About 4Geometry

4Geometry is a purpose-built search platform focused on geometry content across education, research, and practice. It is designed to help people find relevant material -- from geometry textbooks and tutorials to research preprints, interactive diagrams, geometry software and tools -- without wading through unrelated web pages. The site is intended for students, teachers, researchers, developers, designers, and curious learners who want clear access to geometry resources, whether they are looking for Euclidean proofs, computational geometry implementations, or visual examples of non-Euclidean ideas.

Why 4Geometry exists

General-purpose search engines are broad by design. They work well for many tasks, but when you need precise, mathematically relevant results -- for example, an analytic geometry derivation, a classical theorem with proof, or a tutorial on circle inversions -- broad indexing can create noise. Searches can return pages that mention geometric terms casually, product listings that aren't pedagogically helpful, or forum threads that lack authoritative references.

The goal of 4Geometry is to reduce that noise and surface material that is actually useful for geometry learning, teaching, and research. Instead of ranking only by general popularity or keyword frequency, the platform focuses on domain relevance, educational level, content quality, and topical accuracy. We aim to make it easier to find geometry tutorials, euclidean proofs, geometry visualizations, computational geometry papers, and geometry software that genuinely match the intent of the query.

How 4Geometry works -- an overview

4Geometry combines multiple indexing approaches and relevance algorithms to collect and organize publicly available geometry content. The result set is assembled from a combination of:

Academic papers and preprints, including geometry journals and conference proceedings;
Educational materials such as geometry textbooks, course pages, lecture notes, and geometry courses;
Tutorials, blogs, and forums that focus on geometry topics and step by step geometry explanations;
Interactive visualizations, geometry diagrams, 3D models, and geometry diagrams AI outputs that help users see concepts; and
Software, calculators, apps, and tools for analytic geometry, computational geometry, and interactive learning.

A few aspects of the platform's architecture and user-facing features are worth highlighting:

Focused indexing

In addition to crawling public web pages, course sites, and repositories, 4Geometry maintains a geometry-focused index that identifies documents where geometric ideas are central rather than incidental. This helps distinguish a page that mentions a "circle" in passing from a paper or tutorial that studies circle packings, Euclidean theorems, or geometric constructions in depth.

Relevance ranking tuned for geometry

Ranking takes into account several signals that matter for geometric content: topical relevance (does the page meaningfully treat the topic?), educational level (introductory, intermediate, advanced), source type (textbook, research paper, lecture note), and content clarity (presence of diagrams, worked examples, proofs). Ranking is informed by topic specialists and experience-based usage signals so that users can find useful sources more quickly.

AI-assisted features

4Geometry integrates AI systems for complementary, assistive tasks -- not to replace original sources, but to help users navigate them. The AI can:

Summarize papers and research summaries to give quick orientation to a preprint or journal article;
Provide stepwise geometry explanations and guided walkthroughs of geometric proofs, while linking back to original sources for verification;
Suggest and generate diagram ideas and geometry visualizations to illustrate a construction, theorem, or problem;
Help craft effective geometry prompts for interactive diagram tools or geometry diagrams AI;
Assist with proof checking suggestions and point to formal proof assistants or verification tools where applicable, while making clear that formal checking is separate work.

These AI features are designed to accelerate exploration: they highlight promising results, extract key ideas from long documents, and help translate complex mathematics into accessible steps for learners. The AI is explicit about when it is summarizing and always provides links to source material so users can verify details.

What you can find on 4Geometry

The platform is arranged to expose a wide range of resource types and subfields. Examples of content and results you can expect include:

Geometry textbooks, course notes, and references that cover Euclidean geometry, analytic geometry, and differential geometry;
Geometry tutorials and step-by-step geometry walkthroughs aimed at different educational levels;
Research papers, preprints, and research summaries in computational geometry, topology updates, and geometry journals;
Geometry visualizations, interactive diagrams, and 3D models that illustrate theorems, constructions, and counterexamples;
Tools and software: geometry software, geometry apps, calculators, geometry solvers, and proof assistant links;
Community resources: geometry blogs, geometry forums, interviews with researchers, conference announcements, and news about geometry breakthroughs;
Practical materials: geometry kits, rulers, protractors, geometry models, and vendors for geometry supplies when shopping is the goal;
Searchable glossaries, examples, and annotated lists of theorems and euclidean proofs for classroom use.

Every result is labeled by source type and level so you can quickly see whether a page is a research paper, an introductory tutorial, a blog post, a software repository, or a product listing. Filters allow you to restrict results to, for example, geometry courses, geometry papers, or geometry apps.

Who benefits from 4Geometry

Geometry touches many audiences. The platform is intentionally flexible so different users can adjust searches and filters to their needs.

