C

circle

An interactive living book and software repository dedicated to reconstructing Archimedes' circle measurement ("Circvli Dimensio") using original geometric proportions. Leveraging SageMath for symbolic validation and Python/Perl for high-precision numerical computation via decimal/big-number libraries, this project bypasses modern algebraic transformations to prove the flawless accuracy of antike geometric frameworks.

It now expands this foundation into a unified algebraic framework capable of handling higher-order transcendental structures up to \pi^4 and 1/\pi^4, including additive transcendental invariants like \log(2). By introducing a specialized mathematical Gain Function, the engine dynamically bridges ancient geometry with hyper-convergent modern infinite series—such as those of Ramanujan, the Chudnovsky brothers, and the 2024 Saha-Sinha string theory iterations. Through precise lambda (\lambda) parameter tracking to bypass critical systemic singularities and prevent degeneration into the slower Madhava series, the optimized, dual-action polygon generators achieve absolute numeric stability, delivering hundreds of flawless decimal places without relying on circular trigonometric functions.

And much more!

The circle-sdk-demo repository contains a Spring Boot RESTful API service that acts as an integration service with the Circle platform.

Circular progress bar widget written using Qt5.

Generates shapes (circles, triangles, squares, stars) with many options including annotations for Pascal VOC and darknet/yolo