Poincaré half-space model. Take the open upper half-space \[\mathbb{H}^n := \{(x_1,\dots,x_n)\in\mathbb{R}^n \mid x_n 0\}\] equipped with the Riemannian metric whose components on the coordinate tangent vectors are \[g_{ij}(p) \;=\; g_p\!\left(\frac{\partial}{\partial x_i}\bigg|_p,\; \frac{\partial}{\partial x_j}\bigg|_p\right) \;=\; \frac{1}{p_n^2}\,\delta_{ij}.\] Geodesics are semicircles (or rays) orthogonal to the boundary hyperplane \(\{x_n = 0\}\).
We can follow the same thought process to find the high-side estimate (a / b r); this time, we round the product down and then add 1:
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Карина Черных (Редактор отдела «Ценности»)
Александр Курбатов (редактор отдела «Бывший СССР»)