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1
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34250790778
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R. Hoffmann, Catalista. Selected Poems, Huerga & Fierro, Madrid, 2002, p. 64 (bilingual book with the Spanish translation by F. García Olmedo).
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R. Hoffmann, Catalista. Selected Poems, Huerga & Fierro, Madrid, 2002, p. 64 (bilingual book with the Spanish translation by F. García Olmedo).
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4
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34250701675
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Escher repeatedly visited the Alhambra, the Moorish palace of Granada, where he was inspired by the splendid arabesques featuring order and symmetry. A mathematical study of such ornamentations has revealed that they exactly match the 17 plane groups possible for all two-dimensional patterns: A. F. Costa González, B. Gómez García, Arabescos y Geometría (Video Tape), UNED, Madrid, 1995.
-
Escher repeatedly visited the Alhambra, the Moorish palace of Granada, where he was inspired by the splendid arabesques featuring order and symmetry. A mathematical study of such ornamentations has revealed that they exactly match the 17 plane groups possible for all two-dimensional patterns: A. F. Costa González, B. Gómez García, Arabescos y Geometría (Video Tape), UNED, Madrid, 1995.
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6
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34250744218
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In chemistry, we often refer to left-right symmetry (or left-handed/right-handed forms) in an attempt to convey exactly what a mirror does. That is, conventional mirrors reverse only the left and right sides of things, but not up and down. From a mathematical viewpoint this assumption is also wrong: The mirror does not reverse left and right at all, it reverses front and back! This is simply a result of a bilateral symmetry common not only to humans but also to other animals and objects, meaning that the left side is a mirror reflection of the right. When one moves the right hand, one sees that the mirror image moves its left hand. Thus, left-right reversal is the convenient terminology we have developed to distinguish a bilaterally symmetric object from its enantiomorph. Perhaps, the great physicist Richard Feynman described the concept most clearly: It is the same with a book. If the letters are reversed left and right in a mirror, it is because we turned the book about a
-
In chemistry, we often refer to left-right symmetry (or left-handed/right-handed forms) in an attempt to convey exactly what a mirror does. That is, conventional mirrors reverse only the left and right sides of things, but not up and down. From a mathematical viewpoint this assumption is also wrong: The mirror does not reverse left and right at all, it reverses front and back! This is simply a result of a bilateral symmetry (common not only to humans but also to other animals and objects), meaning that the left side is a mirror reflection of the right. When one moves the right hand, one sees that the mirror image moves its left hand. Thus, left-right reversal is the convenient terminology we have developed to distinguish a bilaterally symmetric object from its enantiomorph. Perhaps, the great physicist Richard Feynman described the concept most clearly: "It is the same with a book. If the letters are reversed left and right in a mirror, it is because we turned the book about a vertical axis to face the mirror. We could just as easily turn the book from bottom to top instead, in which case the letters will appear upside down." (J. Gleick, Genius: Richard Feynman and Modern Physics, Abacus, London, 1994, p. 331).
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8
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34250717458
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For an English translation see: Immanuel Kant's Prolegomena to Any Future Metaphysics (Ed.: B. Logan), Routledge, London, 1996. Full contents of Prolegomena in English are also available online: http://philosophy.eserver.org/kant-prolegomena.txt (see First Part, Section 12).
-
For an English translation see: Immanuel Kant's Prolegomena to Any Future Metaphysics (Ed.: B. Logan), Routledge, London, 1996. Full contents of Prolegomena in English are also available online: http://philosophy.eserver.org/kant-prolegomena.txt (see First Part, Section 12).
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10
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34250712903
-
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Jonathan Cape, London
-
E. MacCurdy, Leonardo da Vinci's Notebooks Arranged and Rendered into English, Vol. 1, Jonathan Cape, London, 1938, p. 61.
-
(1938)
Leonardo da Vinci's Notebooks Arranged and Rendered into English
, vol.1
, pp. 61
-
-
MacCurdy, E.1
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11
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34250733527
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The book was, however, dated 1872 and published by Macmillan, London, the same publishing house that had published Alice's Adventures in Wonderland in 1864. Both books were illustrated by John Tenniel.
