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Design
Published in Wanda Grimsgaard, Design and Strategy, 2023
Irrational numbers: An irrational number is a real number that cannot be written as a fraction of two integers. There are a number of numerical ratios, a number of industrial standard sizes and a number of proportions, which include four irrational numbers of significant importance for the understanding and analysis of natural structures and processes (Bringhurst,1996), for example: Pi (π) = 3.14159... = the ratio of a circle’s circumference to its diameter√2 = 1.41421... = the diagonal of a square (A format)ϕ = 1.61803... = the golden ratio
Basic Mathematical Calculations for Data Analytics
Published in Adedeji B. Badiru, Data Analytics, 2020
lne=1,e is the real number such that ∫1edtt=1e=limn→∞(1+1n)n=2.7182818284…
Reporting and Propagating Error in Calculations
Published in Robert M. Bethea, R. Russell Rhinehart, Applied Engineering Statistics, 2019
Robert M. Bethea, R. Russell Rhinehart
Whether explicitly stated or implied, you should report only significant digits. We adopt the following as a reporting convention. An integer has no decimal point and is used to represent the number of whole events or whole things. For example, there are 4327 people on the payroll. A real number has a decimal point and is used to represent the value of a variable that can have fractional values. For example, there are 0.4536 kg/lbm. Some uncertainty is associated with both integers and real numbers. For instance, if you tried to count out 2000 items, you might lose track and probably be off by 10 or so. The number of items should then be reported as 2000 ± 10 to explicitly acknowledge the counting precision. Similarly, the speed of light in a vacuum is reported as 2.997925 × 108 m/s ± 0.000003 × 108 m/s.
Comparative analysis of quaternion modulation system with OFDM systems
Published in International Journal of Electronics Letters, 2021
Anam Zahra, Qasim Umar Khan, Shahzad Amin Sheikh
A complex number is defined by, where are real numbers and is an imaginary number such that. Complex numbers are two-dimensional vectors space over the real numbers. In addition to, quaternions are constructed by adding two new imaginary units and with one real part. A quaternion is an extension of the complex number system (Catoni, Bordoni, Cannata, & Zampetti, 1997). In 1843, Irish mathematician William Rowan Hamilton was the first person who described quaternions and practically applied them in three-dimensional mechanics (Farouki, Al-Kandari, & Sakkalis, 2002). The mathematical notation of quaternions represents three-dimensional rotations of objects. A quaternion can be written as a sum of one real part and three imaginary parts.