Abstract
The design process starts with a need, as spelled out by the client. In engineering design, as well as in other design areas, the need is described by the client in rather ambiguous, fuzzy, sometimes contradictory terms. After a series of exchanges between client and designer, be this an engineer, an industrial designer, or an architect, the need is formulated in terms of a list of functional requirements, with some specific features that are spelled out as design specifications, or specs for brevity.
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Notes
- 1.
Usual abbreviation for “counterclockwise”
- 2.
Only the array is of interest, its coefficient, d in Eq. (1.5), being left out.
- 3.
In the book, we are interested only in two- and three-dimensional vectors, hence our limited definition, which doesn’t consider n-dimensional vectors common in linear algebra, or even \(\infty \)-dimensional vectors, proper of functional analysis.
- 4.
“det” is abbreviation for determinant. A concept formally defined in Subsection 1.4.6.
- 5.
The signed magnitude of a vector is a real number, positive, negative, or zero, whose absolute value is identical to the magnitude of the vector.
- 6.
Any row, in fact.
- 7.
Its proof pertains to classical advanced books, e.g., Finkbeiner (1966).
- 8.
The fastest supercomputer in the world, as per Lohr (2018).
- 9.
Castelvecchi (2019).
- 10.
Dahlquist and Björck (1974).
- 11.
These formulas can be proven by various means; this proof not being pertinent to the book material, it is left aside.
- 12.
Chapman and Milne (1939).
- 13.
Such a matrix is, sometimes, referred to as a “unit” or, even, as a “unitary” matrix, but this is misleading, as a “unitary matrix” has a precise definition in linear algebra, namely, as the counterpart of an orthogonal matrix when the matrix is defined over the complex field, i.e., the set of the complex numbers. This is not the case in the book.
- 14.
The quoted qualifier is intended to stress that the “size” of a system of equations is relative, depending on the tools at hand. The book catering to beginners, a large system of linear equations would be one involving 10 or less equations in as many unknowns.
References
Castelvecchi D (2019) Into the dark ages. Nature 572:298–301
Chapman S, Milne EA (1939) The proof of the formula for the vector triple product. Math Gaz 23(253):35–38
Dahlquist G, Björck Å (1974) Numerical methods. Prentice-Hall Inc., Englewood Cliffs
Finkbeiner DT II (1966) Introduction to matrices and linear transformations. W.H. Freeman and Company, San Francisco
Lohr S (2018) Move over China, US is again home to world’s speediest supercomputer. New York Times, 19 July
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Angeles, J., Pasini, D. (2020). Introduction to Geometry Construction. In: Fundamentals of Geometry Construction. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-43131-0_1
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