What's the difference between number and quaternion?
Number
Definition:
(n.) That which admits of being counted or reckoned; a unit, or an aggregate of units; a numerable aggregate or collection of individuals; an assemblage made up of distinct things expressible by figures.
(n.) A collection of many individuals; a numerous assemblage; a multitude; many.
(n.) A numeral; a word or character denoting a number; as, to put a number on a door.
(n.) Numerousness; multitude.
(n.) The state or quality of being numerable or countable.
(n.) Quantity, regarded as made up of an aggregate of separate things.
(n.) That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural.
(n.) The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one.
(n.) The measure of the relation between quantities or things of the same kind; that abstract species of quantity which is capable of being expressed by figures; numerical value.
(n.) To count; to reckon; to ascertain the units of; to enumerate.
(n.) To reckon as one of a collection or multitude.
(n.) To give or apply a number or numbers to; to assign the place of in a series by order of number; to designate the place of by a number or numeral; as, to number the houses in a street, or the apartments in a building.
(n.) To amount; to equal in number; to contain; to consist of; as, the army numbers fifty thousand.
Example Sentences:
(1) However, as other patients who lived at the periphery of the Valserine valley do not appear to be related to any patients living in the valley, and because there has been considerable immigration into the valley, a number of hypotheses to explain the distribution of the disease in the region remain possible.
(2) These included bringing in the A* grade, reducing the number of modules from six to four, and a greater attempt to assess the whole course at the end.
(3) When micF was cloned into a high-copy-number plasmid it repressed ompF gene expression, whereas when cloned into a low-copy-number plasmid it did not.
(4) Use of the improved operative technique contributed to reduction in number of complications.
(5) Nutritionally rehabilitated animals had similar numbers of nucleoli to control rats.
(6) Simplicity, high capacity, low cost and label stability, combined with relatively high clinical sensitivity make the method suitable for cost effective screening of large numbers of samples.
(7) The hemodynamic efficiency of the drive was tested in a number of in vivo experiments.
(8) The final number of fibers--140,000-165,000--is reached by the sixth week after birth.
(9) On removal of selective pressure, the His+ phenotype was lost more readily than the Ura+ Trp+ markers, with a corresponding decrease in plasmid copy number.
(10) This article describes a number of syndromes affecting the nail unit.
(11) At the time, with a regular supply of British immigrants arriving in large numbers in Australia, Biggs was able to blend in well as "Terry Cook", a carpenter, so well in fact that his wife, Charmian, was able to join him with his three sons.
(12) Since 1979 there has been an increase of 17,122 in the number of beds available in nursing homes.
(13) Other haematological parameters remained normal, with the exception of the absolute number of lymphocytes, which initially fell sharply but soon returned to, and even exceeded, control levels.
(14) All the twins were born in years 1973-1987, the total number was 2,226 boys and 2,302 girls.
(15) The number of neoplastic cells in each cell suspension was determined by cytologic criteria.
(16) aeruginosa and Enterococci) were significantly reduced in number during the manipulation (Fig.
(17) Because of the small number of patients reported in the world literature and lack of controlled studies, the treatment of small cell carcinoma of the larynx remains controversial; this retrospective analysis suggests that combination chemotherapy plus radiation offers the best chance for cure.
(18) Further, at the end of treatment fewer patients had depressive symptoms and the total daily number of hours of wellbeing and normal movement increased.
(19) The country has no offshore wind farms, though a number of projects are in the research phase to determine their profitability.
(20) Despite a 10-year deadline to have the same number of ethnic minority officers in the ranks as in the populations they serve, the target was missed and police are thousands of officers short.
Quaternion
Definition:
(n.) The number four.
(n.) A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
(n.) A word of four syllables; a quadrisyllable.
(n.) The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
(v. t.) To divide into quaternions, files, or companies.
Example Sentences:
(1) During visually guided movements, arm follows gaze, and the nine-dimensional rotatory configuration space for eye-head-arm-synergies (three degrees of freedom for each system) is reduced to a two-dimensional plane in the space of quaternion vectors.
(2) Many testable predictions made by quaternion models also turn up in models based on other mathematics.
(3) Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion.
(4) The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements.
(5) In other words, angular eye positions in space (expressed as quaternions) were constrained to a two-dimensional surface.
(6) Findings 1 and 3 show that saccadic control signals accurately reflect the properties of three-dimensional rotations, as predicted by a new quaternion model of the saccadic system; models that approximate rotational kinematics using vectorial addition and integration do not predict these findings.
(7) Tweed and Vilis (Journal of Neurophysiology, 58, 832-849, 1987) have argued that quaternion algebra provides the most appropriate description of the rotations of the eye, and have derived a three-dimensional model of gaze control based on quaternion operations.
(8) A canonical unitary representation of the Euclidean group on the range space of the Gabor transform is constructed from mathematical properties of the Euclidean group and the quaternions.
(9) The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position.
(10) In this paper we present algorithms for computing eye position quaternions and eye angular velocity (not the derivative of position in three dimensions) from two search coils (not necessarily orthogonal) on one eye in two or three magnetic fields, and for locating primary position using quaternions.
(11) In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions.