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...

We report on damage-free fiber-guidance of milli-Joule energy-level and 600-femtosecond laser pulses into hypocycloid core-contour Kagome hollow-core photonic crystal fibers. Up to 10 meter-long fibers were used to successfully deliver Yb-laser pulses in robustly single-mode fashion. Different pulse propagation regimes were demonstrated by simply changing the fiber dispersion and gas. Self-comp...

(a) f has two distinct roots with identical norm v if and only if p is located on a real double point of the hypotrochoid, (b) f has a root of multiplicity 2 with norm v if and only if the corresponding hypotrochoid is a hypocycloid and p is a cusp of it, and (c) f has more than two roots with norm v if and only if p = 0 if and only if the hypotrochoid is a rhodonea curve with a multiple point ...

The problem of biped locomotion at steady speeds is discussed through the Lagrangian formulation developed for velocity-dependent, body driving forces. Human walking on a level surface is analyzed in terms of the data on the resultant ground-reaction force and the external work. It is shown that the trajectory of the human center of mass is due to a superposition of its rectilinear motion with ...

The modal content of 7 and 19 cell Kagomé anti resonant hollow core fibers (K-ARF) with hypocycloid core surrounds is experimentally investigated through the spectral and spatial (S2) imaging technique. It is observed that the 7 and 19 cell K-ARF reported here, support 4 and 7 LP mode groups respectively, however the observation that K-ARF support few mode groups is likely to be ubiq...

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...