Observable universeThe observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from New Horizons.
Age of the universeIn physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe, which indicate an age of 13.787 billion years as interpreted with the Lambda-CDM concordance model as of 2021; and a measurement based on the observations of the local, modern universe, which suggest a younger age.
Hyperbolic geometryIn mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) The hyperbolic plane is a plane where every point is a saddle point.
Buddhist cosmologyBuddhist cosmology is the description of the shape and evolution of the Universe according to Buddhist scriptures and commentaries. It consists of a temporal and a spatial cosmology. The temporal cosmology describes the timespan of the creation and dissolvement of alternate universes in different aeons. The spatial cosmology consists of a vertical cosmology, the various planes of beings, into which beings are reborn due to their merits and development; and a horizontal cosmology, the distribution of these world-systems into an infinite sheet of existential dimensions included in the cycle of samsara.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Mathematical physicsMathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics).
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
Quantum cosmologyQuantum cosmology is the attempt in theoretical physics to develop a quantum theory of the universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe. Classical cosmology is based on Albert Einstein's general theory of relativity (GTR or simply GR) which describes the evolution of the universe very well, as long as you do not approach the Big Bang.
Philosophy of space and timePhilosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology and epistemology of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity (particularly the nature of identity over time).
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
