منابع مشابه
Tangent Circles in the Ratio 2 : 1
In this article we consider the following old Japanese geometry problem (see Figure 1), whose statement in [1, p. 39] is missing the condition that two of the vertices are the opposite ends of a diameter. (The authors implicitly correct the omission in the proof they provide on page 118.) We denote by O(r) the circle with centre O, radius r. Problem [1, Example 3.2]. The squares ACBD and ABCD h...
متن کاملConstructing phylogenetic trees efficiently using compatibility criteria
The Character Compatibility Problem is a classical problem in computational biology concerned with constructing phylogenetic trees of minimum possible evolution from qualitative character sets. This problem arose in the 1970s, and until recently the only cases for which efficient algorithms were found were for binary (i.e. twostate) characters and for two characters at a time, while the complex...
متن کاملConstructing G quadratic Bézier curves with arbitrary endpoint tangent vectors
Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and ...
متن کاملConstructing symplectic forms on 4–manifolds which vanish on circles
Given a smooth, closed, oriented 4–manifold X and α ∈ H2(X,Z) such that α · α > 0, a closed 2–form ω is constructed, Poincaré dual to α, which is symplectic on the complement of a finite set of unknotted circles Z . The number of circles, counted with sign, is given by d = (c1(s) 2−3σ(X)−2χ(X))/4, where s is a certain spin structure naturally associated to ω . AMS Classification numbers Primary...
متن کاملConstructing G1 quadratic Bézier curves with arbitrary endpoint tangent vectors
Quadratice Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and...
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: Mathematics Magazine
سال: 2020
ISSN: 0025-570X,1930-0980
DOI: 10.1080/0025570x.2020.1682447