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Topic: Chirality (mathematics)

Related Topics

Asymmetry

Mirror image

Symmetry

Spontaneous symmetry breaking

Chirality

Entropy

Hysteresis

Ferromagnetism

Swastika

Paramagnetism

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	Science Fair Projects - Chirality (mathematics)
		In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly can't be mapped to its mirror images by rotations and translations alone.
		The word chirality is derived from the greek χειρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the greek εναντιος (enantios) 'opposite' and μορφη (morphe) 'form'.
		For example the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Chirality_(mathematics) (614 words)

	Chirality - Wikipedia, the free encyclopedia
		Chirality (Greek handedness, derived from the word stem χειρ~, ch[e]ir~ - hand~) is an asymmetry property important in several branches of science.
		A chiral object and its mirror image are called enantiomorphs (Greek opposite forms) or, when referring to molecules, enantiomers.
		Racemic acid is the racemic form of tartaric acid forming a mixture of two enantiomorphic crystals each form consisting of one of the two enantiomers.
	en.wikipedia.org /wiki/Chirality (216 words)

	Chiral Mechanics
		Chiral effects in elasticity cannot be expressed within classical elasticity since the modulus tensor, which is fourth rank, is unchanged under an inversion.
		A chiral plate bent to hyperbolic shape is predicted to exhibit size effects from the Cosserat characteristic length, and a shear force from the chirality.
		Chiral structures have been observed in trees by Dr. Cherkaev of the Mathematics Department at the University of Utah.
	silver.neep.wisc.edu /~lakes/chiral.Cmp.html (2477 words)

	Symmetry
		The most familiar example is the left-right or mirror image symmetry exhibited for instance by the letter T: when this letter is reflected along a vertical axis, it remains the same.
		In mathematics, one studies the symmetry of a given object by collecting all the operations that leave the object unchanged.
		For a geometrical object, this is known as its symmetry group; for an algebraic object, one uses the term automorphism group.
	www.ebroadcast.com.au /lookup/encyclopedia/sy/Symmetry.html (329 words)

	Describing Chirality: Home page
		Basically, chirality is "handedness," that is the existence of left/right opposition.
		This background is to be kept in mind when appreciating the importance of chirality, whether in science or in everyday life.
		Chirality is an old theme in many branches of chemistry and biology, with overwhelming practical importance, and physicists have long paid interest in symmetry matters.
	chirality.ouvaton.org /homepage.htm (682 words)

	Pharyngula: Chirality in Euhadra
		Chirality is a fascinating aspect of bilaterian morphology.
		Snail chirality is one of those things there are a great many papers in developmental biology about, and that's the direction from which I've always approached it—as an illuminating molecular and cellular process, part of the complex story of how genes are translated into form.
		With mathematical modeling, the authors showed that the separation will be incomplete because of gene flow, so the two types will reach an equilibrium, but outside of chance variations, one will not replace the other.
	scienceblogs.com /pharyngula/2006/04/chirality_in_euhadra.php (1348 words)

	Eotvos and Novel Equivalence Principle Tests
		Chirality and parity are emergent phenomena - components collectively evolve discrete symmetry system properties absent and unpredictable from any smaller subset.
		The rigorous abstract mathematics of chirality has been extensively examined and reduced to QCM software.
		Optical rotation is not diagnostic of geometric chirality.
	www.mazepath.com /uncleal/eotvos.htm (7753 words)

	Creation Could Be Left-Handed
		This approach was called the gauge description of chirality, because it is associated with a new class of geometries called gauge geometries.
		The chiral nature of the clusters, which means they exist in distinct right-handed and left-handed variations, dramatically affects the way in which they absorb polarised light.
		The chiral properties varied by the size of the cluster, and therefore were only observed clearly when the clusters were separated by weight.
	flatrock.org.nz /topics/science/creation_could_be_left_handed.htm (2424 words)

