Interactive generators for number patterns, magic squares, mirror identities, selfie fractions and recreational mathematics—collected in one place.
Create natural-number expressions using ordered digit sequences, running equalities or repetitions of a single chosen digit.
Explore amicable relationships through divisor sums, digit-split powers and products.
Create expressions for natural numbers using ordered digits from 1 to 9 and from 9 to 1.
Find representations of an individual natural number using repetitions of each selected digit from 1 through 9.
Generate verified families by growing repeated blocks of one chosen digit, for a single target or a complete interval.
1 to 1,000,000 Natural Numbers
Explore the author’s running-type and fraction-type collections, with structural generation when a requested identity is not stored.
Search and extend verified single-letter pattern families, with an individual representation fallback when no family is currently identified.
Discover chains of equal expressions built from consecutive increasing or decreasing digit runs.
Build verified running equalities with Triangular and Fibonacci functions, including nested and mixed compositions.
Explore square, consecutive, triple and general k-factor patterns—including mirror-style searches, interval exploration and downloadable results.
Explore square-number growth, palindromic structures and paired reversal patterns from individual seeds or whole intervals.
Discover substring, insertion and mirror-style patterns produced by growing pairs of consecutive natural numbers.
Explore coordinated triple products and test their growing forms for insertion, substring and reversal-based patterns.
Use one master workspace for square, double, triple and higher-factor multiplication patterns through eight factors.
Explore digit-preserving growth, pandigital-type structures and Pythagorean triples constructed from consecutive Fibonacci numbers.
Discover digit-preserving families among primitive and multiple Pythagorean triples with odd or even first legs.
Generate expanding Pythagorean families whose coordinated digit spines form normal, pandigital and carry-extended patterns.
Watch four consecutive Fibonacci values produce a changing Pythagorean triple through a synchronized graph, golden spiral and right triangle.
Explore selfie fractions, determinants, digit-power identities and ten digit-order number generators.
Discover digit-split fraction identities, insertion families and independently verified examples.
Investigate multiplication-containing digit splits, pattern families and zero-extension constructions.
Explore 3×3 and 4×4 circulant determinants and discover arithmetic, selfie-style and scaling identities.
Find numbers reconstructed from signed sums of their digits raised to the first, second and third powers.
Build a number from its own digits using arithmetic, powers, square roots and factorials.
Find digit-order identities using triangular and Fibonacci functions, separately or together.
Search for digit-order representations using quadratic and cubic functions.
Construct selfie identities with binomial coefficients and optional factorials or square roots.
Search binomial-coefficient selfie identities with optional Fibonacci and triangular functions, factorials and square roots.
Use Stirling numbers of the first or second kind in digit-order expressions.
Explore triangular, square, pentagonal and hexagonal functions in selfie representations.
Find identities that use the integer partition function p(n).
Search digit-order expressions using double factorials and primorials.
Build representations with the nth prime, divisor count or divisor sum.
Explore digit-order identities with Lucas, Pell and Catalan functions.
Find numbers whose digits combine to a perfect power, with digit partitions and verified identities.
Explore verified digit-pattern families where the same multiset of digits produces a structured identity.
Search signed digit-power representations with optional division and download all verified solutions.
Explore same-digit equalities with signed powers, factorials, Fibonacci and triangular values, or quadratic and cubic functions.
Match signed sums of numbers with powers formed from their same digits. Search by final value and choose one or all solutions.
Match digit factorial expressions with digit powers and search multiple solutions across result values.
Use Fibonacci values, triangular values or both alongside factorial expressions.
Compare factorial expressions with quadratic or cubic digit values, separately or mixed.
Explore prime staircases, extension chains, embedded palindromic prime trees and digit-based prime families in one dedicated collection.
Generate repeating decimal blocks and explore their colored multiplication and rotation families.
Repeat a fixed digit block at the front, between or end of a seed, and follow each prime pattern to its next composite member.
Split a repeated digit block across distinct positions in a prime seed and explore successive prime members.
