Dozenal Calc vs Popo Math

A "dozenal calculator" — a scientific calculator that computes not in tens, but in twelves. With its own symbols for the digits. What base 12 can do that base 10 can't In the decimal system, 1/3 is an infinite repeating fraction (0.333…). In base 12 it's short and exact: 0.4. Sixths, ninths, and every fraction whose denominator is built from twos and threes also become finite in dozenal. No coincidence: twelve has six divisors, ten only four. Dozenal Calc computes exactly — a rational track runs in parallel with floating-point arithmetic. Repeating fractions appear with a bar over the recurring digits, for example 1/7 as 0.186A3 with a repetend bar. Features • Basic arithmetic, parentheses, signs • Power, square root, nth root, logarithm to any base • Trigonometric and hyperbolic functions including their inverses • Constants π, e, φ, √2; factorial, absolute value, reciprocal, modulo • Parallel addition (a⊕b) for resistor circuits • Memory (STO/RCL/MC) with exact rational preservation • Angle modes DEG / RAD / GRAD • Numeral-system switch (base 12/10) in the settings — input AND result, applies to both calculators • Light and dark theme Unit converter One swipe to the left opens the second calculator: it converts imperial and metric units into one another — length, area, volume, weight, time, angle, money (£/sh/d), temperature and more. Compound entries like 3 ft 5 in, breakdown into part units, and math right inside the entry (× ÷ ⊕ ^ √ log) with memory and constants. Results travel between the two calculators at the press of a key. A color code keeps the worlds apart: green for the world of ten (metric, base 10), violet for the world of twelve (imperial, base 12). Hands-on theory — now with pictures A richly illustrated read explains why twelve in particular is a special number, in three blocks: • Twelve and the World — from the dodecagon and dodecahedron through pyrite, garnet, viruses and quasicrystals to music, art, architecture and calendars • Dozenal Mathematics — divisors and periods, the number bases compared, a history of place-value systems • Dozenal Society — the movement for twelve, new digits for ten and eleven, the TGM measurement system and related dozenal calculators Many chapters show public-domain historical illustrations — from Haüy's pyrite plate through Leonardo's dodecahedron to Vermeer's balance — each with a tappable source citation. Plus a dedicated unit theory on measure and number, two illustrated operating manuals for both calculators, and recommendations for dozenal-friendly calculators on every platform. Fourteen languages Deutsch, English, Français, Español, Italiano, فارسی, Русский, Gaeilge, हिन्दी, 简体中文, 繁體中文, Cymraeg, 日本語, العربية — freely selectable in the info menu. What Dozenal Calc doesn't do • No ads, no tracking, no analytics • No internet connection, no permissions • No personal data The app works completely offline. What you type stays on your device. Who is it for? For teachers who want to show how a different number system transforms everyday work with fractions — and for anyone who wants to see mathematics from an unfamiliar perspective. License: MIT. Contact: dozenal@weltanschauung.app

The more you play, the more you love math. Popo Math is a math practice app where you train with cute buddies. Its content follows the Japanese elementary math curriculum, grades 1 to 6. Every right answer makes the confetti, lights and music livelier, and the last question is a big party! Mistakes never cost points, and hints and pictures appear, so anyone can make it to the end. ■ It gets livelier with every answer Right answers add Sparkle, and the effects and music power up step by step. Rounds are short, so "One more!" comes naturally. ■ 58 units In curriculum order: making 10, carrying, times tables, division, decimals, fractions, mixed numbers, telling time, units of length and volume, rounding, factors and multiples, ratios, solving for x and more. You can also pick a unit to practice. ■ Real column math Like on grid paper, write one box at a time, starting with the ones place. You write the carries and borrows yourself, and long division goes divide → multiply → subtract → bring down. Once you get good, carries fly up on their own. ■ Find out WHY it was wrong The app recognizes the kind of mistake (a forgotten carry, a times-table mix-up, a remainder that's too big, the decimal point in the wrong place…) and explains it with a short tip and a picture (ten frames, dot arrays, blocks, fraction bars). ■ Step by step until it clicks New units are solved one step at a time, the way the textbook does it. Once you know them, answer in one go. ■ Times Tables map and Time Attack The 81 squares light up one by one as you learn them. Race each table and beat your best time. ■ A review just before you forget The app tracks every single problem, and an algorithm based on memory research (FSRS) schedules reviews automatically. Missed problems go to the Mistake Notebook. ■ Little things that make you come back Daily missions, daily stickers, a streak calendar, trophies and a collection. ■ 4 buddies cheer you on Pick your favorite: Popo, Hamu, Pyoko or Penta. ■ Three languages Japanese, Simplified Chinese and English — switch in Settings. ■ For parents ・No ads. All features are currently free to use ・No account needed; no names or email addresses are entered ・Progress is stored only on the device and in your own iCloud, never sent to the developer (it carries over to a new iPhone through iCloud) ・No analytics or tracking tools ・The evening reminder (6 pm) only arrives if you allow it Requires an iPhone with iOS 17 or later.