# Grid tilings and a mathematical proof > A mathematical puzzle is presented through turquoise grid tilings, highlighted empty cells, inequalities, sequence plots, and hands-on paper constructions, framed by discussion of AI and mathematical understanding. - Kind: Video - Page: https://meetreference.com/v/video-grid-tilings-and-a-mathematical-proof-8d48ba/ - Ready-to-use agent handoff: https://meetreference.com/v/video-grid-tilings-and-a-mathematical-proof-8d48ba/agent.txt - Authorship: Not stated - Made with: Not stated - Model: not stated - Built with: manim - Style: Math & science; diagrammatic, minimalist, educational, high-contrast, geometric - Length and format: 2 min, 16:9 (1280x720 source) - Playback: a muted visual reference. The original soundtrack is available only at the source. - Shared by 3Blue1Brown in YouTube, Sep 18, 2026: https://www.youtube.com/watch?v=Nbwv5wHQoj0 - Prompt fidelity: Unavailable in this entry. The recreation brief is written by Reference. ## Before you start Guidance from Reference, separate from the creator's instructions. 1. Read the reference and inspect the project, installed libraries, and available agent skills before writing code. Reuse suitable tools already present. 2. Prefer the creator-reported libraries and skills when they fit the task. Explain what useful additions help with, and install missing project dependencies or relevant skills from official sources when the environment and the user's existing permissions allow it. Respect the project's package manager and setup rules; do not ask again for routine setup already authorized. 3. Distinguish tools used by the creator from your own recommendations. A listed tool is not automatically required, and an empty tools or requirements list means the setup is unknown, not that nothing is needed. 4. Ask concise questions when missing inputs or choices materially affect the result: paid services, credentials, the user's assets, or a different production approach. Use existing answers and permissions; continue independent work while waiting. 5. If a useful library, skill, or service cannot be installed or used, explain an available alternative and its expected effect on quality, features, or effort. Get the user's choice before a material compromise; otherwise state the fallback and continue. Never silently simplify the result or claim to have used a tool you did not use. ## Recreating this video This is a visual reference. No original creator prompt is available. The following brief was written by Reference after inspecting the work. Use a consistent grid and limited color vocabulary to explain a packing, scheduling, or allocation problem. Pair the abstract diagram with a physical paper version, then place successive bounds beside clearly marked examples. Reserve a contrasting highlight color for the cells or quantities that carry the argument. 1. Open the live work or source and inspect the frame images below. 2. Adapt its layout, hierarchy, palette, and interaction patterns to the user's own content and brand. 3. Compare the result against the reference. Use your own assets and credit the original creator. ## What it looks like Written by Reference from the video frames, not by the creator. A sequence of mathematical illustrations using gridded square diagrams, colored markers, and inequality labels. - Color: Black backgrounds with cyan and teal grids, white mathematical text, and yellow and muted red highlights. - Type: Clean instructional graphic with serif-style mathematical notation and thin diagram lines. - Framing: Each illustration is centered within a black panel, with formulas above or beside the diagrams and labeled axes around some grids. - Structure: The artwork alternates between square grid diagrams with highlighted cells or points and simpler grid-count illustrations, alongside expressions involving k² and 2k. Storyboard, nine frames spread across the video: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/storyboard.webp - Frame 1 at 5.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f1.webp - Frame 2 at 15.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f2.webp - Frame 3 at 25.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f3.webp - Frame 4 at 35.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f4.webp - Frame 5 at 45.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f5.webp - Frame 6 at 55.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f6.webp - Frame 7 at 65.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f7.webp - Frame 8 at 75.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f8.webp - Frame 9 at 85.0s: https://meetreference.com/media/video-grid-tilings-and-a-mathematical-proof-8d48ba/f9.webp ## How it was made, per the creator - Notes: Reference shows a muted excerpt from 25:12 to 26:42. Watch the complete video at the original source. ## Links - Watch: https://www.youtube.com/watch?v=Nbwv5wHQoj0 - Original post: https://www.youtube.com/watch?v=Nbwv5wHQoj0 - Discovery collection: https://www.youtube.com/@3blue1brown/videos