferris Wheel

Solar Analemma

The Waterfall Swing

Spirals and Polygons

Spiraling