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Relationship Between Mathematics And Physics
The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since antiquity, and more recently also by historians and educators. Generally considered a relationship of great intimacy, mathematics has been described as "an essential tool for physics" and physics has been described as "a rich source of inspiration and insight in mathematics". Some of the oldest and most discussed themes are about the main differences between the two subjects, their mutual influence, the role of mathematical rigor in physics, and the problem of explaining the effectiveness of mathematics in physics. In his work ''Physics'', one of the topics treated by Aristotle is about how the study carried out by mathematicians differs from that carried out by physicists. Considerations about mathematics being the language of nature can be found in the ideas of the Pythagoreans: the convictions that "Numbers rule the world" and "All is number", and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume). In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the "infinity- th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. In the 3rd century BC Archimedes used what ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit Of A Function
Although the function is not defined at zero, as becomes closer and closer to zero, becomes arbitrarily close to 1. In other words, the limit of as approaches zero, equals 1. In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which may or may not be in the domain of the function. Formal definitions, first devised in the early 19th century, are given below. Informally, a function assigns an output to every input . We say that the function has a limit at an input , if gets closer and closer to as moves closer and closer to . More specifically, the output value can be made ''arbitrarily'' close to if the input to is taken ''sufficiently'' close to . On the other hand, if some inputs very close to are taken to outputs that stay a fixed distance apart, then we say the limit ''does not exist''. The notion of a limit has many applications in modern calc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, achieved the Unification of theories in physics#Unification of gravity and astronomy, first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and Leibniz–Newton calculus controversy, shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating calculus, infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science. In the , Newton formulated the Newton's laws of motion, laws of motion and Newton's law of universal g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamics (mechanics)
In physics, dynamics or classical dynamics is the study of forces and their effect on motion. It is a branch of classical mechanics, along with ''statics'' and ''kinematics''. The ''fundamental principle of dynamics'' is linked to Newton's second law. Subdivisions Rigid bodies Fluids Applications Classical dynamics finds many applications: * ''Aerodynamics'', the study of the motion of air * '' Brownian dynamics'', the occurrence of Langevin dynamics in the motion of particles in solution * '' File dynamics'', stochastic motion of particles in a channel * ''Flight dynamics'', the science of aircraft and spacecraft design * ''Molecular dynamics'', the study of motion on the molecular level * '' Langevin dynamics'', a mathematical model for stochastic dynamics * '' Orbital dynamics'', the study of the motion of rockets and spacecraft * '' Stellar dynamics'', a description of the collective motion of stars * '' Vehicle dynamics, the study of vehicles in motion Generalizations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable. Infinitesimal calculus was formulated separately ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Botany
Botany, also called plant science, is the branch of natural science and biology studying plants, especially Plant anatomy, their anatomy, Plant taxonomy, taxonomy, and Plant ecology, ecology. A botanist or plant scientist is a scientist who specialises in this field. "Plant" and "botany" may be defined more narrowly to include only land plants and their study, which is also known as phytology. Phytologists or botanists (in the strict sense) study approximately 410,000 species of Embryophyte, land plants, including some 391,000 species of vascular plants (of which approximately 369,000 are flowering plants) and approximately 20,000 bryophytes. Botany originated as history of herbalism#Prehistory, prehistoric herbalism to identify and later cultivate plants that were edible, poisonous, and medicinal, making it one of the first endeavours of human investigation. Medieval physic gardens, often attached to Monastery, monasteries, contained plants possibly having medicinal benefit. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medicine
Medicine is the science and Praxis (process), practice of caring for patients, managing the Medical diagnosis, diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, and Health promotion, promoting their health. Medicine encompasses a variety of health care practices evolved to maintain and restore health by the prevention (medical), prevention and treatment of illness. Contemporary medicine applies biomedical sciences, biomedical research, medical genetics, genetics, and medical technology to diagnosis (medical), diagnose, treat, and prevent injury and disease, typically through pharmaceuticals or surgery, but also through therapies as diverse as psychotherapy, splint (medicine), external splints and traction, medical devices, biologic medical product, biologics, and Radiation (medicine), ionizing radiation, amongst others. Medicine has been practiced since Prehistoric medicine, prehistoric times, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Politics
Politics () is the set of activities that are associated with decision-making, making decisions in social group, groups, or other forms of power (social and political), power relations among individuals, such as the distribution of Social status, status or resources. The branch of social science that studies politics and government is referred to as political science. Politics may be used positively in the context of a "political solution" which is compromising and non-violent, or descriptively as "the art or science of government", but the word often also carries a negative connotation.. The concept has been defined in various ways, and different approaches have fundamentally differing views on whether it should be used extensively or in a limited way, empirically or normatively, and on whether conflict or co-operation is more essential to it. A variety of methods are deployed in politics, which include promoting one's own political views among people, negotiation with other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