Students

Whether preparing for coursework, competitions, or independent study, students can find geometry tutorials, worked geometry problems, diagrams, and step-by-step geometry explanations. The AI chat can offer guided help on problem-solving and point to textbooks, geometry calculators, or geometry solver tools for practice.

Educators

Teachers and instructors can assemble lesson plans using classroom-ready resources: printable diagrams, interactive geometry visualizations, collections of euclidean proofs, and curated lists of geometry textbooks and references appropriate to an educational level. Filters for source type and educational geometry make it easier to find materials suited to a lesson.

Researchers

Researchers working in computational geometry, differential geometry, topology, or analytic geometry can search for recent preprints, conference reports, and geometry journals. The platform surfaces research summaries, related works, and citations, and points to technical resources like code repositories and computational geometry software.

Developers and software engineers

Developers building geometric algorithms or visualization tools can find geometry software, geometry libraries, example implementations, and geometry calculators. Search facets can narrow to computational geometry, analytic geometry algorithms, or geometry visualizations.

Designers, architects, and makers

Design professionals often need geometric references, templates, and 3D models. The search brings up geometry examples, construction diagrams, and geometry models that are relevant to design workflows, along with suppliers for equipment and geometry kits.

Hobbyists and lifelong learners

For people exploring geometry for personal interest, the platform aggregates approachable tutorials, geometry blogs, and community discussions so learners can follow topics from elementary geometry to more advanced areas like non-Euclidean ideas or topology updates.

Search features and tools

The user interface combines a traditional search box with a set of task-oriented modes and filters. Typical features include:

Search modes: Web, News, Shopping, Chat -- choose the mode depending on whether you want papers, announcements, product listings, or interactive help;
Filters and facets: Refine results by subfield (Euclidean geometry, analytic geometry, computational geometry, differential geometry, topology), source type (textbook, research paper, tutorial, blog), educational level, and publication date;
Result annotations: Each item shows why it matched your query -- key phrases, topical tags, and whether it contains diagrams, proofs, or code;
Diagram and visualization viewer: Preview geometry diagrams, interactive constructions, and 3D models inline when available;
AI chat assistant: Ask for summaries, step-by-step explanations, or diagram suggestions. The assistant links to sources and highlights where it used a particular document to build an answer;
Export and citation tools: Copy citations in common formats to help with coursework and research bibliographies;
API and integration options: For educators and institutions, there are options to integrate geometry search into course platforms or learning management systems;
Shopping and supplies: When looking for geometry calculators, rulers, protractors, geometry kits, or 3D model vendors, the Shopping mode surfaces relevant sellers and product details with clear labeling.

Searching effectively -- tips and examples

A focused search is usually clearer when it includes the type of result you want. Here are a few constructive patterns:

To find proofs and theorems: include words like "proof", "theorem", "euclidean proofs", or "geometric proofs" and add a scope such as "introductory" or "advanced". Example: "circle inversion proof tutorial euclidean proofs".
To find computational resources: combine the topic with "computational geometry", "code", "implementation", or "geometry software". Example: "Delaunay triangulation computational geometry code".
To find visualizations or diagrams: add "diagram", "visualization", "3D model", or "geometry diagrams AI". Example: "hyperbolic plane visualization diagram interactive".
To limit to educational content: include "geometry tutorials", "geometry courses", "course notes", or "geometry textbooks". Example: "analytic geometry tutorials step by step geometry".

Using filters for educational level and source type will quickly surface the kind of material you need. If you are unsure where to start, open the AI chat and ask for a short reading list or for a summary of key references on a topic.

Transparency, sourcing, and quality

We aim to help users assess results quickly. That means indicating the source type (e.g., "textbook", "preprint", "lecture note", "blog post"), showing why a result matched your query, and making it easy to reach the original source for verification. Where possible, results highlight whether a paper is peer-reviewed, a preprint, or an open-access resource.

The platform also provides ways to report incorrect or low-quality content and to flag mislabeled items. Editorial content and curated lists are maintained with source references, and user feedback helps improve how material is prioritized for geometry learners and practitioners.

AI, proof checking, and formal tools -- what to expect

The integrated AI assistant can offer guided explanations, outline proofs, and point to formal proof assistant tools when appropriate. It is not a formal proof checker. When a rigorous, machine-verified proof is required, the search results will link to proof assistant repositories and resources that specialize in formal verification.

For everyday learning and exploratory research, AI summaries and step-by-step explanations are designed to clarify ideas and highlight key references. For formal verification or publication-level claims, users should consult primary sources and formal proof systems linked from the results.

