N-Division Points of Hypocycloids
نویسندگان
چکیده
We show that the n-division points of all rational hypocycloids are constructible with an unmarked straightedge and compass for all integers n, given a pre-drawn hypocycloid.We also consider the question of constructibility of n-division points of hypocycloids without a pre-drawn hypocycloid in the case of a tricuspoid, concluding that only the 1, 2, 3, and 6-division points of a tricuspoid are constructible in this manner.
منابع مشابه
String baryon model “triangle”: hypocycloidal solutions
The considered model of baryon consists of three pointlike masses (quarks) bounded pairwise by relativistic strings forming a curvilinear triangle. Classic analytic solutions for this model corresponding to a planar uniform rotation about the system center of mass are found and investigated. These solutions describe a rotating curve composed of segments of a hypocycloid. The curve is a curvilin...
متن کاملOn nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
متن کاملA new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces
In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.
متن کاملComparative assessment of N-terminal pro-B-type natriuretic peptide, nitric oxide and echocardiography for diagnosis of dilated cardiomyopathy in dogs
The aim of the study was to evaluate the clinical usefulness of N-terminal pro-brain natriuretic peptide (NT-Pro BNP) and nitric oxide (NO) with echocardiography (gold standard test) in diagnosis of canine cardiomyopathy. Out of 374 cases, 82 cases showing cardiovascular abnormalities including 16 cases of cardiomyopathy were further selected for standardization of biomarkers. Significant (P
متن کاملEvaluation of the Effect of Nebulized N-Acetylcysteine on Respiratory Secretions in Mechanically Ventilated Patients: Randomized Clinical Trial
Background: The purpose of our study was to evaluate an inexpensive and available method to reduce mucous impactions in mechanically ventilated patients.Methods: This randomized clinical trial was conducted on 40 mechanically ventilated patients aged 15-90 years. The patients were randomly allocated into two arms; 20 cases and 20 controls. The cases received N-acetylcysteine via their nebulizer...
متن کامل