Pure Mathematics + Cybersecurity
Break a secret with number theory: how RSA works
Encrypt and decrypt a message with small primes by hand, then in code, and see why large primes matter.
- Advanced
- 1–2 weeks
- Free
606 projects · 13 streams · every class
Pure Mathematics projects 12
Patterns, proofs and constructions in algebra, geometry, number theory and calculus.
12 Pure Mathematics projects
Pure Mathematics + Biology
Explore the Fibonacci sequence in nature
Count spirals on pine cones, sunflowers and pineapples and test whether they are Fibonacci numbers.
- Beginner
- 2–7 days
- Free
Pure Mathematics · Trigonometry
Measure heights with trigonometry
Make a clinometer and find the height of your school building, a tree and a tower.
- Easy
- 1 day
- Under 250
Pure Mathematics · Geometry
Prove the Pythagorean theorem five ways
Build paper dissections and algebraic proofs of the theorem and compare how each convinces.
- Easy
- 2–7 days
- Under 250
Pure Mathematics + Fine Arts
Explore tessellations and design your own
Find which regular polygons tile the plane and create an Escher-style tile.
- Beginner
- 1 day
- Under 250
Pure Mathematics · Calculus
Find the best shape for a container
Find the dimensions of a can that hold a fixed volume with the least material, and compare with real cans.
- Intermediate
- 2–7 days
- Under 250
Pure Mathematics · Algebra
Make and analyse a magic square
Build 3×3 and 4×4 magic squares and prove why the centre of a 3×3 must be 5.
- Beginner
- 1–3 hours
- Free
Pure Mathematics + Programming
Visualise fractals with code
Draw the Koch snowflake, Sierpinski triangle and Mandelbrot set and measure a fractal dimension.
- Intermediate
- 2–7 days
- Free
Pure Mathematics + Geography
Investigate the four-colour theorem with maps
Colour maps of states and districts with as few colours as possible and link it to graph colouring.
- Easy
- 1 day
- Under 250
Pure Mathematics · Combinatorics
Find patterns in Pascal's triangle
Build 16 rows of the triangle and discover at least six patterns hidden in it.
- Easy
- 1–3 hours
- Free
Pure Mathematics · Algebra
Create a mathematical card trick and explain it
Learn three self-working card tricks and prove with algebra why each works.
- Easy
- 1 day
- Under 250
Pure Mathematics + Programming
Map your school as a graph and find shortest paths
Model corridors and rooms as a graph and find the fastest route between any two rooms.
- Intermediate
- 2–7 days
- Free
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