Start with a prime and successively add or subtract the even steps 2, 4, 6, 8, … while every running value remains prime.
Build chains of primes by prepending, appending or inserting digits while every successive number remains prime.
Wrap a starting number with reversed and forward digits to construct embedded patterns and search for successive prime values.
Explore prime branches by wrapping each parent with reversed and forward digit blocks. Adaptive block lengths let branches continue when shorter blocks fail.
Rearrange subsets of a prime number’s digits to reveal related primes and identify the richest digit families.
Explore families of primes connected through digit patterns, transformations and numerical relationships.
Combine selected day, month and year values to discover prime numbers hidden in calendar dates.
Trace digit-square journeys and separate happy numbers into prime and non-prime families.
Find prime pairs that sum to each even number in an interval, with options for distinct, twin and mirror-prime pairs.
Explore ordinary, cubic, patterned-palindromic, patterned-square and square-sum identities that remain true under digit reversal.
Search ordinary addition identities that remain true when every number is reversed.
Search sums of cubes that remain true when every base and the final sum are reversed.
Group palindromic mirror sums into prefix-extension families and isolate coordinated double-side patterns.
Construct zero-insertion square-sum families from mirror-number seeds and separate the palindromic families.
Search k-term combinations whose terms and reversals produce verified square-mirror identities.
Explore square-sum cycles and paths, perimeter magic polygons, open magic stars and closed magic stars.
Search an integer interval for a closed square-sum cycle, a complete open path or the longest verified chain.
Construct extra-point inclusion magic polygons using distinct consecutive numbers and one common sum on every side.
Generate and explore open magic stars in which every line shares one verified magic constant.
Explore closed-star and necklace-style arrangements while preserving their numbers and magic sums.
Construct concentric, cornered, cyclic, sandwich, striped and digital-reflection magic squares across odd and even orders.
Create nested magic squares whose successive borders preserve their own magic structure.
Generate magic-square constructions with structured corner groups and verified common sums.
Build even- and odd-order magic squares using cyclic or sandwich-type border arrangements.
Explore striped and semi-striped cyclic or sandwich-type constructions for even and odd orders.
Construct magic squares with the direct strips method.
Open generator ↗Build odd-order squares from full-width three-row and two-row magic rectangles.
Open generator ↗Generate striped and semi-striped cornered magic squares for even and odd orders.
Open generator ↗Explore sequential-entry magic squares across orders 3 to 12.
Open generator ↗Explore sequential-entry magic squares across orders 13 to 24.
Open generator ↗Explore magic squares with blocks from 3×3 to 14×14 in one generator.
Open generator ↗Orders 8-108; small rectangular strips, orientations, Excel exports and research references.
Open generator ↗Orders 10-108; concentric and cyclic borders with expanded inner-block arrangements.
Open generator ↗Orders 3–25: choose water reflection, upside-down, or all three transformations; verify sums and export squares side by side in Excel.
Explore water-reflection magic squares for orders 3-40, with digit-family choices, water flips, verification and Excel downloads.
Explore the second generator for upside-down and mirror-looking digital magic squares.
Generate digital magic squares with upside-down symmetry using the dedicated generator.
Construct higher-order digital magic squares with upside-down and mirror-looking behavior.
Created by Inder J. Taneja
Choose a construction and its parameters, then explore the algebraic square and verification sums.
Open generatorChoose a construction and its parameters, then explore the algebraic square and verification sums.
Open generatorChoose a construction and its parameters, then explore the algebraic square and verification sums.
Open generatorChoose a construction and its parameters, then explore the algebraic square and verification sums.
Open generatorOpen any collection to watch the magic cubes rotate and explore the controls provided in each design.
One cube + analysis
Open interactive collection ↗Two spinning cubes
Open interactive collection ↗Three spinning cubes
Open interactive collection ↗Three spinning cubes
Open interactive collection ↗Three spinning cubes
Open interactive collection ↗Six spinning cubes
Open interactive collection ↗Six spinning cubes
Open interactive collection ↗Six spinning cubes
Open interactive collection ↗Explore upside-down, mirror-looking and rotation-safe digital magic-square designs presented on six rotating faces.
