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Topic: Crystal mathematics

	Crystallographic restriction theorem - Wikipedia, the free encyclopedia
		The crystallographic restriction theorem in its basic form is the observation that the rotational symmetries of a crystal are limited to 2-fold, 3-fold, 4-fold, and 6-fold.
		This is strictly true for the mathematical formalism, but in the physical world crystals are finite, and quasicrystals occur with other symmetries, such as 5-fold.
		In mathematics, a crystal is modeled as a discrete lattice, generated by a list of independent finite translations.
	en.wikipedia.org /wiki/Crystallographic_restriction_theorem (1296 words)

	file_nav_name Encyclopedia Index (Site not responding. Last check: 2007-10-01)
		Mathematics education is the study of practices and methods of both the teaching and learning of mathematics.
		The Faculty of Mathematics is one of six faculties of the University of Waterloo in Waterloo, Ontario.
		A Bachelor of Mathematics is an undergraduate academic degree awarded for a courses taken in the study of mathematics...
	www.brainyencyclopedia.com /topics/mathematics.html (8154 words)

	History of Mathematics [encyclopedia] (Site not responding. Last check: 2007-10-01)
		By the late 12th-c much mathematical knowledge had been developed and held in the Islamic culture around the S shores of the Mediterranean, and it was beginning to percolate into Christian Europe through trading posts in such places as Sicily and Spain.
		Mathematical activity in France (Gaspard Monge, Pierre Simon Laplace, Augustin Louis Cauchy), and subsequently in Germany (Carl Gauss, Carl Jacobi, Peter Dirichlet, Bernhard Riemann) was strongly developed and professionalized, in both research and teaching directions.
		By the late 12th-c much mathematical knowledge had been developed and held in the Islamic culture around the southern shores of the Mediterranean and it was beginning to percolate into Christian Europe through trading posts in such places as Sicily and Spain.
	www.kosmoi.com /Science/Mathematics/History (2656 words)

	SIAM News
		Describing in some detail a number of the languages that are in extremis, Crystal, who is a student of linguistics and a prolific author, details the various reasons for the death of a language, what is lost when one of them dies, and what, if anything, can be done to preserve them.
		Mathematics is written down (for the most part linearly) in symbols, and its sentences, symbols and all, can be read aloud.
		The riches of mathematics, without contemplative judgments, would, Poincaré wrote, "soon become an encumbrance and their increase will produce an accumulation as incomprehensible as all the unknown truths are to those who are ignorant." The unity is now further threatened by self-contained, self-publishing chat groups.
	www.siam.org /siamnews/03-01/language.htm (1702 words)

	KSU Department of Mathematical Sciences: Careers In Mathematics
		Mathematical ecology is a growing and active area of interdisciplinary research between mathematics and ecology, using almost every part of mathematics (linear algebra, analysis, differential equations, stochastic processes, numerical simulations, statistics) to understand and model complex biosystems.
		Today's mathematical ecology researchers are faced with the far more daunting task of simulating several inter-connected networks of organisms across different scales of time, size and space.
		Part of crystal formation follows the principle of a minimum surface area for a fixed volume, but the orientation of a crystal also affects its formation: Heat is diffused more easily away from the surface than into it, so crystals in the direction of the exterior form faster than others.
	www.math.kent.edu /career/careers.html (902 words)

	Crystal Walcott: Mathematics Education Graduate Programs, School of Education, Indiana University at Bloomington
		Crystal Walcott: Mathematics Education Graduate Programs, School of Education, Indiana University at Bloomington
		I am a second-year doctoral student in mathematics education.
		Currently, I work as project manager of the IU-NAEP Mathematics Project Focus I. My research interests include children's use of visualization in the understanding of geometric concepts and the use of informal assessment in the mathematics classroom.
	www.indiana.edu /~mathed/walcottc.html (254 words)

	Crystal Wings of Mount Shasta; Crystals, Books, Workshops, Tools for Transformation
		Crystals have been an important part of the healing world as long as man has walked upon this earth.
		Marcel Vogel was an IBM inventor who discovered the power of a four-sided crystal wand whose shape was based on the Tree of Life and the mathematics of the pyramids.
		With the advent of the Dream Crystal, as well as the 21-sided and 33-sided cuts, it became obvious that these shapes were asking to be reborn.
	www.crystalwings.com /crystalsback.html (1350 words)

