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On the Number of Lines which meet Four Regions* in Hyper-Space

Published online by Cambridge University Press:  24 October 2008

R. Vaidyanathaswamy
R. Vaidyanathaswamy
Affiliation:
Trinity College
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Extract

The problem of finding the number of r-dimensional regions which are situated in a space Sn of n dimensions, and which satisfy a suitable number of conditions of certain assigned types (called “ground-conditions”) has been investigated by Schubert. A special class of such problems arises when the r-dimensional region is merely required to intersect k regions Pλ of rλ dimensions (λ = 1, 2 … k) situated in general position in Sn where for the finiteness of the sought number we must have

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 22 , Issue 1 , February 1924 , pp. 49 - 53
Copyright
Copyright © Cambridge Philosophical Society 1924

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References

† Math. Annalen, Bd. 26, 38.

‡ For an account of this principle see Schubert, Kalkul der Abzahlenden Geometric, or preferably Zeuthen, “Abzahlenden Methoden” (Ency. Math. Wiss.).

§ Math. Annalen, Bd. 59.