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

Let $\mathcal{S}$ be a finite set of integer points in $\mathbb{R}^d$, whichwe assume has many symmetries, and let $P\in\mathbb{R}^d$ be a fixed point. Wecalculate the distances from $P$ to the points in $\mathcal{S}$ and compare theresults. In some of the most common cases, we find that they lead to unexpectedconclusions if the dimension is sufficiently large. For example, if$\mathcal{S}$ is the set of vertices of a hypercube in $\mathbb{R}^d$ and $P$is any point inside, then almost all triangles $PAB$ with $A,B\in\mathcal{S}$are almost equilateral. Or, if $P$ is close to the center of the cube, thenalmost all triangles $PAB$ with $A\in \mathcal{S}$ and $B$ anywhere in thehypercube are almost right triangles.

Counterintuitive patterns on angles and distances between lattice points in high dimensional hypercubes