Search results
Results from the WOW.Com Content Network
In geometry, the limiting points of two disjoint circles A and B in the Euclidean plane are points p that may be defined by any of the following equivalent properties: The pencil of circles defined by A and B contains a degenerate (radius zero) circle centered at p. [1] Every circle or line that is perpendicular to both A and B passes through p ...
A curve of constant width defined by an 8th-degree polynomial. Circles have constant width, equal to their diameter. On the other hand, squares do not: supporting lines parallel to two opposite sides of the square are closer together than supporting lines parallel to a diagonal. More generally, no polygon can have constant width. However, there ...
Let O 1 and O 2 be the centers of the two circles, C 1 and C 2 and let r 1 and r 2 be their radii, with r 1 > r 2; in other words, circle C 1 is defined as the larger of the two circles. Two different methods may be used to construct the external and internal tangent lines. External tangents Construction of the outer tangent
Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness.This is misleading. [3]Although constant diameter is a necessary condition for roundness, it is not a sufficient condition for roundness: shapes exist that have constant diameter but are far from round.
In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of ...
No two interiors of Ford circles intersect, even though there is a Ford circle tangent to the x-axis at each point on it with rational coordinates. If p / q {\displaystyle p/q} is between 0 and 1, the Ford circles that are tangent to C [ p / q ] {\displaystyle C[p/q]} can be described variously as