A tangent, in differential geometry, is a straight line touching a curve at a single point without crossing it there. A tangent, in mathematics, is a function of an angle that gives the ratio of the sine to the cosine, in either the real or complex numbers. Symbols: tan, tg.
Differential geometry, in geometry and mathematical analysis, is the study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra.
Mathematical analysis, in mathematics, is the mathematical study of functions, sequences, series, limits, derivatives and integrals.
Mathematics is an abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
Shape is the appearance of something in terms of its arrangement in space, especially its outline; often a basic geometric two-dimensional figure.
Two-dimensional means existing in two dimensions, not creating the illusion of depth; lacking detail or believability.
A figure is a drawing or diagram conveying information. Figure, in logic, is the form of a syllogism with respect to the relative position of the middle term.
Logic is a method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method. Logic in logic philosophy is the study of the principles and criteria of valid inference and demonstration. Logic in mathematics is the mathematical study of relationships between rigorously defined concepts and of mathematical proof of statements. Logic in mathematics is aA formal or informal language together with a deductive system or a model-theoretic semantics. Logic is any system of thought, whether rigorous and productive or not, especially one associated with a particular person. Logic is the part of a system (usually electronic) that performs the boolean logic operations, short for logic gates or logic circuit.
A thought is form created in the mind, rather than the forms perceived through the five senses; an instance of thinking. Thought is the operation by which such forms arise or are manipulated; the process of thinking; the agency by which thinking is accomplished. Thought is a way of thinking (associated with a group, nation or region). Thought is the careful consideration of multiple factors; deliberation.
Form is the shape or visible structure of a thing or person.
Mind is the ability of rational thought; the ability to be aware of things; the ability to remember things; the ability to focus the thoughts; somebody that embodies certain mental qualities; judgment, opinion, or view; desire, inclination, or intention; in philosophy, the non-material substance or set of processes in which consciousness, perception, affectivity, judgement, thinking, and will are based; attention, consideration or thought.
Rational means capable of reasoning; logically sound, not self-contradictory or otherwise absurd; (of a person or personal characteristics) healthy or balanced intellectually, exhibiting reasonableness; (in mathematics, arithmetic, number theory, not comparable) of a number, capable of being expressed as the ratio of two integers; (in mathematics, arithmetic, not comparable) of an algebraic expression, capable of being expressed as the ratio of two polynomials; (in chemistry) expressing the type, structure, relations, and reactions of a compound—graphic—said of formulae, (in physics) expressing a physical object.
Reasoning means the deduction of inferences or interpretations from premises; abstract thought; ratiocination.
An interpretation is an act of interpreting or explaining something unclear; a translation; a version. An interpretation is a sense given by an interpreter; an exposition or explanation given; meaning. Interpretation is the power of explaining. An interpretation is an artist’s way of expressing his thought or embodying his conception of nature. An interpretation is an act or process of applying general principles or formulae to the explanation of the results obtained in special cases. An interpretation, in physics, is an approximation that allows aspects of a mathematical theory to be discussed in ordinary language.
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