Search results
Results from the WOW.Com Content Network
In general, any two disjoint, non-concentric circles can be aligned with the circles of a system of bipolar coordinates. In that case, the radical axis is simply the -axis of this system of coordinates. Every circle on the axis that passes through the two foci of the coordinate system intersects the two circles orthogonally.
The radii of the three given circles are known, as is the distance d non from the common concentric center to the non-concentric circle (Figure 7). The solution circle can be determined from its radius r s, the angle θ, and the distances d s and d T from its center to the common concentric center and the center of the non-concentric circle ...
Polyconic: parallels are non-concentric arcs of circles. c. 1000: Nicolosi globular: Pseudoconical [4] Compromise Abū Rayḥān al-Bīrūnī; reinvented by Giovanni Battista Nicolosi, 1660. [1]: 14 c. 1000: Azimuthal equidistant =Postel =zenithal equidistant: Azimuthal Equidistant Abū Rayḥān al-Bīrūnī
If α and β are disjoint and non-concentric, then the locus of points of tangency of γ and δ again forms two circles, but only one of these is the (unique) circle of antisimilitude. If α and β are tangent or concentric, then the locus of points of tangency degenerates to a single circle, which again is the circle of antisimilitude. [3]
The circles of positive τ lie in the right-hand side of the plane (x > 0), whereas the circles of negative τ lie in the left-hand side of the plane (x < 0). The τ = 0 curve corresponds to the y-axis (x = 0). As the magnitude of τ increases, the radius of the circles decreases and their centers approach the foci.
Then the inversive distance (usually denoted δ) is defined as the natural logarithm of the ratio of the radii of the two concentric circles. In addition, any two non-intersecting circles may be inverted into congruent circles, using circle of inversion centered at a point on the circle of antisimilitude.
Many a science-fiction story was birthed from ice, so it’s easy to be unsettled at photos from Alaska showing concentric circles spread hundreds of feet across a frozen lake.
The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. [6] For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii.