caa a22 4500 605462232 CHVBK 20210128100247.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10114-015-1699-0 doi (NATIONALLICENCE)springer-10.1007/s10114-015-1699-0 Measure of segments which intersect a convex body from rotational formulae [Elektronische Daten] [Ximo Gual-Arnau, Silena Herold-García] Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in ℝ3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Convex body nationallicence flower nationallicence integral geometry nationallicence stereology nationallicence rotational formulae nationallicence segment nationallicence support set nationallicence Gual-Arnau Ximo Departament de Matemàtiques-INIT, Universitat Jaume I., 12071, Castelló, Spain aut Herold-García Silena Departamento de Computación, Universidad de Oriente, 90900, Santiago de Cuba, Cuba aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 345-352 1439-8516 31:2<345 2015 31 10114 https://doi.org/10.1007/s10114-015-1699-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-1699-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gual-Arnau Ximo Departament de Matemàtiques-INIT, Universitat Jaume I., 12071, Castelló, Spain aut NATIONALLICENCE 700 1- Herold-García Silena Departamento de Computación, Universidad de Oriente, 90900, Santiago de Cuba, Cuba aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 345-352 1439-8516 31:2<345 2015 31 10114