-
The book was, however, dated 1872 and published by Macmillan, London, the same publishing house that had published Alice's Adventures in Wonderland in 1864. Both books were illustrated by John Tenniel.
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12
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34250759366
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E. A. Abbott, Flatland - A Romance of Many Dimensions, Dover Publications, 1956 (reprinted from the 6th edition).
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E. A. Abbott, Flatland - A Romance of Many Dimensions, Dover Publications, 1956 (reprinted from the 6th edition).
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15
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34250714936
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Der barycentrische Calcul (The Calculus of Centers of Gravity), J
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Leipzig
-
A. F. Möbius, Der barycentrische Calcul (The Calculus of Centers of Gravity), J. Ambrosius Barth Verlag, Leipzig, 1827.
-
(1827)
Ambrosius Barth Verlag
-
-
Möbius, A.F.1
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16
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34250743694
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3rd ed, W. H. Freeman, New York, Chap. 18, pp
-
M. Gardner, The New Ambidextrous Universe, 3rd ed., W. H. Freeman, New York, 1990, Chap. 18, pp. 165-171.
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(1990)
The New Ambidextrous Universe
, pp. 165-171
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Gardner, M.1
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17
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34250760380
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The problem has been addressed repeatedly, also by R. Feynman prior to Gardner's hypothesis: The Feynman Lectures on Physics, 1, Addison-Wesley, Reading, MA, 1965, Chap. 52.
-
The problem has been addressed repeatedly, also by R. Feynman prior to Gardner's hypothesis: The Feynman Lectures on Physics, Vol. 1, Addison-Wesley, Reading, MA, 1965, Chap. 52.
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18
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33749605994
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Recent thought experiments point to a reliable solution of the Ozma problem by showing that parity violation modifies sum-frequency generation that would then distinguish two different configurations: N. Ji, R. A. Harris, J. Phys. Chem. B 2006, 110, 18744-18747
-
Recent thought experiments point to a reliable solution of the Ozma problem by showing that parity violation modifies sum-frequency generation that would then distinguish two different configurations: N. Ji, R. A. Harris, J. Phys. Chem. B 2006, 110, 18744-18747.
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19
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0002872160
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Prentice Hall, Chaps. 2-4, pp
-
S. R. Buxton, S. M. Roberts, Guide to Organic Stereochemistry, Prentice Hall, 1996, Chaps. 2-4, pp. 25-59.
-
(1996)
Guide to Organic Stereochemistry
, pp. 25-59
-
-
Buxton, S.R.1
Roberts, S.M.2
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22
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34250788675
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-
A long-held, erroneous idea is that Pasteur discovered the optical activity of tartaric acid. This phenomenon was first observed by Jean-Baptiste Biot (1774-1862), who pursued studies on polarimetry from 1812 until his death. Biot recognized that rotation of polarized light by quartz is an inherent property of the crystal Mémoire sur un nouveau genre d'oscillation que les molécules de lumière èprouvent en traversant certains cristaux: J.-B. Biot, Mem. Inst. 1812, 13, 1-371;
-
A long-held, erroneous idea is that Pasteur discovered the optical activity of tartaric acid. This phenomenon was first observed by Jean-Baptiste Biot (1774-1862), who pursued studies on polarimetry from 1812 until his death. Biot recognized that rotation of polarized light by quartz is an inherent property of the crystal ("Mémoire sur un nouveau genre d'oscillation que les molécules de lumière èprouvent en traversant certains cristaux": J.-B. Biot, Mem. Inst. 1812, 13, 1-371;
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23
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34250771123
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for dextro-and levorotatory quartz, pp. 262-263, while this behavior of some natural liquids or solutions of solids (oil of turpentine, oil of lemon, camphor in alcohol, sugar in water) seems to be a property of individual molecules (Phénomènes de polarisation successive, observès dans les fluides homogènes: J.-B. Biot, Bull. Soc. Philomath. Paris 1815, 190-192).
