The Twin Circles of Archimedes in a Skewed Arbelos

نویسندگان

  • Hiroshi Okumura
  • Masayuki Watanabe
  • M. Watanabe
چکیده

Any area surrounded by three mutually touching circles is called a skewed arbelos. The twin circles of Archimedes in the ordinary arbelos can be generalized to the skewed arbelos. The existence of several pairs of twin circles, under certain conditions, is demonstrated.

برای دانلود 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

Ubiquitous Archimedean Circles of the Collinear Arbelos

For a point O on the segment AB in the plane, the area surrounded by the three semicircles with diameters AO, BO and AB erected on the same side is called an arbelos. It has lots of unexpected but interesting properties (for an extensive reference see [1]). The radical axis of the inner semicircles divides the arbelos into two curvilinear triangles with congruent incircles called the twin circl...

متن کامل

The Arbelos and Nine-Point Circles

We construct some new Archimedean circles in an arbelos in connection with the nine-point circles of some appropriate triangles. We also construct two new pairs of Archimedes circles analogous to those of Frank Power, and one pair of Archimedean circles related to the tangents of the arbelos.

متن کامل

Three Constructions of Archimedean Circles in an Arbelos

We give ruler and compass constructions of three Archimedean circles in an arbelos, each with the endpoints of a diameter on the smaller semicircles. In the first case, the diameter contains the intersection of the defining smaller semicircles of the arbelos. In the second case, these endpoints are the intersections of the smaller semicircles with the lines joining the endpoints of the base of ...

متن کامل

The Arbelos with Overhang

We consider a generalized arbelos consisting of three semicircles with collinear centers, in which only two of the three semicircles touch. Many Archimedean circles of the ordinary arbelos are generalized to our generalized arbelos.

متن کامل

A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE

One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimede...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004