Privacy and advertising

Respecting user privacy is a priority. Personal search histories are not sold to advertisers. Advertisements, when present, are clearly labeled and can be filtered by users. Users have options to tailor personalization or to opt out of certain tracking features. For institutional integrations, administrative controls allow administrators to configure privacy and data retention behaviors that meet institutional policies.

Integrations, APIs, and educator support

4Geometry is designed to fit into classroom and research workflows. Educators and institutions can explore API access and premium bundles to embed search, offer a curated reading list, or provide an interactive diagram widget inside a course page. These integration options are intended to make geometry resources accessible within existing platforms such as learning management systems and course websites.

Developers can use search results to link to geometry software, calculators, and proof assistant tools, and can embed interactive visualizations or geometry diagrams AI outputs in their own applications. Documentation is available for common integration patterns.

The broader geometry ecosystem

Geometry is a broad field that intersects with many mathematical and applied disciplines. On 4Geometry you will find material covering:

Euclidean geometry and classical euclidean proofs, including synthetic constructions and textbook references;
Analytic geometry and coordinate methods, with tutorials that connect algebra to geometric reasoning;
Computational geometry, algorithms, and code implementations for geometric data structures;
Non-Euclidean geometry and differential geometry, with connections to topology updates and mathematical physics;
Geometry education resources and pedagogical materials aimed at classroom use and educational geometry research;
Conferences, preprints, journals, and research summaries highlighting ongoing developments and announced breakthroughs;
Applied geometry resources for design, architecture, and engineering, including geometry tools and geometry models used in practice.

The platform is intended to be a bridge across these areas, helping users navigate from elementary geometric constructions to advanced research papers and from algorithmic descriptions to interactive visualizations.

Community, contribution, and editorial content

4Geometry includes editorial collections, recommended reading lists, and curated tutorials. Community contributions, such as suggested resources, flagged errors, or recommended tutorials, help keep curated lists current and relevant. If you have a resource to suggest, an editorial correction, or a tutorial you think others will find useful, we encourage you to use the contact channels or contribution workflows on the site.

Community activity also appears in features like geometry blogs and geometry forums, where practitioners discuss problems, share visualizations, and announce geometry conferences or workshops.

Getting started -- a short walkthrough

To begin, enter a query in the home search box. Choose a mode depending on your task: "Web" for a wide sweep of pages, "News" for recent announcements and mathematics news, "Shopping" for geometry supplies and models, or "Chat" to open the AI assistant for stepwise help. Use filters on the result page to narrow by subfield, source type, or educational level.

If you want an immediate, hands-on example, you can ask the AI chat to "summarize an introductory treatment of circle inversion," or "find analytic geometry tutorials with worked examples." The AI will list recommended pages and point to textbooks, tutorials, and diagrams that match the intent.

Common use scenarios

A few typical scenarios where 4Geometry can be helpful:

Homework help: Use the platform to find geometry tutorials, example problems, and diagram generators to practice geometric constructions. The AI chat can suggest a step-by-step approach and link to reference materials.
Lesson preparation: Assemble a sequence of geometry resources -- warm-up problems, lecture notes, diagrams, and a set of homework problems -- using curated lists and printable diagrams.
Research discovery: Track recent preprints, find related work for a theorem, or gather computational geometry software relevant to an implementation task.
Tooling and prototyping: Locate libraries, geometry apps, calculators, and model vendors that support prototyping, visualization, and applied geometry work.

Accessibility and platform availability

The site is built with standard accessibility practices and is usable on desktop and mobile devices. Interactive geometry visualizations and many geometry apps are accessible through common browsers; some advanced tools may require specific plugins or downloads, in which case the search result will indicate any special requirements.

Limitations and responsible use

While 4Geometry aims to make geometry content easier to find and understand, users should keep a few sensible practices in mind:

Verify critical claims by consulting primary sources, especially for research or publication work. AI summaries and tutorial pages are starting points, not substitutes for original papers or textbooks.
When formal verification is required, consult specialist proof assistants and formal proof repositories linked from the results; the platform's AI does not perform independent formal proofs.
Be mindful of licensing and reuse terms on content such as diagrams, code, and 3D models. The result page will indicate license information when available.

Contact and support

If you have questions about using the platform, want to suggest a resource, or need help integrating 4Geometry into a course, please reach out:

Final note

4Geometry is intended to be a practical, dependable tool for connecting people to geometric knowledge, from elementary constructions to contemporary research. It combines curated indexing, domain-aware ranking, and AI-assisted guidance to help users find geometry tutorials, proofs, visualizations, software, and references that match their needs. We continue to evolve the platform with user feedback and contributions from the geometry community, with a focus on clarity, relevance, and usability.

Whether you are looking for geometry textbooks, interactive diagrams, computational geometry code, or a quick summary of a theorem, 4Geometry aims to make it straightforward to find and evaluate useful resources.