example of a real projective line is the projectively extended real line, which is often called the projective line. Formally, a real projective line P(R) is...

In projective geometry and mathematics more generally, a projective line is, roughly speaking, the extension of a usual line by a point called a point...

values are increasing and unbounded. The projectively extended real line may be identified with a real projective line in which three points have been assigned...

called the projective plane; the qualifier "real" is added to distinguish it from other projective planes such as the complex projective plane and finite...

concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

In mathematics, real projective space, denoted ⁠ R P n {\displaystyle \mathbb {RP} ^{n}} ⁠ or ⁠ P n ( R ) , {\displaystyle \mathbb {P} _{n}(\mathbb {R}...

P1(Z). The projective line over a division ring results in a single auxiliary point ∞ = U[1, 0]. Examples include the real projective line, the complex...

undefined on the projective line, but is defined in its extension to a wheel. Starting with the real numbers, the corresponding projective "line" is geometrically...

In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action...

the real line can be compactified in several different ways. The one-point compactification of R is a circle (namely, the real projective line), and the...

action. Excluding (0,0) from P makes [x : y] projective coordinates which describe the real projective line, a one-dimensional space. Since the origin is...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates...

real case, a point at infinity completes a line into a topologically closed curve. In higher dimensions, all the points at infinity form a projective...

points of a non-singular projective cubic fall into one or two 'ovals'. One of these ovals crosses every real projective line, and thus is never bounded...

In a cyclic order, such as the real projective line, two pairs of points separate each other when they occur alternately in the order. Thus the ordering...

zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three...

In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space...

throws was described as "projective arithmetic" by John Stillwell (2005). In a section called "Projective arithmetic", he says The real difficulty is that the...

one-point compactification of the real numbers, which is the real projective line. Projective geometry also refers to a line at infinity in plane geometry...

geometry, smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane E {\displaystyle...

fibers over real projective space RPn with fiber S0. The Hopf construction gives circle bundles p : S2n+1 → CPn over complex projective space. This is...

projective geometry asserts that is not so in the case of real projective spaces of dimension at least two. Synonyms include projectivity, projective...

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...

simply as ∞ {\displaystyle \infty } . There is also a distinct projectively extended real line where + ∞ {\displaystyle +\infty } and − ∞ {\displaystyle -\infty...

duality and beyond that to duality in any finite-dimensional projective geometry. A projective plane C may be defined axiomatically as an incidence structure...

still has a total order; moreover, it is a complete lattice. The real projective line adds only one value ∞. It is also a compact space. Again, it is no...

{\displaystyle X} into a projective space. A line bundle is ample if some positive power is very ample. An ample line bundle on a projective variety X {\displaystyle...