In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the Bankoff circle or Bankoff triplet circle is a certain
Archimedean circle that can be constructed from an
arbelos
In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...
; an Archimedean circle is any circle with area equal to each of
Archimedes' twin circles. The Bankoff circle was first constructed by
Leon Bankoff in 1974.
[.]
Construction
The Bankoff circle is formed from three
semicircle
In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, radians, or a half-turn). It has only one line ...
s that create an
arbelos
In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...
. A circle ''C''
1 is then formed tangent to each of the three semicircles, as an instance of the
problem of Apollonius. Another circle ''C''
2 is then created, through three points: the two points of tangency of ''C''
1 with the smaller two semicircles, and the point where the two smaller semicircles are tangent to each other. ''C''
2 is the Bankoff circle.
Radius of the circle
If ''r'' = ''AB''/''AC'', then the radius of the Bankoff circle is:
:
References
External links
* {{MathWorld, title=Bankoff Circle, urlname=BankoffCircle
Bankoff Circleby Jay Warendorff, the
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hos ...
.
Online catalogue of Archimedean circles Floor van Lamoen.
Arbelos
Elementary geometry