Pi-Scope — dimensional analysis in the browser

Pi-Scope turns a set of dimensioned physical variables into the dimensionless groups that govern them, using the Vaschy–Buckingham (Π) theorem. It pairs a rigorous scientific engine with a modern, bilingual, theme-aware interface — and, in its showcase deployment, runs the actual Python engine inside the browser.

👉 Try the live demo · Source on GitHub

Scientific context

Dimensional analysis is a cornerstone of physics and engineering. The Buckingham Π theorem states that any physically meaningful relation between n variables involving k independent base dimensions can be rewritten as a relation between just n − k dimensionless groups. Reducing the number of parameters this way is what makes wind-tunnel scaling, similarity laws and the famous numbers of fluid mechanics (Reynolds, Mach, Nusselt…) possible.

Concretely, the dimensionless groups form a basis of the null space of the dimensional matrix — the matrix whose columns are each variable’s exponents over the SI base dimensions. Pi-Scope assembles that matrix, computes its rank and a null-space basis with exact rational arithmetic (no floating-point drift), and renders each group as clean LaTeX.

The flagship example reproduces the similarity parameters of Chen, Greitzer, Tan & Marble, “Similarity Analysis of Compressor Tip Clearance Flow Structure” (1990) — eleven variables reduced to eight independent dimensionless groups.

Technical implementation

The project is built as a decoupled, professional full-stack application, then deployed in a way that needs no server at all:

• Scientific engine — Python + SymPy. A web-framework-free core extends the analysis to all seven SI base dimensions (mass, length, time, temperature, current, amount of substance, luminous intensity), computes the null-space basis symbolically, and reduces each group to its smallest integer exponents.
• Backend — FastAPI. A typed REST API (Pydantic schemas, automatic OpenAPI docs) exposes the engine, a curated variable library organised by physics domain, and citeable worked examples.
• Frontend — React + TypeScript + Tailwind. A responsive engineering-grade UI with KaTeX equation rendering, the explicit dimensional matrix, light/dark themes, full French/English internationalisation, and JSON/LaTeX export.
• In-browser execution — Pyodide (WebAssembly). For the public demo, the exact same Python engine is compiled to WebAssembly and runs client-side via Pyodide. The result is a 100 % static, offline-capable site hosted directly on GitHub Pages — instant, free, and with no cold starts.
• Engineering quality. Unit + integration tests, linting and static typing (Ruff, Mypy), Docker images, and GitHub Actions CI/CD for both the API and the static demo.

Skills demonstrated

• Scientific computing & modelling: dimensional analysis, exact linear algebra, symbolic mathematics.
• Software architecture: clean separation of a reusable engine, an API layer, and a UI; typed end-to-end.
• Web integration: React/TypeScript front end and the non-trivial feat of running a real Python scientific stack in the browser via WebAssembly.
• Delivery & DevOps: automated testing, containerisation, and continuous deployment to GitHub Pages.

This project is a compact demonstration of taking a piece of applied physics from a research script all the way to a polished, deployable product.