Square-Sum Cycle and Open-Path Generator
Search an integer interval for a closed square-sum cycle, a complete open path or the longest verified chain.
- Cycle and path search
- Verified diagrams
- Downloads
Interactive generators for number patterns, magic squares, mirror identities, selfie fractions and recreational mathematics—collected in one place.
Every generator is presented equally in one consistent collection. Select any card to begin exploring.
Search an integer interval for a closed square-sum cycle, a complete open path or the longest verified chain.
Discover digit-split fraction identities, insertion families and independently verified examples.
Investigate multiplication-containing digit splits, pattern families and zero-extension constructions.
Search k-term combinations whose terms and reversals produce verified square-mirror identities.
Explore 3×3 and 4×4 circulant determinants and discover arithmetic, selfie-style and scaling identities.
Construct extra-point inclusion magic polygons using distinct consecutive numbers and one common sum on every side.
Open 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 ↗These sections are prepared for the HTML generators you choose to add next.
Interactive constructions, digital designs and verification tools.
13 COLLECTIONS ADDEDExplore equal sums, reversed terms and same-digit identities.
1 GENERATOR ADDEDSearch patterned, digit-split and multiplicative selfie fractions.
2 EXPLORERS ADDEDInvestigate primes, blocks, borders and concentric structures.
READY TO ADD1 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.