A Way to remember the Entire Unit Circle for Trigonometry
Dimension
The first four spatial dimensions. In mathematics[edit] In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded. A tesseract is an example of a four-dimensional object. Although the notion of higher dimensions goes back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. The rest of this section examines some of the more important mathematical definitions of the dimensions. Dimension of a vector space[edit] Manifolds[edit] A connected topological manifold is locally homeomorphic to Euclidean n-space, and the number n is called the manifold's dimension. For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point. Varieties[edit] The dimension of an algebraic variety may be defined in various equivalent ways. Time[edit]
General relativity
General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916[1] and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Einstein's theory has important astrophysical implications. History[edit] Albert Einstein developed the theories of special and general relativity. The Einstein field equations are nonlinear and very difficult to solve.
Cosmology
The Hubble eXtreme Deep Field (XDF) was completed in September 2012 and shows the farthest galaxies ever photographed by humans. Except for the few stars in the foreground (which are bright and easily recognizable because only they have diffraction spikes), every speck of light in the photo is an individual galaxy, some of them as old as 13.2 billion years; the observable universe is estimated to contain more than 200 billion galaxies. Cosmology (from the Greek κόσμος, kosmos "world" and -λογία, -logia "study of"), is the study of the origin, evolution, and eventual fate of the universe. Physical cosmology is the scholarly and scientific study of the origin, evolution, large-scale structures and dynamics, and ultimate fate of the universe, as well as the scientific laws that govern these realities.[1] Religious cosmology (or mythological cosmology) is a body of beliefs based on the historical, mythological, religious, and esoteric literature and traditions of creation and eschatology.
Newton's laws of motion
First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3]Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object.Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.[4] Newton used them to explain and investigate the motion of many physical objects and systems.[5] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. Overview Newton's first law Impulse
Density
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume,[2] although this is scientifically inaccurate – this quantity is more specifically called specific weight. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water. The density of a material varies with temperature and pressure. The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. History[edit] From the equation for density (ρ = m / V), mass density has units of mass divided by volume. Measurement of density[edit] Homogeneous materials[edit] where
Inflation (cosmology)
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10−36 seconds after the Big Bang to sometime between 10−33 and 10−32 seconds. Following the inflationary period, the Universe continues to expand, but at a less rapid rate.[1] Inflation was developed in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation).[2] Many physicists also believe that inflation explains why the Universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the Universe is flat, and why no magnetic monopoles have been observed. Overview Space expands . . Duration Reheating
Introduction to general relativity
High-precision test of general relativity by the Cassini space probe (artist's impression): radio signals sent between the Earth and the probe (green wave) are delayed by the warping of spacetime (blue lines) due to the Sun's mass. General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational effect between masses results from their warping of spacetime. By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses. In Newton's model, gravity is the result of an attractive force between massive objects. General relativity has developed into an essential tool in modern astrophysics. Although general relativity is not the only relativistic theory of gravity, it is the simplest such theory that is consistent with the experimental data. Tidal effects[edit]
