Ordinary planes, coplanar quadruples, and space quartics
نویسندگان
چکیده
منابع مشابه
On Sets Defining Few Ordinary Planes
Let S be a set of n points in real three-dimensional space, no three collinear and not all co-planar. We prove that if the number of planes incident with exactly three points of S is less than Kn for some K = o(n 1 7 ) then, for n sufficiently large, all but at most O(K) points of S are contained in the intersection of two quadrics. Furthermore, we prove that there is a constant c such that if ...
متن کاملRegular Polytopes in Ordinary Space
The three aims of this paper are to obtain the proof by Dress of the completeness of the enumeration of the Grünbaum–Dress polyhedra (that is, the regular apeirohedra, or apeirotopes of rank 3) in ordinary space E3 in a quicker and more perspicuous way, to give presentations of those of their symmetry groups which are affinely irreducible, and to describe all the discrete regular apeirotopes of...
متن کاملAdjugates of Diophantine Quadruples
Philip Gibbs Diophantine m-tuples with property D(n), for n an integer, are sets of m positive integers such that the product of any two of them plus n is a square. Triples and quadruples with this property can be classed as regular or irregular according to whether they satisfy certain polynomial identities. Given any such m-tuple, a symmetric integer matrix can be formed with the elements of ...
متن کاملTribonacci Diophantine Quadruples
In this paper, we show that there does not exist a quadruple of positive integers a1 < a2 < a3 < a4 such that aiaj + 1 (i 6= j) are all members of the Tribonacci sequence (Tn)n≥0.
متن کاملDoes monocular visual space contain planes?
The issue of the existence of planes-understood as the carriers of a nexus of straight lines-in the monocular visual space of a stationary human observer has never been addressed. The most recent empirical data apply to binocular visual space and date from the 1960s (Foley, 1964). This appears to be both the first and the last time this basic issue was addressed empirically. Yet the question is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2019
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12251