BS BR 4 (2).txt - Notes The history of vector analysis is...

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NotesThe history of vector analysis is particularly interesting. It was largelyinventedby Grassman in the mid-1800s but was ignored and reinvented later (Crowe,1994). Grassman now has a following in the graphics field of researchers whoare developing Geometric Algebra based on some of his ideas (Doran & Lasenby,2003). Readers interested in why the particular scalar and vector products arein some sense the right ones, and why we do not have a commonly-used vectordivision, will find enlightenment in the concise About Vectors (Hoffmann, 1975).Another important geometric tool is the quaternion invented by Hamilton in themid-1800s. Quaternions are useful in many situations, but especially whereorientationsare concerned (Hanson, 2005).Exercises1. The cardinality of a set is the number of elements it contains. Under IEEEfloating point representation (Section 1.5), what is the cardinality of thefloats?2. Is it possible to implement a function that maps 32-bit integers to 64-bitintegersthat has a well-defined inverse? Do all functions from 32-bit integers
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Quadratic equation, Mathematics in medieval Islam, Quaternion

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