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Complex exponential function: The exponential function exactly maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic spirals in the complex plane with centre at : () = (+) + ⏟ = + = ( + ) ⏟ The pitch angle of the logarithmic spiral is the angle between the line and the imaginary axis.
Growth like this is observed in real-life activity or phenomena, such as the spread of virus infection, the growth of debt due to compound interest, and the spread of viral videos. In real cases, initial exponential growth often does not last forever, instead slowing down eventually due to upper limits caused by external factors and turning ...
Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.
A congruent number is defined as the area of a right triangle with rational sides. Because every congruum can be obtained (using the parameterized solution) as the area of a Pythagorean triangle, it follows that every congruum is congruent. Conversely, every congruent number is a congruum multiplied by the square of a rational number. [7]
The statement is often used as a justification in elementary geometry proofs when a conclusion of the congruence of parts of two triangles is needed after the congruence of the triangles has been established. For example, if two triangles have been shown to be congruent by the SSS criteria and a statement that corresponding angles are congruent ...
Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function; Exponential generating function; Exponential-Golomb coding; Exponential growth; Exponential hierarchy; Exponential integral; Exponential integrator; Exponential map ...
The smallest 5-Con triangles with integral sides. In geometry, two triangles are said to be 5-Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths (of non-corresponding sides). The 5-Con triangles are important examples for understanding the solution of triangles. Indeed, knowing ...
Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources: "Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. ...