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Rotation - Wikipedia, the free encyclopedia This is a consequence of Euler's rotation theorem. In astronomy, rotation is a commonly observed phenomenon. One consequence of the rotation of a planet is the phenomenon of precession. en.wikipedia.org /wiki/Rotation   (907 words)

Rotation group - Wikipedia, the free encyclopedia Such a rotation is a linear transformation that preserves the length of vectors, and also preserves the orientation, or handedness, of space. The composition of two rotations is a rotation, and every rotation has a unique inverse which is again a rotation. Such generalized rotations are known as Lorentz transformations and the group of all such transformations is called the Lorentz group. en.wikipedia.org /wiki/Rotation_group   (1538 words)

City University Mathematics Preprint Series: 107   (Site not responding. Last check: 2007-10-09) As the rotation rate is increased there is an abrupt change in the form of the most unstable convection cells as their aspect ratio and slope parallel to the walls both become of order one in magnitude. As the rotation rate is further increased there is a second less abrupt transition when the internal Rossby radius of deformation based on the vertical scale of the cells becomes of the same order of size as the slot width. The effect of rotation on double-diffusive instabilities caused by more general horizontal temperature and salinity gradients in a salt-stratified fluid is also investigated, with particular reference to the case of heating the salinity gradient from a single sidewall. www.staff.city.ac.uk /~ra359/Papers/107.html   (262 words)

FACFULTY EVALUATION PILOT REPORT Rotation Year 1: Major portfolios for all those in their first three years of teaching mathematics at ACC, all those who received a Needs Improvement or Unacceptable rating in the previous year, and all those whose last names begin with the letters A through G. All others submit the annual portfolio. Rotation Year 2: Major portfolios for all those in their first three years of teaching mathematics at ACC, all those who received a Needs Improvement or Unacceptable rating in the previous year, and all those whose last names begin with the letters H through O. All others submit the annual portfolio. Rotation Year 3: Major portfolios for all those in their first three years of teaching mathematics at ACC, all those who received a Needs Improvement or Unacceptable rating in the previous year, and all those whose last names begin with the letters P through Z. All others submit the annual portfolio. www.austincc.edu /cbelko/tf0304/mtheval.htm   (1013 words)

School Science and Mathematics: Computer use and visualization in students' construction of reflection and rotation ...   (Site not responding. Last check: 2007-10-09) Use of The Geometer's Sketchpad (Jackiw, 1991) for the dynamic presentation of rotations and reflections is an appropriate vehicle to facilitate full participation, while encouraging the development of all students' visualization abilities in the middle school mathematics program. The traditional instructional environment was based on a textbook-based approach using chapters related to transformational geometry from Transition Mathematics (Usiskin et al., 1990), the adopted textbook for the eighth-grade students in the study. Their discovery of the properties of reflection and rotation was aided by the use of computer software that allows for student conjectures and provides visual feedback. www.findarticles.com /p/articles/mi_qa3667/is_199711/ai_n8777986   (1124 words)

Mathematics Magazine: An elementary introduction to the Hopf fibration   (Site not responding. Last check: 2007-10-09) First, notice that a rotation about the origin in R^sup 3^ can be specified by giving a vector for the axis of rotation and an angle of rotation about that axis. The rotation determined by the vector v and the angle [theta] is the same as the rotation determined by the pair (kv, [theta] + 2n[pi]), where k is any positive scalar and n is any integer. The angle of a rotation is the same as the angle made by its corresponding complex number, thought of as a vector in R^sup 2^, with the positive real axis. www.findarticles.com /p/articles/mi_qa3789/is_200304/ai_n9170471   (1520 words)

Morley's Redux and More Due to the definition of rotation angles, A, B, and C are the intersections of trisectors. All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA). In fact the trend of melding of theoretical physics with mathematics was reciprocated on the part of mathematics by fostering its experimental nature. www.maa.org /editorial/knot/MorleysRedux.html   (1900 words)

[No title]   (Site not responding. Last check: 2007-10-09) Mathematics majors are encouraged to minor in areas in which mathematics can be extensively applied, such as computer science, biology, physics, chemistry, economics, business administration, psychology and statistics. Mathematics majors who intend to pursue a graduate program are advised to satisfy the intermediate reading level in one of the following foreign languages: German, French or Russian. Students will be expected to use a variety of technologies (such as graphing calculators, computers, etc.) throughout the mathematics major course work, as part of a concerted effort to meet the changes in the way mathematics is now being done, and also to meet the technological challenges of the twenty-first century. www.wpunj.edu /admroot/catalog/math95.htm   (1872 words)

[No title] Although the literature of mathematics and physics is sprinkled with comments about the questionable value of quaternions and about its recondite nature, yet a few comments in the literature note that Euler's parameters are quaternions -- and this information has been disseminated widely ONLINE [20].) More that is implicit in the rotation operator. For translation, the planes are parallel; for rotation, the distinct planes intersect. It should be clear from this that, currently, "the history of rotation mathematics and physics with applications in medicine, biomechanics, space geodesy, etc." is very inadequately written and should be a challenge to readers of this magazine to inflate. members.fortunecity.com /jonhays/rotationyield.htm   (2293 words)

