English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The classical Buffon problem requires a precise presentation in order to bemeaningful. We reinterpret the classical problem in the planar setting with aneedle whose length is equal to the grating width and find analogs of thisproblem in the settings of the sphere and the Poincar\'e disk. We show that theprobability that the needle intersects the grating in these non euclideansettings tends to the probability of the intersection in the planar setting asthe length of the needle tends to zero. Finally, we calculate the Gaussiancurvature of the spaces from probability deficits related to the generalizedBuffon problem, obtaining a result similar to the Bertrand-Diguet-PuiseuxTheorem.

Buffon's Problem determines Gaussian Curvature in three Geometries