	Research from the Department of Biology
		This particular crystal is made up of a telomere end binding protein complexed with single strand DNA and belongs to the hexagonal space group P6 Once high quality crystals are obtained, X-ray reflections are measured.
		Diffraction patterns such as the one shown above are related to the geometry and symmetry of the crystal as well as the structure of the individual repeating unit from which the crystal is built.
		Mathematics is used to translate the intensity and phase information into an electron density map.
	www.biology.utah.edu /posters2.php?id=21 (401 words)

	Crystal page (Site not responding. Last check: 2007-10-01)
		This is not the place for an exposition of representation theory, Lie algebras, or crystal graphs.
		A crystal graph of a representation pi is a weighted graph whose vertices are indexed by the elements of S
		A crystal graph product of two crystal graphs is a crystal graph obtained from the two given graphs by rules given in Kashiwara's paper [K].
	web.usna.navy.mil /~wdj/crystal.htm (1093 words)

	Applied Mathematics (Site not responding. Last check: 2007-10-01)
		The language, tools and theorems of mathematics are applied in a vast range of disciplines within engineering and computer science, the physical sciences, the biomedical sciences, management and economics, psychology, etc. As a field of study and research applied mathematics lies at the borderline between mathematics and its applications.
		While not easily defined with any great precision applied mathematics involves the application of interesting mathematical tools to significant applied problems or to the development of novel mathematics adapted to particular applications.
		Nilima Nigam): Computational mathematical sciences are now having a huge impact on the biological sciences, from models of disease-spread to gene transcription to evolutionary biology.
	www.math.mcgill.ca /department/appliedmath.php (625 words)

	Crystal Awareness Institute -- DaEl Walker
		Mathematics is the language of energy, and geometry is the graphics.
		Crystals grids can be used to charge objects with bioenergy, change emotional states, and even be used for healing.
		Imagine you see a beam of light move from the center crystal to number one to form a rid of solid light connecting the number five crystal to number one.
	www.crystalawareness.com /crystalgrid (722 words)

	300-302
		By the year 1801, the fundamental laws of crystal morphology had been well established, and in the last two decades of that century, theories of the internal symmetries of crystals were being discussed [2].
		Each possible crystal lattice is characterized by having a smallest structural unit, called a unit cell, and when those cells are stacked together face-to-face, an infinite region of space can be filled without leaving a single hole.
		Quite notable in the mathematics of crystal symmetry is the impossibility of a three dimensional crystal possessing a five-fold axis of rotation.
	nvl.nist.gov /pub/nistpubs/sp958-lide/html/300-302.html (1461 words)

	Earth's Core Crystal - Crystalinks
		"Hexagonal crystals have a unique directionality," says Stixrude, "which must be aligned and oriented with Earth's spin axis for every crystal in the inner core." This led Stixrude and Cohen to try a computational experiment.
		A hexagonal crystal, one of the three known structures iron can take, is different from the cubic crystalline structures iron takes at the planet's surface.
		As the rocks cool from lava, for instance at the deep mid-ocean ridges where the earth's surface plates are formed, crystals line up with the direction of the magnetic field.
	www.crystalinks.com /corecrystal.html (2406 words)

	math lessons - The Crystal Maze
		The Crystal Maze was a game show, produced by Chatsworth Television and shown on Channel 4 in the United Kingdom from 1990 to 1995.
		After competing in all four zones, the remaining contestants went into the 'Crystal Dome' at the centre of the maze, in which gold and silver tokens were blown around.
		The Crystal Maze was referenced in the movie Dungeons & Dragons, which featured a maze with similar puzzles, with its owner played by Richard O'Brien.
	www.mathdaily.com /lessons/The_Crystal_Maze (378 words)

