Titlebook: Circles, Spheres and Spherical Geometry; Hiroshi Maehara,Horst Martini Textbook 2024 The Editor(s) (if applicable) and The Author(s), unde

EXALT

Scarlett Cornelissen,Yoichi MineAn inversion with respect to a circle in . (or with respect to a sphere in .) is a one-to-one transformation of . (or .) that interchanges the inside of the circle (sphere) and the outside of the circle (sphere). Inversions have nice properties, and they turn out to be convenient when we study arrangements of circles, or spheres.

BILK

教育学

Bakut tswah Bakut,Sagarika DuttHow many unit balls can touch one and the same unit ball simultaneously? (We assume that unit balls cannot overlap each other.) This problem is known as the problem of thirteen balls, or the .. Applying spherical geometry and a lemma on planar graphs, we answer this problem.

Conclave

Bakut tswah Bakut,Sagarika DuttIn this chapter, we study the probabilities concerning several random variables or events, determined by random points or random great circles on the sphere.

musicologist

https://doi.org/10.1007/978-94-017-7520-5or a family . of spherical caps on ., its intersection graph . is defined as the graph whose vertices are the centers . of the caps ., ., and two vertices . are adjacent if and only if .. We present a sufficient condition for the connectedness of ..

Orgasm

Marta Mirazón Lahr,Robert A. FoleyFirst, we compute the volume of an .-dimensional ball . of radius . in ., and we prove that for every fixed ., the volume of the .-dimensional ball tends to 0 as . tends to .. How many unit balls in . can touch . simultaneously?

无情

AGOG

https://doi.org/10.1007/978-1-349-08168-4Let . be the centers and . be the radii of the disjoint circles ., respectively.

认识

暂时中止

Bend Formulas,If a Steiner cycle . for . is given, the following question occurs: what can we say about the relation between the radii of the circles?