3D Rotation In 2D the axis of rotation is always perpendicular to the xy plane, i.e., the Z axis, but in 3D the axis of rotation can have any spatial orientation. Rotate so that the rotation axis is aligned with one of the principle coordinate axes. Rotate V about Y to align with Z. For rotation about X axis we need to find cos A, sin A where A = angle between projection of U (in YZ plane) and Z axis. www.siggraph.org /education/materials/HyperGraph/modeling/mod_tran/3drota.htm   (718 words)

Mathematics (760) course rotation   (Site not responding. Last check: 2007-10-09) This course does not count towards a mathematics major or minor in either liberal arts or secondary education or towards a mathematics minor in elementary education. This course will supply a thorough grounding in the mathematical topics which are central to the study of computer science, and which form the basis for many modern applications of mathematics to the social sciences. This course is designed to give students experience and to improve their skill in reading, writing, and understanding mathematics by requiring them to research one or more mathematical topics and then write a report about their activities and discoveries. math.uww.edu /mathcsdept/760rota.htm   (2181 words)

Doctoring the spin on Venus (June 2001) - News - PhysicsWeb The rotation of rocky planets with dense atmospheres - such as the Earth and Venus - is determined by atmospheric tides, gravitational forces, friction between the mantle and the crust, and the 'obliquity' angle between the planet's equator and the plane of its orbit around the Sun. Such planets can have either retrograde or 'prograde' rotation - that is, the west-to-east rotation commonplace in the solar system - and their rotation axis may or may not have flipped during its evolution. For the rotation axis of Venus to flip, Correia and Laskar calculated that the planet's equator must once have been strongly tilted compared with the plane of its orbit around the Sun - that is, it must have had a high obliquity. physicsweb.org /article/news/5/6/6   (443 words)

GeoGL Manual - Mathematics   (Site not responding. Last check: 2007-10-09) The first parameter to the rotatePoint() function is the point to rotate, while the second parameter is a vector containing the rotation. The expected form of the rotation vector is 3 Euler rotation values (x,y,z), in degrees, where each value represents a rotation around an axis. Once the rotation Matrix is created, it is multiplied by the point p that is to be rotated. www.mobydisk.com /softdev/software./geogl/docs/mathematics.html   (1334 words)

Rotations on a Sphere Rotations around some arbitrary axis are essential for any computer study of plate tectonics, but it can be astonishingly hard to find out how to do it. Since the mathematics were worked out long ago, most books on plate tectonics simply refer readers to mathematics texts, but since this is not a very widely-used operation, mathematics texts and references tend to omit it. If we have two rotations, each represented as a matrix, the result of both rotations is the product of their two matrices. www.uwgb.edu /dutchs/MATHALGO/sphere0.htm   (780 words)

Seminole Patchwork Topics There are four rigid motions of the plane, a rigid motion is a motion that does not alter the size or shape of the object being moved. The four rigid motions are reflection, rotation, translation, and glide reflection. Rotations are limited to 180° (half-turn) since the pattern must retain its original orientation. www2.austin.cc.tx.us /hannigan/Presentations/NSFMar1398/SPTopics.html   (1309 words)

Ethnomathematics Digital Library (EDL)   (Site not responding. Last check: 2007-10-09) Mathematics teachers should not teach theory and then look for applications, but rather, analyze and elucidate the mathematics that grows out of students' activities. Another doctoral dissertation examines the traditional mathematical practices of the Vai of Liberia and how these practices are studied and reconciled in elementary school settings. Examples of how mathematics teachers can bring elements of the local culture into their teaching, particularly geometric examples from Mozambique, to enhance cultural confidence are discussed. www.ethnomath.org /search/browseResources.asp?type=cultural&id=73   (1049 words)

Welcome to the Mathematics Department at BSC   (Site not responding. Last check: 2007-10-09) The mathematics faculty members are readily available to students during office hours and actively encourage students to take advantage of this. The difference between the BS in mathematics program and the BA in mathematics program is that there is a foreign language requirement for the B. and not for the BS. Students in the mathematics secondary education program take electives and professional courses for teacher certification by the State of New York in addition to the courses required for the mathematics major. math.buffalostate.edu /~math   (367 words)

GameDev.net - Do We Really Need Quaternions? Quaternions should be relegated to their proper place in mathematics: an interesting phenomenon, useful in an academic sense to demonstrate the properties of set theory and abstract algebra, but not a proper tool for software engineers. The rotation matrix R is so intrinsically useful, it is worth taking the time to look at the derivation. You can also do relative rotations without changing the properties of the rotation matrix, because the set of special orthogonal matrices is closed under multiplication. www.gamedev.net /reference/programming/features/whyquats   (1576 words)

Mathematics of Perspective Drawing We'll focus on mathematical concepts and derive the basic formulas that are at the heart of all rendering machines. A mathematical theory of perspective drawing could only be developed when the Renaissance freed painters to depict nature in a way closer to what they observed [IW]. coordinate of the rotated object) is division by constant. www.math.utah.edu /~treiberg/Perspect/Perspect.htm   (5252 words)