	Michel PETITJEAN homepage / The Mathematical Theory of Chirality
		Chirality is sensitive to the dimension of the space: a non isocele triangle is chiral in the plane, and is achiral in the 3D space.
		It is why the quantitative measure of chirality is a problem related to the theory of probability metrics [1], and also to the Monge-Kantorovitch transportation problem [2], for which the cost of transporting a distribution of mass to an other one has to be minimized.
		Chirality is known to be related to indirect symmetry, and has been quantified to evaluate how a set is similar to its inverted image, via an optimal superposition method.
	petitjeanmichel.free.fr /itoweb.petitjean.html (3189 words)

	Describing Chirality: Research results
		Chirality is only defined negatively; the chiral objects are the objects that fail to be achiral.
		Whereas chirality indeed plays a tremendous role in organic chemistry or biochemistry, chirality does not depend on carbon atoms properties.
		It was mathematically proved that chirality is amenable to a rich description for a large class of objects that includes molecules.
	www.chiral.com /description/research.htm (621 words)

	Bookworkz:: Chiral Drugs
		Chiral Drugs is a comprehensive listing of over 2500 chiral drugs, classified by therapeutic class, and including structures and physical properties for each entry in the listing.
		Chiral Drugs provides an introduction to the types of sources and methods currently in use for obtaining chiral molecules and is an invaluable resource for researchers in the pharmaceutical and biotechnology sectors as well as to those working in the basic biochemical sciences.
		Chiral Intermediates provides an introduction to the types of sources and methods currently in use for obtaining chiral molecules and is an invaluable resource for information on available chiral molecules.
	www.bookworkz.com /education/chemistry/0566084112.html (522 words)

	Reference.com/Encyclopedia/Chirality (chemistry)
		It is the symmetry of a molecule (or any other object) that determines whether it is chiral or not.
		Many biologically-active molecules are chiral, including the naturally-occurring amino acids (the building blocks of proteins), and sugars.
		Hexol is a chiral cobalt complex which was first investigated by Alfred Werner.
	www.reference.com /browse/wiki/Chirality_(chemistry) (2037 words)

	Philosophy of Teleportation
		Chirality is also a big concern of the string physicsits who are trying to generate the Standard Model as a low energy limit.
		It's odd to think that it is mathematically unique as the midlier between two dimensional space which is so simple, and four dimensional euclidean space which has so many ways to go that a lot of stuff gets lost.
		We think three dimensional space is simple and normal because we live in it, but is is as unique among the infinity of higher dimensional spaces as andpi; is among the infinity of real numbers.
	www.physicsforums.com /showthread.php?t=22540 (2197 words)

	Kalée Gregory: Chirality Module Design (Site not responding. Last check: 2007-10-27)
		Chirality is an intersting and important topic in chemistry, and chirality in molecules is detected with light.
		However, chirality is a subject that is not treated in high school curricula.
		In lab, various activities on polarization, symmetry, and chirality would give the students a means for choosing a project on one of those topics to explore during the second half of the quarter.
	kalee.tock.com /portfolio/chirality.html (523 words)

	Converter - Theory
		The basic approach taken during the two- to three-dimensional conversion process is to assign distance bounds to all atom pairs of the molecule, together with planarity and chirality (using wedged bond information) constraints, and then to supply the bounds and constraints as input to a distance geometry program for generation of 3D coordinates.
		This shows that the chirality of the quadruple of atoms bonded to an asymmetric carbon atom is capable of distinguishing between a molecule and its mirror image.
		Although the chirality of a quadruple changes sign if any pair of atoms in it are swapped, for most purposes we can just number the atoms in any order and use this same order for the atoms in each quadruple.
	www.scripps.edu /rc/softwaredocs/msi/insight2K/converter/02_Theory.html (3160 words)

