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Knuth's up-arrow notation (()) Allows for super-powers and super-exponential function by increasing the number of arrows; used in the article on large numbers. Text notation exp _ a ^ n(x) Based on standard notation; convenient for ASCII. J Notation x ^^: (n-1) x: Repeats the exponentiation.
For example, a rhombicuboctahedron can be called an expanded cube, expanded octahedron, as well as a cantellated cube or cantellated octahedron. A regular {p,q,r} 4-polytope (4-polytope) expands into a new 4-polytope with the original {p,q} cells, new cells {r,q} in place of the old vertices, p-gonal prisms in place of the old faces, and r ...
Examples of geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space). Geometric calculus , an extension of GA that incorporates differentiation and integration , can be used to formulate other theories such as complex analysis and differential geometry , e.g. by using the Clifford ...
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula = is the quantitative representation in mathematical notation of mass–energy equivalence. [1]
The cis notation was first coined by William Edwin Hamilton in Elements of Quaternions (1866) [23] [24] and subsequently used by Irving Stringham (who also called it "sector of x") in works such as Uniplanar Algebra (1893), [25] [26] James Harkness and Frank Morley in their Introduction to the Theory of Analytic Functions (1898), [26] [27] or by George Ashley Campbell (who also referred to it ...
Nicolas Chuquet used a form of exponential notation in the 15th century, for example 12 2 to represent 12x 2. [11] This was later used by Henricus Grammateus and Michael Stifel in the 16th century. In the late 16th century, Jost Bürgi would use Roman numerals for exponents in a way similar to that of Chuquet, for example iii 4 for 4 x 3 .
The polynomials, exponential function e x, and the trigonometric functions sine and cosine, are examples of entire functions. Examples of functions that are not entire include the square root, the logarithm, the trigonometric function tangent, and its inverse, arctan. For these functions the Taylor series do not converge if x is far from b.
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem . [ 127 ]