If a stranger entered the circle, he had to do so to the woman's right so as not to come between her and her husband.

* If a circle passing through two of the input points doesn't contain any other of them in its interior, then the segment connecting the two points is an edge of a Delaunay triangulation of the given points.

If we draw an ellipse twice as long as it is wide, and draw the circle centered at the ellipse's center with diameter equal to the ellipse's longer axis, then on any line parallel to the shorter axis the length within the circle is twice the length within the ellipse.

Formulae connecting a tangential angle, the angle anchored at the ellipse's center ( called also the polar angle from the ellipse center ), and the parametric angle t < ref > If the ellipse is illustrated as a meridional one for the earth, the tangential angle is equal to geodetic latitude, the angle is the geocentric latitude, and parametric angle t is a parametric ( or reduced ) latitude of auxiliary circle </ ref > are:

If the manifold is a circle these are called loop groups, and have central extensions whose Lie algebras are ( more or less ) Kac – Moody algebras.

If the circle is replaced by an ellipse, and rotated about the major axis, the shape becomes a prolate spheroid, rotated about the minor axis, an oblate spheroid.

If a particular point on a sphere is ( arbitrarily ) designated as its north pole, then the corresponding antipodal point is called the south pole and the equator is the great circle that is equidistant to them.

If one measures by arc length one finds that the shortest path connecting two points lying entirely in the sphere is a segment of the great circle containing the points ; see geodesic.

If an object moves with angular velocity ω around a circle of radius r centered at the origin of the x-y plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.

( If one of the basic hand-shape glyphs is used, such as the simple square or circle, this band breaks it in two ; however, if there are lines for fingers extended from the base, then they become detached from the base, but the base itself remains intact.

If the handle is circular with the stem as the axis of rotation in the center of the circle, then the handle is called a handwheel.

If B is a circle, then these eigenfunctions have an angular component that is a trigonometric function of the polar angle θ, multiplied by a Bessel function ( of integer order ) of the radial component.

If we expand a function f in a power series inside a circle of radius R, this means that

If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.

If the Earth were a perfect sphere and there were no atmosphere, the radio horizon would be a circle.

If we take to be a circle, where < math > r <

If there is no radial component, then the particle moves in a circle.

If modeled on the practice of using dictionaries, there would be no circle in an illustration of the activity of looking up a word whose entry provides a definition in terms of that word ( or in terms of another word defined in terms of this word ).

If conditions are completely clear, the circle is empty.

If conditions are partly cloudy, the circle is partially filled in.

If the axis of revolution does not touch the circle, the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.

If your motion is not strictly in a line or a circle your hand will describe an ellipse and the wave will be elliptically polarized.

If they conceive of the circle casting as cutting a line in the air with the tool of air, then they may choose to purify the circle with the remaining three elements of fire, water, and earth ; this would involve using a candle to purify the circle, and omitting the incense, since the circle has already been imbued with the element of air.

If the first allele is dominant to the second, then the fraction of the population that will show the dominant phenotype is p < sup > 2 </ sup > + 2pq, and the fraction with the recessive phenotype is q < sup > 2 </ sup >.

If T is a ( p, q )- tensor ( p for the contravariant vector and q for the covariant one ), then we define the divergence of T to be the ( p, q − 1 )- tensor

*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.

This can be done for all m of the p < sub > i </ sub >, showing that m ≤ n. If there were any q < sub > j </ sub > left over we would have

* If q is a prime power, and if F

If X is a positive random variable and q > 0 then for all ε > 0

If we compress data in a manner that assumes q ( X ) is the distribution underlying some data, when, in reality, p ( X ) is the correct distribution, the Kullback – Leibler divergence is the number of average additional bits per datum necessary for compression.

If Alice knows the true distribution p ( x ), while Bob believes ( has a prior ) that the distribution is q ( x ), then Bob will be more surprised than Alice, on average, upon seeing the value of X.

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

# If p is an odd prime, then any prime q that divides 2 < sup > p </ sup > − 1 must be 1 plus a multiple of 2p.

#* Proof: If q divides 2 < sup > p </ sup > − 1 then 2 < sup > p </ sup > ≡ 1 ( mod q ).

# If p is an odd prime, then any prime q that divides must be congruent to ± 1 ( mod 8 ).

If R is an integral domain and f and g are polynomials in R, it is said that f divides g or f is a divisor of g if there exists a polynomial q in R such that f q = g. One can show that every zero gives rise to a linear divisor, or more formally, if f is a polynomial in R and r is an element of R such that f ( r ) = 0, then the polynomial ( X − r ) divides f. The converse is also true.

If F is a field and f and g are polynomials in F with g ≠ 0, then there exist unique polynomials q and r in F with

If we shift the constant term to the right hand side, factor a p and multiply by q < sup > n </ sup >, we get

If we instead shift the leading term to the right hand side and multiply by q < sup > n </ sup >, we get

Sherlock Holmes's straightforward practical principles are generally of the form, " If p, then q ," where " p " stands for some observed evidence and " q " stands for what the evidence indicates.

A proposition such as " If p and q, then p ." is considered to be logical truth because it is true because of the meaning of the symbols and words in it and not because of any facts of any particular world.

If q is the product of that curvature with the circle's radius, signed positive for epi-and negative for hypo -, then the curve: evolute similitude ratio is 1 + 2q.

If H is a subgroup of G, the set of left or right cosets G / H is a topological space when given the quotient topology ( the finest topology on G / H which makes the natural projection q: G → G / H continuous ).