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Mathematics & other curiosities

A place for
curious thinking.

Explore mathematical ideas through problems, proofs, code, and experiments. Follow a question, test a pattern, and see where curiosity leads.

Explore the notebook About the notebook ↗

What is the area of the shaded square?

The tilted square a b ? a2 b2

Four congruent right triangles. Two marked lengths.

Ways to explore

Follow a thread
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Problems ↗

A question to think about, with a solution to uncover when you’re ready.

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Explorations ↗

Follow an idea through mathematics, code, images, and experiments.

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Learning modules ↗

Build understanding step by step, with explanations and hands-on learning.

A little time to play

Puzzles, just for the fun of it.

Pick a game and settle in. Slide a block, fit a tile, or find a path across Hex.

Play a puzzle

From the notebook

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Exploration

Hex: a game with no middle ground

Build a connection, challenge the computer, and walk a coastline to discover why Hex can never end in a draw.

gamestopologygraph theory
Learning module five lessons of 60–90 minutes, plus problem work

Derivatives: from rates to local linearity

Build the derivative from secant slopes, derive the rules, master demanding computations, and discover what differentiability really requires.

calculusderivativesreal analysis
Exploration

Three utilities: from the plane to a mug

Connect three houses to gas, water, and electricity. The plane refuses—but a mug, a donut, and a square with joined edges reveal a way through.

topologygraph theorypuzzles

A window into research

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