	Radiation Notes: Diffraction and Microscopy
		A crystal may be loosely defined as a piece of solid matter in which the atoms are regularly arrayed in space.
		The intensity of each beam and its relative phase are determined by the structure within each unit cell of the crystal, while the directions of the beams are determined by the three dimensional regularity of the packing of the unit cells within the crystal.
		Alternatively, if a rectangular crystal is set with its axes parallel to the x, y, and z coordinate axes, the plane could be specified by the direction and length of the shortest vector from the origin to the plane (a vector which will of course be perpendicular to the plane).
	oak.cats.ohiou.edu /~piccard/radnotes/diffract.html (5483 words)

	fUSION Anomaly. Quartz Crystal
		Quartz is a crystal, which means it has an extremely regular arrangement of atoms that vibrate at a very stable frequency.
		American Indian shamans and healers use rock crystals for curing, scrying, and many other purposes, and their ancient use in the Americas is known from archaeological reports.
		Uluhru (Ayers Rock) is a giant blue crystal that absorbs cosmic energy, which is then channelled around the planet via the crystal grid matrix of the earth: an ancient Internet.
	fusionanomaly.net /quartzcrystal.html (1774 words)

	Mining and Travel
		She is a scientist and holds Bachelor of Science and Master of Arts degrees in mathematics.
		She has been working with stones since she was a child, always evidencing an interest in the geological and mystical properties of these children of Mother Earth.
		Her desire to share her research and knowledge with her brothers and sisters of the planet she has taught crystal workshops in Brazil, the Republic of South Africa and now Australia and held private consultations in India and Nepal in addition to her work in the United States.
	www.crystal-world.com /html/others/Melody3.htm (233 words)

	Professional Resume
		Computer Recognition of People’s Handwriting, Singular Integral Equations, Conformal Geometry, Crystal Twinning, Stable Configurations in Liquid Crystals, Potential Flows in Space, the Sobolev Trace Imbedding Theorem and the Moving Planes, Surfaces of Constant Mean Curvatures, Free Boundaries, Crystal Precipitation.
		Mathematical Methods of Physics (Textbook: Mathematical Methods for Physicists by Arfken and Weber).
		On a kinematic compatibility equation related to elastic stress-free joints and crystal twins.
	www.math.utoledo.edu /~bou/ou.htm (408 words)

	Exciting Math-Physics Interfaces
		Our School of Mathematics has a very strong group of mathematicians working on the interface between string theory and mathematics.
		The mathematics of shape change guides the search for the most effective atomic composition and crystallographic orientation of the film.
		Mathematical and computational challenges are presented by the disparate space and time scales, from atomistic to continuum, needed to model small materials.
	www.math.umn.edu /arb/newsletter04/math-physics_interfaces.html (435 words)

	A whirlpool of numbers
		Primes cannot be broken down into simpler components; they play a role in mathematics that is similar to the role of the elements in chemistry.
		In fact, there are areas of mathematics that have been developed by mathematicians on the assumption that the Riemann Hypothesis is true.
		Nick Mee studied mathematics at the University of Cambridge, was Senior Wrangler in 1985 and went on to complete a Ph.D. with the title "Supersymmetric Quantum Mechanics and Geometry".
	plus.maths.org /issue25/features/whirlpool/index.html (2874 words)

	Chaotic Chomp: Science News Online, July 22, 2006
		By using mathematical tools originally developed for calculating properties of physical systems, Friedman and Landsberg show that the exact location of winning and losing cookies in Chomp varies unpredictably with small changes in the size of the initial array.
		In the case of Chomp, the geometry of winning positions for small values of x and winning positions for large values of x is roughly the same, after a suitable change in scale.
		Mathematics that's often used to characterize crystallization is providing new insights into simple games that don't depend on chance.
	www.sciencenews.org /articles/20060722/bob10.asp (2288 words)

	Amazon.com: Crystal Identification With The Polarizing Microscope: Books: R.E. Stoiber,S.A. Morse (Site not responding. Last check: 2007-10-01)
		A major goal of this text is to allow precise determination of refractive index and the essential composition of crystals belonging to important mineral groups such as olivine, feldspar and pyroxene.
		The optic orientation of optically biaxial crystals is illustrated with examples from each crystal system portrayed in stereographic projection.
		Principles and applications of crystal identification with the dispersion method are developed in a separate chapter.
	www.amazon.com /Crystal-Identification-Polarizing-Microscope-Stoiber/dp/0412048213 (832 words)

