Prime numbers and hidden patterns
Divisibility, the sieve of Eratosthenes and regularities that help explore primes.
ReadMathematics
Articles by topic
Clear, organized learning paths that build strong foundations in mathematics and computer science.
Number theory
Algorithms
Between the points and beyond: interpolation, regression and least squares
Lines, exponentials, powers and parabolas: identify the question, calculate coefficients and examine data in a visual laboratory.
ReadReverse algorithms: cards, Josephus and outcomes to construct
Two problems about starting at the end: prepare a deck and construct winning seats in Josephus. With a laboratory, a birthday application and a chosen pair.
ReadNumerical approximations: algorithms for approaching a result
Bisection, Newton, Taylor and numerical integration explained with examples. Two interactive laboratories show steps and errors.
ReadGraph algorithms: BFS, Dijkstra and Kruskal proved step by step
Three different questions: reaching a destination in fewer steps, finding the cheapest route, and connecting every point at minimum total cost. One graph helps us distinguish the objectives.
ReadThe solution is not enough: Fibonacci’s inheritance
A numerical answer can be correct without explaining why a procedure works. Two problems from the Liber Abaci lead to a proof and a generalisation.
ReadTeaching and learning through problems: from natural language to algebra
A complete teaching pathway for understanding a problem, translating it from natural language into algebra, and choosing strategies such as invariants, divisibility, and working backwards.
ReadAlgorithms: 10 fundamental methods that solve problems
Search, sorting, graphs, dynamic programming, and compression: core idea, pseudocode, complexity, and use cases.
Read
Geometry
Fractals: from simple rules to nature’s complexity
Sierpiński, Cantor, Koch, Mandelbrot and Julia explained through constructions, calculations and natural examples. A laboratory for building, measuring and exploring.
ReadGeometry: 25 problems of varied difficulty with solutions
From plane figures to optimization: 25 geometry problems ordered by difficulty, with reasoned solutions to reveal after trying.
ReadFind the symbol: the hidden geometry of the cards
Build 57 cards with 8 symbols each and exactly one match in every pair: finite projective planes, modular arithmetic and a step-by-step proof.
ReadOne extra metre: the rope around the Earth
A rope encircles the Earth. Add one metre: how far does it rise? A surprising result that does not depend on the radius.
ReadArticles 49–60 of 72