What is GRG?
GRG (Generative Radial Geometry) is a radius-first view of geometry:
the radius sets the geometric scale; local radial constructions provide finite estimates of circumference and area.
We work in turns (fractions of a full rotation), with product-only 2D formulas and modular method blocks
Original · Trapezoidal · Radial.
Radius-generated measures
GRG starts from a radius, a full Turn, and a chosen resolution.
The current formulation uses a finite binary radial framework with local chord–tangent kernels.
Earlier projection, trapezoidal, and radial approaches remain available for comparison.
Blocks & exploration
Lightweight tools and mini-apps will appear gradually to support this exploration.
Explore the current GRG formulation
Start with the binary radial framework: geometric definitions, circumference and area kernels, and explicit accuracy proofs.
Read the Current Formulation
Generative Radial Geometry (GRG)
A Binary Radial Framework
What is GRG?
GRG studies circumference and area through local radial constructions. The current formulation defines geometric ratios from internal chords and external tangents, then applies measurement kernels at a chosen binary resolution.
Why it matters
The framework makes resolution and local geometric elements explicit. Its accuracy can be analysed independently of an implementation. Numerical stability and computational efficiency require separate measurements.
How it works — in brief
Resolve one Turn into binary sectors. Construct an internal chord and an external tangent side for a symmetric sector. Use their lengths and triangular areas to obtain finite circumference and area estimates. Refinement controls the geometric error.
What you can do with it
Potential applications include geometric modelling, radial sampling, graphics, and teaching. These are directions for investigation; performance and suitability must be evaluated for each task.
Explore Geometry Reimagined
Explore the construction, its verified kernel properties, and the questions that remain open.
Why this site grows by blocks.
I started from an original projection idea, then a trapezoidal variant seemed better, and later a fully radial formulation emerged. While testing error behavior, I noticed the possible extensions to surfaces require separate verification.
To avoid endless rewrites, GRG advances as modular blocks—each method has its own card/tab. The binary radial formulation is the current reference; the research history stays visible.
From Compass to Code
Traditional tools like compasses and rulers meet the power of algorithms. A bridge between history and innovation.
Redefining the Circle
A full Turn, binary sector resolution, and complementary chord–tangent elements define the current measurement framework.
Community A Community of Discovery Management
Join researchers, students, and innovators exploring a new path in mathematics and digital geometry.
Construction, Accuracy, and Open Questions
GRG develops finite radial constructions with explicit geometric elements. The current two-dimensional formulation includes accuracy proofs; extensions to other shapes and to three dimensions require their own analysis.
From Circle to Community
Generative Radial Geometry is not only a method, but a shared exploration. The documentation invites questions, reproducible tests, and comparisons of clearly defined constructions.
A New Way to Think Geometry
GRG explores a radius-first approach: the circle is reconstructed from the inside, and angles are handled in turns (fractions of a full rotation). The project evolves through modular blocks rather than rewrites, aiming for clear, reproducible methods without claiming a single final answer.
My research began with the circle’s area and developed into a study of finite radial constructions.
Stefano Ferragina
My investigation began with the circle’s area and developed through several radial constructions. The current focus is a finite binary radial framework, with explicit kernels and verifiable accuracy properties. Earlier methods remain part of the documented research history.