Evolving Evolutoids

نویسندگان

  • Peter J. Giblin
  • John P. Warder
چکیده

The envelope of straight lines normal to a plane curve C is its evolute; the envelope of lines tangent to C is the original curve, together with the entire tangent line at each inflexion of C. We introduce some standard techniques of singularity theory and use them to explain how the first of these envelopes turns into the second, as the (constant) angle between the set of lines forming the envelope and the set of tangents to C changes from 12π to 0. In particular we explain how cusps disappear and what happens at inflexions, where the evolute goes to infinity. We also study the family of “wavefronts” or “parallels” associated with these envelopes. MSC2010 Classification: 53A04, 53A05, 57R45, 58K05.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Evolving Role of Physicians - Don’t Forget the Generalist Primary Care Providers; Comment on “Non-physician Clinicians in Sub-Saharan Africa and the Evolving Role of Physicians”

The editorial “Non-physician Clinicians in Sub-Saharan Africa and the Evolving Role of Physicians” by Eyal et al describes non-physician clinicians’ (NPC) need for mentorship and support from physicians. We emphasise the same need of support for front line generalist primary healthcare providers who carry out complex tasks yet may have an inadequate skill mix.

متن کامل

Potentials of Evolving Linear Models in Tracking Control Design for Nonlinear Variable Structure Systems

Evolving models have found applications in many real world systems. In this paper, potentials of the Evolving Linear Models (ELMs) in tracking control design for nonlinear variable structure systems are introduced. At first, an ELM is introduced as a dynamic single input, single output (SISO) linear model whose parameters as well as dynamic orders of input and output signals can change through ...

متن کامل

Is the Role of Physicians Really Evolving Due to Non-physician Clinicians Predominance in Staff Makeup in Sub-Saharan African Health Systems?; Comment on “Non-physician Clinicians in Sub-Saharan Africa and the Evolving Role of Physicians”

Health workforce shortages in Sub-Saharan Africa are widely recognized, particularly of physicians, leading the training and deployment of Non-physician clinicians (NPCs). The paper by Eyal et al provides interesting and legitimate viewpoints on evolving role of physicians in context of decisive increase of NPCss in Sub-Saharan Africa. Certainly, in short or mid-term, NPCs will continue to be a...

متن کامل

A New Generation of Physicians in Sub-Saharan Africa?; Comment on “Non-physician Clinicians in Sub-Saharan Africa and the Evolving Role of Physicians”

This commentary follows up on an editorial by Eyal and colleagues in which these authors discuss the implications of the emergence of non-physician clinicians (NPCs) on the health labour market for the education of medical doctors. We generally agree with those authors and we want to stress the importance of clarifying the terminology to describe these practitioners and of defining more formall...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • The American Mathematical Monthly

دوره 121  شماره 

صفحات  -

تاریخ انتشار 2014