p vs Curvia

p-adelic shows a number in all of its completions at once. Type 1/3, √2, a polynomial or log 7 and watch the adelic strip: one column for the real line and one for each prime p, each streaming the number's digits in base p and growing leftward as you turn the precision dial. There is no "p-adic mode" to switch into — you always see the whole picture, the way number theorists think about it. THE STRIP • A column per place: ∞ plus the primes that matter for your input, and any prime you pin. • Streaming precision from 5 to 200 digits; every column updates together. • Exact periodicity for rationals: the repeating block is marked with an overline, and long runs of digits fold into pills you can tap open. • Tap a column to focus it; the focused card shows valuations, unit parts, Legendre symbols and the Laurent form. DEEP DIVE • Digits, Laurent series and Witt-vector views of the same number. • Nested balls: zoom into ℤₚ ball by ball, following your number's digits. • The Bruhat–Tits tree and the Berkovich line of the chosen place. ALGEBRAIC NUMBERS • √d, roots of unity ζₙ, Teichmüller representatives, and any algebraic number given by its minimal polynomial, e.g. algebraic(x³ − 2). • See whether a prime splits, stays inert or ramifies; extend the field with one tap and cycle through the Galois conjugates. POLYNOMIALS • Newton polygons at every prime and at ∞, with slopes, multiplicities and the Krasner check. SPECIAL FUNCTIONS • p-adic exp, log and Artin–Hasse, with their convergence disks. • Factorials with Legendre's formula, Morita's Γₚ with the Wilson check. • Kubota–Leopoldt ζₚ and L-values, Hilbert symbols with the reciprocity check, and Tate's local factors. LEARN AND REUSE • A Library of worked examples for every idea above, from −1 = …(p−1)(p−1)(p−1) to the Berkovich line of ∛2. • History you can reopen with one tap. • VoiceOver describes every visualization; text and digits follow Dynamic Type. PRIVATE BY DESIGN Everything is computed on your device. The app has no account, no analytics and makes no network connections. For students meeting p-adic numbers for the first time, teachers who want a live picture to point at, and researchers who need a Newton polygon or a Hilbert symbol checked in seconds.

**Most people never get to see how beautiful mathematics really is. Curvia changes that.** Behind every equation hides a shape — glowing, breathing, impossibly intricate. Curvia lets you see those shapes, and play with them, with no math required. Drag one slider and a Fourier series draws a heart. Nudge another and a strange attractor blooms into a slow three-dimensional storm. You don't study the math here. You feel it. It's the math class you wish you'd had: not problems to solve, but wonder to fall into. **A hundred ideas of mathematics, made visible** • Curves — harmonographs, roses, spirographs, the Fourier machine that draws a heart. • Attractors & Chaos — Lorenz, Aizawa and other strange attractors, tumbling in 3D. • Fractals — Koch snowflakes, Sierpinski, dragon curves, Pythagoras trees. • Escape-Time sets — Mandelbrot, Julia, the marbled Lyapunov, and more. These aren't decorations. They're the real, famous objects of mathematics — the ones usually trapped inside textbooks — finally something you can touch. **See the formula behind the beauty** Tap once and the equation appears beneath any piece. The point isn't to teach you — it's to let you fall for the math first, through its beauty, so the symbols stop being scary and start being magic. Wonderful for the curious, for kids, and for anyone who was ever told they're "not a math person." **Made to feel effortless** • Live sliders — every move reshapes the figure instantly. • "Surprise me" — one tap reveals a whole new piece. • Hand-tuned glowing palettes. • Tap the heart to keep the ones you love. **Keep the wonder with you** Save any piece to carry a little mathematical beauty on your screen — as an image, a video, or a true live wallpaper that animates when you press your lock screen. (Live videos and live wallpapers are part of Curvia Pro, a one-time unlock.) No account. No clutter. Everything stays on your device. Math is the engine. Wonder is the product. > *Curvia isn't a math tool and it isn't a design app — it's an invitation to see that mathematics was beautiful all along.*