Math Links

Great Math site Exceptionally clear and helpful explanations by Paul Bourke at The Swinburne Centre for Astrophysics and Supercomputing is hosted by the School of Biophysical Sciences and Electrical Engineering at Swinburne University of Technology in Melbourne, Australia.
The Centre is one of the newest and most rapidly growing research centres in Australia. It operates a significant supercomputing facility and a virtual reality theatre and concentrates on problems in astrophysics that benefit from these unique resources.
The Centre for Astrophysics and Supercomputing is dedicated to inspiring a fascination in the Universe through research and education.

Paul Bourke's Clear Explanation: Quaternions Quaternion Encyclopedia: Octonion Octonion extension of Quaternion

The Octonians by John Baez Abstract: The octonions are the largest of the four normed division algebras. While somewhat neglected due to their nonassociativity, they stand at the crossroads of many interesting fields of mathematics. Here we describe them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also touch upon their applications in quantum logic, special relativity and supersymmetry.


Wolfram infocenter: Hoop Algebras includes quaternions, spinors, ... 74 yr old Roger Beresford provides mathematica notebook: HoopAlgebras.nb

Matrix and Quaternion FAQ by chez Skal computer animantion math

Programming with MathLab: Quaternions quatdemo

Eric W. Weisstein's Quaternions at makers of Mathematica

Eric W. Wesstein's Quaternion References

Altmann, S. L. Rotations, Quaternions, and Double Groups. Oxford, England: Clarendon Press, 1986.

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985.

Arvo, J. Graphics Gems II. New York: Academic Press, pp. 351-354 and 377-380, 1994.

Baker, A. L. Quaternions as the Result of Algebraic Operations. New York: Van Nostrand, 1911.

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 230-234, 1996.

Conway, J. and Smith, D. On Quaternions and Octonions. Natick, MA: A. K. Peters, 2001.

Crowe, M. J. A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. New York: Dover, 1994.

Dickson, L. E. Algebras and Their Arithmetics. New York: Dover, 1960.

Downs, L. "CS184: Using Quaternions to Represent Rotation."

Du Val, P. Homographies, Quaternions, and Rotations. Oxford, England: Oxford University Press, 1964.

Ebbinghaus, H. D.; Hirzebruch, F.; Hermes, H.; Prestel, A; Koecher, M.; Mainzer, M.; and Remmert, R. Numbers. New York: Springer-Verlag, 1990.

Goldstein, H. Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, p. 151, 1980.

Hamilton, W. R. Lectures on Quaternions: Containing a Systematic Statement of a New Mathematical Method. Dublin: Hodges and Smith, 1853.

Hamilton, W. R. Elements of Quaternions. London: Longmans, Green, 1866.

Hamilton, W. R. The Mathematical Papers of Sir William Rowan Hamilton. Cambridge, England: Cambridge University Press, 1967.

Hardy, A. S. Elements of Quaternions. Boston, MA: Ginn, Heath, & Co., 1881.

Hardy, G. H. and Wright, E. M. "Quaternions." §20.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 303-306, 1979.

Hearn, D. and Baker, M. P. Computer Graphics: C Version, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 419-420 and 617-618, 1996.

Joly, C. J. A Manual of Quaternions. London: Macmillan, 1905.

Julstrom, B. A. "Using Real Quaternions to Represent Rotations in Three Dimensions." UMAP Modules in Undergraduate Mathematics and Its Applications, Module 652. Lexington, MA: COMAP, Inc., 1992.

Kelland, P. and Tait, P. G. Introduction to Quaternions, 3rd ed. London: Macmillan, 1904.

Kuipers, J. B. Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality. Princeton, NJ: Princeton University Press, 1998.

Mishchenko, A. and Solovyov, Y. "Quaternions." Quantum 11, 4-7 and 18, 2000.

Nicholson, W. K. Introduction to Abstract Algebra, 2nd ed. New York: Wiley, 1999.

Salamin, G. Item 107 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 46-47, Feb. 1972.

Shoemake, K. "Animating Rotation with Quaternion Curves." Computer Graphics 19, 245-254, 1985.

Smith, H. J. "Quaternions for the Masses."

Tait, P. G. An Elementary Treatise on Quaternions, 3rd ed., enl. Cambridge, England: Cambridge University Press, 1890.

Tait, P. G. "Quaternions." Encyclopædia Britannica, 9th ed. 1886. Reprinted in Tait, P. §CXXIX in Scientific Papers, Vol. 2. pp. 445-456.

Weisstein, E. W. "Books about Quaternions."

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