Four digital cubes
Open digital collection ↗Four digital cubes
Open digital collection ↗Four digital cubes
Open digital collection ↗Three digital cubes
Open digital collection ↗Three digital cubes
Open digital collection ↗6-face · 12-faces · 24-Faces · 36-Faces
Cube · Double-Cube · 4D-Hypercube · Six Cubes
Order 3×3 · 6 rotating faces
Open rotatable cube ↗Order 3×3 · 12 rotating faces
Open rotatable cube ↗Order 3×3 · 24 rotating faces
Open rotatable cube ↗Order 3×3 · 36 rotating faces
Open rotatable cube ↗Order 4×4 · 6 rotating faces
Open rotatable cube ↗Order 4×4 · 12 rotating faces
Open rotatable cube ↗Order 4×4 · 24 rotating faces
Open rotatable cube ↗Order 4×4 · 36 rotating faces
Open rotatable cube ↗Order 5×5 · 6 rotating faces
Open rotatable cube ↗Order 5×5 · 12 rotating faces
Open rotatable cube ↗Order 5×5 · 24 rotating faces
Open rotatable cube ↗Order 5×5 · 36 rotating faces
Open rotatable cube ↗Order 6×6 · 6 rotating faces
Open rotatable cube ↗Order 6×6 · 12 rotating faces
Open rotatable cube ↗Order 6×6 · 24 rotating faces
Open rotatable cube ↗Order 6×6 · 36 rotating faces
Open rotatable cube ↗Order 7×7 · 6 rotating faces
Open rotatable cube ↗Order 7×7 · 12 rotating faces
Open rotatable cube ↗Order 7×7 · 24 rotating faces
Open rotatable cube ↗Order 7×7 · 36 rotating faces
Open rotatable cube ↗Order 8×8 · 6 rotating faces
Open rotatable cube ↗Order 8×8 · 12 rotating faces
Open rotatable cube ↗Order 8×8 · 24 rotating faces
Open rotatable cube ↗Order 8×8 · 36 rotating faces
Open rotatable cube ↗Order 9×9 · 6 rotating faces
Open rotatable cube ↗Order 9×9 · 12 rotating faces
Open rotatable cube ↗Order 9×9 · 24 rotating faces
Open rotatable cube ↗Order 9×9 · 36 rotating faces
Open rotatable cube ↗Order 10×10 · 6 rotating faces
Open rotatable cube ↗Order 10×10 · 12 rotating faces
Open rotatable cube ↗Order 10×10 · 24 rotating faces
Open rotatable cube ↗Order 10×10 · 36 rotating faces
Open rotatable cube ↗Order 11×11 · 6 rotating faces
Open rotatable cube ↗Order 11×11 · 12 rotating faces
Open rotatable cube ↗Order 11×11 · 24 rotating faces
Open rotatable cube ↗Order 11×11 · 36 rotating faces
Open rotatable cube ↗Order 12×12 · 6 rotating faces
Open rotatable cube ↗Order 12×12 · 12 rotating faces
Open rotatable cube ↗Order 12×12 · 24 rotating faces
Open rotatable cube ↗Order 12×12 · 36 rotating faces
Open rotatable cube ↗Convert and examine number representations, or verify prime magic-square constructions and prepare clearly structured reports.
Convert natural numbers into words, prime factorizations and Roman-numeral representations.
Verify prime magic squares, internal blocks and concentric structures, then create publication-style Excel reports with selectable block coloring.
Verify prime magic squares, internal blocks and deep concentric structures with colored reports.
Open checker ↗Check magic-square sums through the fifth power.
Open checker ↗Verify exact sums of entries, squares and cubes from a TXT matrix.
Open checker ↗1 Send an existing HTML generator or its link.
2 It receives a category, description and launch card.
3 This central page is updated while its address stays the same.