Geometry of Complex Numbers is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean...

complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry...

is one of the simplest complex manifolds. In projective geometry, the sphere is an example of a complex projective space and can be thought of as the...

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary...

as much of the geometry of the Euclidean plane ⁠ R 2 {\displaystyle \mathbb {R} ^{2}} ⁠ can be described with complex numbers, the geometry of the Minkowski...

that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics...

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points...

Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') is a branch of mathematics...

algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with...

In differential geometry and complex geometry, a complex manifold is a manifold with a complex structure, that is an atlas of charts to the open unit...

Elliptic geometry Enumerative geometry Epipolar geometry Euclidean geometry Finite geometry Fractal geometry Geometry of numbers Hyperbolic geometry Incidence...

Schwerdtfeger, Hans (1979) [1962], Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry, Dover, pp. 8–10. Young, John...

start with a field k. In classical algebraic geometry, this field was always the complex numbers C, but many of the same results are true if we assume only...

real numbers. Their primary application is in representing rigid body motions in 2D space. Unlike multiplication of dual numbers or of complex numbers, that...

In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing...

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called...

arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...

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

1-dimensional complex manifold, called the complex line. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are...

ISBN 0-387-97743-0. Yaglom, Isaak Moiseevich (1968) [1963]. Complex Numbers in Geometry. Translated by Primrose, Eric J. F. Academic Press. LCCN 66-26269...

theory, theory of groups and their geometries, and complex analysis. "In 1962 he published Geometry of Complex Numbers: Circle Geometry, Möbius Transformations...

numbers can be used to expand the real number system to the complex numbers, by postulating the imaginary unit i, which is one of the square roots of −1...

b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.} The complex conjugate of z {\displaystyle...

to The Geometry of Complex Numbers". Dover Publications, Inc., Mineola, 2008, ISBN 978-0-486-46629-3, page 61 Berger, Marcel (1987), Geometry I, Berlin:...

Complex numbers ( C {\displaystyle \mathbb {C} } ): Includes real numbers, imaginary numbers, and sums and differences of real and imaginary numbers....

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical...

non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the...

of complex numbers to plane geometry. Complex differential geometry a branch of differential geometry that studies complex manifolds. Complex dynamics the...

The term complex polygon can mean two different things: In geometry, a polygon in the unitary plane, which has two complex dimensions. In computer graphics...

mathematics, specifically algebraic geometry, a period or algebraic period is a complex number that can be expressed as an integral of an algebraic function over...