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Mathematical Curiosities & Special Topics Calculators
Explore unusual patterns, historical systems, paradoxes, constants, and recreational mathematics. Use this collection when explore unusual patterns, historical systems, paradoxes, constants, and recreational mathematics. Start with the calculator matching the values you possess, then use related tools to verify or extend the result.
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Mathematical Curiosities & Special Topics topics
Select a topic to reveal its calculators. Multiple topics can remain open at the same time.Mathematical Curiosities & Special TopicsExplore unusual patterns, historical systems, paradoxes, constants, and recreational mathematics.40 available
- Magic Square CalculatorGenerate a normal magic square and verify its common line sum.Open calculator
- Collatz Sequence ExplorerGenerate a bounded 3n+1 sequence and report its peak and stopping state.Open calculator
- Pi Approximation CalculatorCompare bounded Leibniz and Nilakantha series approximations of π.Open calculator
- Golden Ratio CalculatorScale a short or long segment using the golden ratio.Open calculator
- Ancient Numeral ConverterConvert between canonical Roman numerals and modern integers.Open calculator
- Hilbert Hotel ExplorerDisplay finite prefixes of classic countably infinite room-shift mappings.Open calculator
- Galileo's Paradox ExplorerCompare positive integers and perfect squares through their explicit bijection.Open calculator
- Fractal Iteration CalculatorIterate the Mandelbrot orbit zₖ₊₁=zₖ²+c from z₀=0.Open calculator
- Handshake Problem CalculatorCount unordered pairs among n people.Open calculator
- Tower of Hanoi CalculatorFind the exact minimum move count for n disks.Open calculator
- Josephus Problem CalculatorFind the survivor under repeated cyclic elimination.Open calculator
- Zeno's Paradox ExplorerCompare a finite geometric travel sum with its infinite limit.Open calculator
- Conway's Game of Life ExplorerAdvance a bounded finite grid under Conway's B3/S23 rule.Open calculator
- Logistic Map & Chaos ExplorerGenerate a bounded logistic-map orbit.Open calculator
- Game Theory Payoff CalculatorFind pure-strategy Nash equilibria in a general 2×2 two-player payoff matrix.Open calculator
- Prisoner's Dilemma CalculatorCalculate expected payoffs from independent cooperation probabilities and a supplied dilemma payoff table.Open calculator
- Nim Game SolverClassify a normal-play Nim position and produce one winning move when available.Open calculator
- Luhn Algorithm CalculatorValidate a decimal identifier or calculate its Luhn check digit.Open calculator
- Queueing Theory CalculatorCalculate steady-state M/M/1 queue measures.Open calculator
- Cyclomatic Complexity CalculatorCalculate control-flow cyclomatic complexity from graph counts.Open calculator
- Nontransitive Dice CalculatorCompare exact pairwise win probabilities for three finite dice.Open calculator
- Penney's Game CalculatorFind which of two equal-length H/T patterns appears first in independent fair coin flips.Open calculator
- Birthday Paradox CalculatorFind the probability that at least two people share one of d equally likely birthdays.Open calculator
- Monty Hall Probability ExplorerCompare staying and switching after an informed host leaves one alternative door.Open calculator
- Bertrand's Box Paradox CalculatorCompute the posterior chance that the other coin is gold after observing a gold coin.Open calculator
- Bertrand's Random Chord Paradox ExplorerCompare long-chord probabilities under three different randomization procedures.Open calculator
- Two Envelopes Paradox CalculatorShow the pre-selection mean for two fixed envelopes and explain why switching needs a prior model.Open calculator
- Boy or Girl Paradox CalculatorCompare conditional probabilities under two distinct information protocols.Open calculator
- False Positive Paradox CalculatorCalculate positive predictive value from prevalence, sensitivity, and specificity.Open calculator
- Simpson's Paradox ExplorerCompare two treatments within two groups and after aggregation.Open calculator
- St. Petersburg Paradox CalculatorCalculate the expected payoff of a finitely truncated St. Petersburg game.Open calculator
- Parrondo's Paradox CalculatorEvaluate expected capital change for a bounded pattern of games A and capital-dependent B.Open calculator
- Buffon's Needle SimulatorCompare a repeatable seeded simulation with the short-needle crossing probability.Open calculator
- Benford's Law CalculatorCompare observed leading digits with Benford's expected first-digit distribution.Open calculator
- Coupon Collector CalculatorFind the expected draws needed to observe every one of n equally likely coupon types.Open calculator
- Gambler's Ruin CalculatorFind the probability of reaching a goal before zero and the expected duration.Open calculator
- Secretary Problem & Optimal Stopping CalculatorFind the best reject-then-select threshold for a finite random-order secretary problem.Open calculator
- Gamma Function CalculatorEvaluate the real gamma function with a bounded Lanczos approximation.Open calculator
- Bessel Function CalculatorEvaluate Jₙ(x) for a bounded non-negative integer order.Open calculator
- Error Function CalculatorApproximate erf(x) and erfc(x) on a bounded real interval.Open calculator