	AWM at ICIAM99
		The Association for Women in Mathematics (AWM), the European Women in Mathematics (EWM) and the Society for Industrial and Applied Mathematics (SIAM) are jointly sponsoring two minisymposia (MS212, MS213) for women researchers at the Fourth International Congress on Industrial and Applied Mathematics (ICIAM99), July 5-9, 1999, Edinburgh, Scotland.
		The question whether to do industrial mathematics at the university is to be answered in the light of scientific interest (and output), financial resources, attraction for students, and the profile of the department or university.
		The mathematical model, basically describing the evaporation of the solvent in liquid paint, is a generalised stefan problem, analogous to studies in phase transition problems.
	www.awm-math.org /calendar/iciam99.html (1172 words)

	Flapan
		The goal of the project is to increase chemistry students' knowledge of mathematics and its role in chemistry.
		In order to reinforce and strengthen the Organic Chemistry students' ability to use mathematical and scientific reasoning together, we developed a sophomore organic laboratory in which students first derive the calculus of a kinetic rate process and then use the expression to study a series of alkyl halides being subject to a dehydrohalogenation reaction.
		We have developed three mathematical modules for the physical chemistry course: one preliminary module on background material (Preliminary Module), one on differentiability of functions of several variables (Module I), and another on partial differential equations and boundary value problems (Module II).
	www.math.pomona.edu /flapan_nsf/index.htm (704 words)

	Top Page 1
		This chiral property is known as handedness or enantiomorphous, and the difference between a person's two hands best represents the concept.
		The mathematics is significant because it is able to keep track of an object’s orientation and the orientation of the observer viewing the object.
		The V4 vertices of its dual, the rhombic dodecahedron, are the center of the cube's faces, which are determined by the crossing of the perpendicular edges of a chiral pair of dual tetrahedra that are coincident at their midpoints.
	www.mi.sanu.ac.yu /vismath/dyke/index.html (6091 words)

	Biomathematics Seminar Schedule
		When a helical bacterial flagellum, clamped at one end, is placed in an external flow, it has been observed that regions within the flagellum periodically transform to the opposite handedness and these domains travel down the length of the filament.
		We propose a dynamical model for this phenomenon based on the existence of two competing locally stable states of opposite chirality whose interaction with the flow is through the torque it produces.
		An associated PDE for the shape and chirality dynamics is solved numerically and displays many of the key features seen in experiment.
	math.arizona.edu /~jwatkins/biomathfa00.html (2858 words)

	ScienceDaily: Purdue Scientists Discover Why We're All Lefties Deep Down
		The study also suggests that the chirality of other biomolecules, such as sugars, was determined by serine as well.
		Hold a molecule with left-handed chirality up to a mirror, and you see its right-handed sibling, a molecule that generally possesses the same other properties as its lefty variant.
		Scientists in such fields as mathematics, physics, chemistry, biochemistry, biology, and medicine are currently involved in investigations of porphyrins and their numerous analogues and derivatives.
	www.sciencedaily.com /releases/2003/08/030806075413.htm (2317 words)

	Bates College \| Chemistry
		Abstract:Many molecules exhibit the property of chirality, or “handedness.” Chirality arises when a molecule cannot be superimposed on its own mirror image.
		Chirality can have significant effects as many biological systems have the ability to discriminate between optical isomers.
		Chirality can be achieved by attaching optically pure amino acids to the calix(4)arene.
	www.bates.edu /x20247.xml (343 words)

	Bates College \| Abstracts: HHMI Faculty Development, 2004-2005
		Chiral compounds are those which are not super-imposable on their mirror image; they are, in essence, "left-handed," "right-handed," and both.
		Chirality has great relevance in many areas of chemistry but particularly pharmaceuticals, where a chiral compound may have very different effects ranging from significant medical benefits to catastrophic side effects, so it is essential to understand the chiralitry of compounds and their resultant effects.
		A highly effect way to identify the chirality of compounds is to employ NMR spectroscopy; this has been the focus of my work for many years.
	www.bates.edu /abstracts-hhmi-faculty-development-04-05.xml (816 words)