Crocodile Clips Lesson Plan   (Site not responding. Last check: 2007-10-09) A shape is rotated by rotating each of its vertices by the same angle about the centre of rotation. The angle of rotation is the angle at the centre of rotation between a line to a vertex on the shape and a line to its equivalent vertex on the rotated shape. Ensure Crocodile Mathematics 1.2 (or later) is installed and the simulation files LF0106a and LF0106b are accessible. www.crocodile-clips.com /gpv70/LP/mathematics/LP0106/LP0106.htm   (133 words)

Mathematics   (Site not responding. Last check: 2007-10-09) Given my interest in mathematics it was only matter of time before I attempted an inversion on this word. I completed the final lettering in time for a performance of the mathematical dance performance "Dances for the Mind's Eye" at a ceremony honoring the new math-science wing at the Alabama School of Fine Arts, a school which serves mostly high school aged kids. Half of "Mathematics" was printed on the back of the program, running off the page halfway through the E. At one point in the program I ask audience members to turn to someone next to them and put their programs together to spell "Mathematics" as an inversion. www.scottkim.com /inversions/gallery/mathematics.html   (195 words)

Mathematics Anxiety The Mathematics Anxiety Rating Scale (MARS) is a 98 item inventory intended to measure mathematics anxiety. The Phobus (one of the moons or Mars) inventory for mathematics anxiety makes use of 20 MARS items (10 selected from each factor, some modified) combined with an additional 10 new items designed to be compatible with MARS items and to measure a hypothesized new component of mathematics anxiety. Factor analysis on the items using a varimax rotation and also using rotated equimax confirmed that the new items established a component of Phobus distinct from the two components extracted from the MARS items. www.accd.edu /sac/math/FACULTY/RFerguso/MathAnx.htm   (452 words)

Science & Technology at Scientific American.com: Ask the Experts: Geology: Did the earthquake that spawned the ...   (Site not responding. Last check: 2007-10-09) Models predict that the earthquake should have affected rotation of the earth by shortening the length of a day by about three microseconds, or three millionths of a second. This rotation change is a prediction from a model, and the data [collected by ground- and space-based position sensors] is being analyzed to see if the predicted change actually occurred. The earth wobbles as it rotates because its mass is not balanced about its rotation axis, just like a tire on a car will wobble as it rotates if the tire is not perfectly balanced. www.sciam.com /askexpert_question.cfm?articleID=000DC7E1-F4A0-11E7-B4A083414B7F0000&catID=3&chanID=sa005   (415 words)

AllRefer.com - angle (Mathematics) - Encyclopedia angle, in mathematics, figure formed by the intersection of two straight lines; the lines are called the sides of the angle and their point of intersection the vertex of the angle. If one side and the vertex of an angle are fixed and the other side is rotated about the vertex, it sweeps out a complete circle of 360° or 2 Half a rotation from 0° or 0 radians results in a straight angle, equal to 180° or reference.allrefer.com /encyclopedia/A/angle.html   (295 words)

Michel PETITJEAN homepage / The Mathematical Theory of Chirality In other words, the problem of measuring chirality is just a particular instance of the problem of measuring how similar are two class of equivalence of distributions: the set of all translated and rotated images of the original distribution, and the set of all its translated and rotated and inverted images. When the rotation is fixed or when the optimal rotation is known, computing CHI is a linear programming problem [4]. Computing also the rotation leads to minimize a linear function under polynomial constraints: the linear constraints come from the joint density, and the non linear come from the rotation. petitjeanmichel.free.fr /itoweb.petitjean.html   (2862 words)

Amazon.com: Quaternions and Rotation Sequences: Books   (Site not responding. Last check: 2007-10-09) The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. Mathematics, as with most subjects in science and engineering, has a long and varied history. However the book enlightens us with showing the fundamentals behind a fixed vector (coordinate frame rotate) and fixed coordinate system (vector rotates) and shows us how much of a difference there is in actual coordinates of the resulting transformation. www.amazon.com /exec/obidos/tg/detail/-/0691058725?v=glance   (2844 words)

Beyond 3D: A Rotation of Cubes: Mathematics   (Site not responding. Last check: 2007-10-09) The idea of the shadow is represented mathematically by projection, of which there are two basic types. In this case, the shadows of objects close to the light source are larger than shadows of objects farther from the light. Mapping the corners of the hypercube through this rotation map, and then through the projection map gives the positions in three-space of the shadow of the hypercube. alem3d.obidos.org /en/cuberot/math   (316 words)

2D Rotation   (Site not responding. Last check: 2007-10-09) Example of a 2D rotation through an angle w where the coordinates x, y go into x', y'. Note that w is positive for a counterclockwise rotation and that that rotation is about the origin (0, 0). It would be nice to be able to compose the transformations into one and then apply this total transformation to the object. www.siggraph.org /education/materials/HyperGraph/modeling/mod_tran/2drota.htm   (153 words)

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