An Edge-Minimization Problem for Regular Polygons
نویسندگان
چکیده
منابع مشابه
An Edge-Minimization Problem for Regular Polygons
In this paper we will examine the following problem: What is the minimum number of unit edges required to construct k identical size regular polygons in the plane if sharing of edges is allowed?
متن کاملAn inequality for regular near polygons
Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a1 > 0, c2 > 1. Let θ1 denote the second largest eigenvalue of Γ. We show θ1 ≤ k − a1 − c2 c2 − 1 . We show the following (i)–(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ1; (iii) Γ is a dual polar graph or a Hamming graph.
متن کاملAffinely regular polygons in an affine plane
In this paper we survey results about affinely regular polygons. First, the definitions and classification of affinely regular polygons are given. Then the theory of Bachmann–Schmidt is outlined. There are several classical theorems about regular polygons, some of them having analogues in finite planes, such as the Napoleon–Barlotti theorem. Such analogues, variants of classical theorems are al...
متن کاملOn a problem of Croft on optimally nested regular polygons
We present a solution for the largest regular m-gon contained in a regular n-gon. We find that the answer depends critically on the coprimality of m and n. We show that the optimal polygons are concentric if and only if gcd(m,n) > 1. Our principal result is a complete solution for the case where m and n share a common divisor. For the case of coprime m and n, we present partial results and a co...
متن کاملAn Isodiametric Problem for Equilateral Polygons
The maximal perimeter of an equilateral convex polygon with unit diameter and n = 2m edges is not known when m ≥ 4. Using experimental methods, we construct improved polygons for m ≥ 4, and prove that the perimeters we obtain cannot be improved for large n by more than c/n4, for a particular constant c.
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: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/179