	THEORETICAL PHYSICS: ON THE AETHER AND BROKEN SYMMETRY (Site not responding. Last check: 2007-10-27)
		The symmetry in question is called chiral symmetry, and it involves the behavior of quarks, the principal constituents of the protons and neutrons in atomic nuclei (among other things).
		Chiral symmetry is easiest to describe if we adopt the slight idealization that the lightest quarks, the up quark (u) and down quark (d), are massless.
		The two possible states of chirality of a quark, left and right, are essentially the same concept as left and right circular polarization for photons.
	scienceweek.com /2005/sw050708-6.htm (2750 words)

	Modeling and Applied Mathematics Book Reviews
		Mathematical Biology I: An Introduction, by J. Murray.
		Mathematical Models in Biology: An Introduction, by Elizabeth S. Allman and John A. Rhodes.
		The Mathematics of Voting and Elections: A Hands-On Approach, by Jonathan K. Hodge and Richard E. Klima.
	www.maa.org /reviews/tindex10.html (971 words)

	Polyhedron, Polyhedra, Polytopes - Numericana
		The tetragonal antiwedge is thus the simplest example of a chiral polyhedron.
		Cutting an antiprism the same way, you obtain an antiwedge (the simplest chiral polyhedron is the tetragonal antiwedge, an hexahedron).
		Snub: Snubbing is an interesting chiral process which, roughly speaking, amounts to loosening all faces of a polyhedron and rotating them all slightly in the same direction (clockwise or counterclockwise), creating 2 triangles for each edge and one m-sided polygon for each vertex of degree m.
	home.att.net /~numericana/answer/polyhedra.htm (5442 words)

	Rose-Hulman Undergraduate Mathematics Conference ::: Schedule of Events (Site not responding. Last check: 2007-10-27)
		Although the average human being does not understand the meaning of the word chiral, almost every human being is born with a pair of chiral objects, their hands.
		Along with the geometry of the placement of the mirrors, the mathematics of kaleidoscopes involves linear algebra, group theory and a bit of graph theory.
		The main mathematical tool utilized to carry out these calculations is known as the Reciprocity Gap Functional (closely related to Green's Theorem).
	www.rose-hulman.edu /mathconf/student.php (1103 words)

	Read This: When Topology Meets Chemistry: A Topological Look At Molecular Chirality
		It is natural to model a chemical molecule mathematically by the mathematical structure of a graph; that is, a discrete collection of vertices joined by edges.
		One might ask — and Flapan did ask — whether the chirality of Möbius ladders was an inherent property of the abstract graph, or was determined by the particular way in which that graph was embedded in space.
		In a study which deals with mathematical models which are intended to be applied to problems in chemistry or molecular biology, it is necessary to consider the relations between those models and the physical phenomena they are intended to represent.
	www.maa.org /reviews/topochem.html (2915 words)

	CUR Fellows Awards - Council on Undergraduate Research
		His has won numerous awards for teaching, has published scores of research articles on combinatorics and related fields in top mathematical journals, and is an author of several mathematics textbooks.
		He recognized early on that undergraduates are capable of original investigations in mathematics, and armed with success stories from a pioneering summer program, founded a movement within mathematics.
		The quality of Tom's research has itself been recognized, as illustrated by a recent invitation to give a plenary address at an international conference in his specialty field of chirality, invitations to chair national symposia, and his consistent success in receiving peer-reviewed funding from NSF and numerous foundations and corporations.
	www.cur.org /fellows02bio.html (1153 words)

	THE MYSTERY OF KNOTS (Site not responding. Last check: 2007-10-27)
		One of the most significant unsolved problems in mathematics is the complete classification of knots.
		The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots.
		Mathematical ideas and concepts are extensively discussed, and no advanced background is required.
	www.worldscibooks.com /mathematics/4104.htm (95 words)

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