One 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.
ReadMathematics
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Clear, organized learning paths that build strong foundations in mathematics and computer science.
Geometry
Probability
17 probability problems with worked solutions
From cards to the three doors: 17 probability problems adapted from Giovanni Vittorio Pallottino, with step-by-step solutions and one corrected book error.
ReadProbability and statistics: a course in 20 chapters
From random experiments to Bayes, from distributions to confidence intervals: one course with an index and twenty expandable chapters.
ReadFrom population to confidence intervals: a guided journey through distributions
Random variables, eight distributions, sampling, standard error and confidence intervals: theory and simulations in one coherent path.
ReadFifteen experiments that make probability visible
Dice, coins, an urn, Monty Hall and Poisson: fifteen simulations with observed histograms and theoretical probabilities.
ReadThe power of the complement: 25 probability problems
From dice to birthdays: 25 problems with hints, step-by-step solutions and explicit assumptions to learn the complement method.
ReadProbability: 10 difficult problems solved step by step
Ten advanced challenges with hidden hints and solutions: counting, dependence, Bayes, geometry, waiting times and strategies.
ReadForty-card frustration solitaire: why you almost always lose
The 40-card Neapolitan solitaire explained step by step: matches, dependence, inclusion-exclusion and the exact winning probability.
ReadProbability: 10 famous problems that fool intuition
From Monty Hall to Buffon’s needle: ten puzzles with explicit assumptions, formulas and hidden solutions to help you reason about chance.
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Sequences
Guess the Next Number: 100 Sequences to Challenge Your Logic
One hundred original sequences in seven families, with progressive hints, verified solutions and a six-mode interactive laboratory.
ReadNumber sequences: four numbers do not determine the fifth
From 1, 2, 3, 5 to Fibonacci and Lagrange interpolation: a step-by-step essay explaining why a finite sequence has infinitely many continuations.
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Sets
Sets: 10 very challenging problems with diagrams
Ten advanced set problems: inclusion–exclusion, symmetric differences, families, functions and limits, with hidden hints and illustrated solutions.
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