From 2010 to 2026: the inheritance problem generalized
From Fibonacci’s puzzle to a formula for every child: proof of the general case, four checked examples, and the roles of a and d.
ReadMathematics
Articles by topic
Clear, organized learning paths that build strong foundations in mathematics and computer science.
Algorithms
Graph 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.
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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.
ReadLine symmetry: eight exercises with drawn solutions
Eight line-symmetry exercises for first-year middle school, with clear drawings and illustrated solutions: segments, triangles, four letters and coordinates.
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.
ReadOne chord is enough: finding an annulus area with Pythagoras
A 20 cm tangent chord determines an annulus area without either radius. Diagram, proof, general formula, and exercises with hidden solutions.
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Probability
Combinatorics: from first counts to complex problems
A step-by-step path with examples, justified formulas, a laboratory and an explained-answer quiz.
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