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The "∅" symbol is always drawn as a slashed circle, whereas in most typefaces the letter "Ø" is a slashed ellipse. The diameter symbol ( ⌀ ) (Unicode character U+2300) is similar to the lowercase letter ø, and in some typefaces it even uses the same glyph , although in many others the glyphs are subtly distinguishable (normally, the ...
The torus plays a central role in the Hopf fibration of the 3-sphere, S 3, over the ordinary sphere, S 2, which has circles, S 1, as fibers. When the 3-sphere is mapped to Euclidean 3-space by stereographic projection, the inverse image of a circle of latitude on S 2 under the fiber map is a torus, and the fibers themselves are Villarceau ...
An oriented circle is an ordinary circle with an orientation represented by a binary value attached to it, which is either or . The only exception is a circle of radius zero, which has orientation equal to . A point is defined to be an oriented circle of radius zero.
A new circle C 3 of radius r 1 − r 2 is drawn centered on O 1. Using the method above, two lines are drawn from O 2 that are tangent to this new circle. These lines are parallel to the desired tangent lines, because the situation corresponds to shrinking both circles C 1 and C 2 by a constant amount, r 2, which shrinks C 2 to a point.
One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector. [9] (In the concave case, the line through one of the diagonals bisects the other.) One diagonal is a line of symmetry. It divides the quadrilateral into two congruent triangles that are mirror images of each other. [7]
Creating the line through two points; Creating the circle that contains one point and has a center at another point; Creating the point at the intersection of two (non-parallel) lines; Creating the one point or two points in the intersection of a line and a circle (if they intersect)
Four line segments, each perpendicular to one side of a cyclic quadrilateral and passing through the opposite side's midpoint, are concurrent. [ 23 ] : p.131, [ 24 ] These line segments are called the maltitudes , [ 25 ] which is an abbreviation for midpoint altitude.
Conversely, the polar line (or polar) of a point Q in a circle C is the line L such that its closest point P to the center of the circle is the inversion of Q in C. If a point A lies on the polar line q of another point Q, then Q lies on the polar line a of A. More generally, the polars of all the points on the line q must pass through its pole Q.