	Books, Love is in the Earth
		Internationally known bestselling author of "Love is in the Earth - A Kaleidoscope of Crystals", Melody was born in Cumberland, Maryland and is a scientist residing in the Pacific Northwest and holding a Masters degree in mathematics.
		She has traveled extensively throughout the world conducting comprehensive crystal workshops, private consultations, and awareness seminars.
		This is the first supplement to the internationally acclaimed "Love is in the Earth - A Kaleidoscope of Crystals Update" and " Love is in the Earth - Mineralogical Pictorial".
	www.crystal-world.com /html/books/melody/suppa.htm (118 words)

	Crystal City Public Schools
		The SAT measures verbal and mathematical reasoning, and includes a test of written English.
		The Crystal City High School registration code for both the ACT and SAT is 260-795.
		Results provide students with an early indication of their educational progress relative to career and educational options they are considering.
	www.crystal.k12.mo.us /plan.html (875 words)

	Crystal Group
		Scott Kongable is the president of Crystal Group.
		In this capacity he is responsible for the general supervision and control of the company's business and affairs.
		Prior to joining Crystal Group, Kongable spent ten years in various engineering functions with Rockwell-Collins; most recently as a project engineer in their military Global Positioning System business area.
	www.crystalpc.com /aboutus_managementteam.asp (395 words)

	Winter 1999 - A Clinic for Real-Life Math Problems (Site not responding. Last check: 2007-10-01)
		He had developed an affordable way to position satellite dishes, but he was unsure of the mathematics behind his plan.
		Clinic participants discovered a better mathematical approach, which led to a patent for the inventor.
		The students were able to create a computer program that allows her to simulate the growth of crystals, testing how various conditions influence their growth.
	www.artsci.washington.edu /newsletter/winter99/clinic.html (190 words)

	Mathematics Article Archives by KeepMedia (Site not responding. Last check: 2007-10-01)
		Mathematics is an ever-evolving discipline, but Ash and Grossassert that many non-mathematicians are under the impression thateverything that can be solved has been solved.
		A Russian recluse who solved a complex riddle won the mathematics world's version of a Nobel prize, but true to form refused to accept the honour or attend the royal awards ceremony.
		For the past 12 years, the American Institute of Mathematics has succeeded in luring mathematicians out of their garrets and into a Palo Alto warehouse next to Fry's Electronics.
	www.topix.net /science/mathematics/keepmedia (921 words)

	Crystal Taylor '03 Studies Globalization and Relationship Between Private and Public Sectors
		Crystal Taylor '03 and one of her Lafayette research mentors, Gladstone Hutchinson, dean of studies.
		EASTON, Pa.(www.lafayette.edu), March 22, 2002 — Mathematics major Crystal Taylor '03 (Hyattsville, Md.) is investigating the often complex relationship between the public and private sectors in an intensive research project this semester and is also conducting an independent study on the potential impact of globalization.
		As an EXCEL Scholar, Taylor is collaborating with Gladstone Hutchinson, dean of studies.
	www.lafayette.edu /news.php/view/283 (673 words)

	MIT OpenCourseWare \| Mathematics \| 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall ...
		"Photonic crystal superlensing and local density of states" - demonstrates flat-lens imaging and "superlensing" in a 2d photonic crystal, and correlates this phenomenon with the effect on the local density of states.
		"Two-dimensional analysis of a channel drop filter in a triangular lattice" - demonstrates and analyses channel-drop tunnelling between two waveguides in a triangular-hole lattice crystal in 2d, mediated by a pair of cavities formed of three missing holes in the crystal.
		"Localized propagation modes guided by shear discontinuities in photonic crystals and tunable group velocity in a coupled-resonator optical waveguide (CROW) formed by shear discontinuities in a photonic crystal" - demonstrates how a tunable slow-light group velocity is achieved by a glide-symmetric shear defect in a 2d photonic crystal.
	ocw.mit.edu /OcwWeb/Mathematics/18-325Fall-2005/Projects/index.htm (428 words)

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