منابع مشابه
Conics on the Projective Plane
In this paper, we discuss a special property of conics on the projective plane and answer questions in enumerative algebraic geometry such as ”How many points determine a conic?” and ”How many conics do we expect to pass through m points and tangent to n lines?”
متن کاملArithmetic Progressions on Conics.
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We als...
متن کاملThe Conics of Ludwig Kiepert:
If a visitor from Mars desired to leam the geometry of the triangle but could stay in the earth' s relatively dense atmosphere only long enough for a single lesson, earthling mathematicians would, no doubt, be hard-pressed to meet this request. In this paper, we believe that we have an optimum solution to the problem. The Kiepert conics, though seemingly unknown today, constitute a significant ...
متن کاملOn the Number of Smooth Conics Tangent to Five Fixed Conics
In section 1, we define the abelian groups Ak(X) in a manner analagous to the homology groups Hk(X) by considering cycles of subvarieties modulo rational equivalence. In section 2, we construct, for any Cartier divisor D on X and subvariety V ⊂ X, an intersection class D · [V ] ∈ Ak−1(|D|∩|V |) and state its basic properties. Bezout’s theorem follows easily. In section 3, we discuss the centerp...
متن کاملOn a Theorem of Intersecting Conics
Given two conics over an infinite field that intersect at the origin, a line through the origin will, in general intersect both conic sections once more each, at points C and D. As the line varies we find that the midpoint of C and D traces out a curve, which is typically a quartic. Intuitively, this locus is the “average” of the two conics from the perspective of an observer at the origin. We ...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1933
ISSN: 1802-114X
DOI: 10.21136/cpmf.1933.121797