Science & Education
θ_c = arcsin(n₂/n₁) with the Brewster angle — glass 41.81°, diamond 24.44°, the physics of fibers and sparkle.
critical-angle-total-reflectionScience & Education
Hydrogen level n: r_n = n²a₀, E_n = −13.605693/n² eV, v_n = αc/n, orbital period, plus optional transition energies with named series lines.
bohr-model-calculatorData Visualization
Paste an order or event CSV and get the growth stack in one page: a cohort retention triangle with a heatmap, RFM quintile scoring mapped to the ten standard lifecycle segments, and a strict-order funnel.
cohort-retention-rfm-funnel-analyzerScience & Education
Δλ = (h/m_e·c)(1 − cos θ) for X-ray photons: Compton wavelength, shifted wavelength/energy, recoil electron energy and angle, 0°/180° edge cases.
compton-scattering-calculatorMedia
Turn a field recording into one seamless loop for games, meditation apps, or video background beds — quiet-seam placement, long equal-power crossfade, optional high-pass.
audio-seamless-ambience-loopMedia
Apply EDM-style tempo-synced pumping ducking to any audio without a kick-drum sidechain file — volume-envelope automation in the style of LFO Tool / Kickstart.
audio-sidechain-pump-generatorMath & Numbers
Group exponent λ(n) from prime factorization with φ(n) comparison, primitive-root existence, Korselt's Carmichael-number detection, and optional sample-unit verification.
carmichael-functionMath & Numbers
Generalized pairwise-merge CRT for 2–20 congruences: coprime moduli give the product modulus, consistent non-coprime moduli give the lcm, inconsistent systems are rejected.
chinese-remainder-theoremMath & Numbers
Textbook Hungarian algorithm for 2–8 × 2–8 assignment problems: row/column reductions, augmenting-path zero matching, König line covers, and substitution-verified optimal assignments.
assignment-problem-solverMath & Numbers
Deduplicated, lexicographic permutations / combinations / subsets of up to 12 items with exact multiset counts; display capped at 200 entries.
combinatorial-generationMath & Numbers
Activity-on-node CPM: ES/EF/LS/LF, total float, project duration, and every critical path; cycles and unknown predecessors are rejected.
critical-path-methodMath & Numbers
Minimal SOP via Quine–McCluskey with essential prime implicants, exact minimum cover, Gray-coded Karnaugh map, and full-assignment verification.
boolean-algebra-simplifier