3D Geometry vs LUMO

Solid geometry is hard when you can't picture it. 3D Geometry turns textbook diagrams into 3D models you can rotate, slice and unfold, and gives every length, area and volume as an exact value like 2√2 or 12π. Free to download: the core 3D models, formulas and unfolding animations are free, and every Pro tool can be tried in full once before you decide. FREE FEATURES • 9 solids: cube, cuboid, regular tetrahedron, square pyramid, triangular prism, cylinder, cone, sphere, torus • Textbook labeling (ABCD-A₁B₁C₁D₁); hidden edges turn dashed automatically from any angle • Formulas with exact answers: surface area, volume, diagonals, slant height and more • Unfolding animations: cubes, prisms and pyramids open step by step; a cone unrolls into a sector; a sphere is approximated by orange-peel gores PRO PROBLEM-SOLVING TOOLS • Cross-sections: drag a cutting plane and see the section's shape and area in real time. Reproduce the triangle, rhombus, pentagon and regular hexagon sections of a cube, or slice a cone to get an ellipse, parabola and hyperbola • Angles and distances in space: tap points in 3D to get the angle between skew lines, line–plane angle, dihedral angle, point-to-plane distance and distance between skew lines, with the translated line, projection or common perpendicular drawn for you • Circumscribed and inscribed spheres: center, radius and derivation steps, all visualized • Shortest paths: the classic "ant on a box" problem with three unfoldings compared; unroll a cylinder or cone to turn the curved path into a straight line • Cube nets: folding animations for all 11 nets, opposite faces color-matched, common trick shapes, and a random "will it fold?" quiz • Three views: front, side and top orthographic views in standard layout, with hidden edges dashed • 24 worked exam-style problems: hint, answer, then step-by-step solution, each opening in 3D so you can explore it yourself • Classroom mode: full-screen presentation, whiteboard background, pen annotations, and export to high-resolution images and GIF animations for slides ONE-TIME PURCHASE, NO SUBSCRIPTION Pro is a single in-app purchase that unlocks everything on iPhone, iPad and Mac. WHO IT'S FOR • Middle school students: nets, shortest paths, three views • High school students: cross-sections, circumscribed spheres, angles and distances in space • Math teachers: demonstrate on a projector, annotate, and export animations for lessons Note: the in-app text is currently in Chinese. The 3D models, labels and math notation work in any language.

LUMO helps you build vocabulary your way: with personal flashcard decks, instant translation, and a study flow designed to keep you moving. Create collections for any topic: travel phrases, exam prep, work vocabulary, or words you pick up every day. Type a word, tap Translate, and your flashcard is ready. No switching apps, no copy-paste. STUDY THAT STICKS • Flip cards to reveal the translation • Swipe right when you know it, left when you need more practice • Cards you’re still learning stay in the deck until you master them • Reverse mode: practice from translation to word • Built-in pronunciation: hear words and translations while you study TEST WHAT YOU KNOW • Practice mode: quiz yourself on learned words or your whole deck • Multiple choice, type the answer, listening, match pairs, or a mixed session • Pick session length and swap language direction before you start • See your score, review mistakes, and retry the full session • Separate from Learn: swiping marks cards learned; Practice only tests you MAKE A DECK IN SECONDS • Generate cards by topic, CEFR level, and word type (3 times a day) • English↔Russian from local packs; other pairs via AI • Smart import: paste a list from Notes. Missing translations filled in automatically • Type a word, tap Translate, and your flashcard is ready ORGANIZE YOUR LEARNING • Group words into custom collections • Filter decks by status: New, In progress, or Learned • Track total words and how many you’ve learned • Study again anytime to refresh a finished set WORKS WITH YOUR LANGUAGES Choose source and translation languages including English, Spanish, French, German, Italian, Portuguese, Russian, Polish, Japanese, Korean, Chinese, Turkish, Arabic, Serbian, and Ukrainian. Set your preferred language pair once and build decks faster. YOUR DATA, YOUR DEVICES Sign in with Apple or email. Your collections sync to the cloud so you can pick up where you left off. Decks are stored locally too. Study offline and sync when you’re back online. Optional reminders if you haven’t practiced for 1, 3, or 7 days. DESIGNED FOR iOS A calm, focused interface with light and dark appearance. Available in 14 interface languages, including Ukrainian. Whether you’re starting a new language or sharpening vocabulary you already know, LUMO turns words into flashcards you’ll actually use. Download LUMO and start your next collection today.