-
for dextro-and levorotatory quartz, pp. 262-263), while this behavior of some natural liquids or solutions of solids (oil of turpentine, oil of lemon, camphor in alcohol, sugar in water) seems to be a property of individual molecules ("Phénomènes de polarisation successive, observès dans les fluides homogènes": J.-B. Biot, Bull. Soc. Philomath. Paris 1815, 190-192).
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24
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34250778930
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Later, he advanced a molecular explanation, although the term molecule by that time should be interpreted in a broad, flexible sense, related to Newton's corpuscular theory: the phenomenon] being a property of molecules regardless of their state of aggregation (... une faculté propre à ces molécules indépendamment de leur état d'agrégation; Mémoire sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux: J.-B. Biot, Mem. Acad. Sci. lnst. Fr. 1817, 2, 41-136).
-
Later, he advanced a "molecular" explanation, although the term molecule by that time should be interpreted in a broad, flexible sense, related to Newton's corpuscular theory: "the phenomenon] being a property of molecules regardless of their state of aggregation" ("... une faculté propre à ces molécules indépendamment de leur état d'agrégation"; "Mémoire sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux": J.-B. Biot, Mem. Acad. Sci. lnst. Fr. 1817, 2, 41-136).
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26
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34250764285
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Royal Society of Chemistry, Cambridge, This remarkable discovery has been described in later hagiographies of Pasteur with a certain eureka-like style, but it probably did not occur in the same way
-
P. Ball, Elegant Solutions. Ten Beautiful Experiments in Chemistry, Royal Society of Chemistry, Cambridge, 2005, pp. 101-118. This remarkable discovery has been described in later hagiographies of Pasteur with a certain eureka-like style, but it probably did not occur in the same way.
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(2005)
Elegant Solutions. Ten Beautiful Experiments in Chemistry
, pp. 101-118
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-
Ball, P.1
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27
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34250762152
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L. Pasteur, (Euvres de Pasteur, 1, Masson, Paris, 1922, p. 21 (La dissymétrie moléculaire).
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L. Pasteur, (Euvres de Pasteur, Vol. 1, Masson, Paris, 1922, p. 21 (La dissymétrie moléculaire).
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28
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34250745938
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Extracted from a conference given by Pasteur at the Société Chimique de Paris on Dec. 22, 1883. See also L. Pasteur, Euvres de Pasteur, 1, Masson, Paris, 1922, pp. 370-372.
-
Extracted from a conference given by Pasteur at the Société Chimique de Paris on Dec. 22, 1883. See also L. Pasteur, (Euvres de Pasteur, Vol. 1, Masson, Paris, 1922, pp. 370-372.
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29
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34250696049
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See L. Pasteur, Euvres de Pasteur, 1, Masson, Paris, 1922, p. 329, 372-374.
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See L. Pasteur, (Euvres de Pasteur, Vol. 1, Masson, Paris, 1922, p. 329, 372-374.
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30
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34250719268
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Heyden, London, Chap. 4, pp
-
O. B. Ramsay, Stereochemistry, Heyden, London, 1981, Chap. 4, pp. 72-78.
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(1981)
Stereochemistry
, pp. 72-78
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Ramsay, O.B.1
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31
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4544286629
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Ashgate, Burlington, VT
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P. J. Ramberg, Chemical Structure, Spatial Arrangement. The Early History of Stereochemistry, 1874-1914, Ashgate, Burlington, VT, 2003.
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(2003)
Chemical Structure, Spatial Arrangement. The Early History of Stereochemistry, 1874-1914
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Ramberg, P.J.1
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32
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34250709606
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See, Heyden, London, Chap. 5, pp
-
See O. B. Ramsay, Stereochemistry, Heyden, London, 1981, Chap. 5, pp. 92-94.
-
(1981)
Stereochemistry
, pp. 92-94
-
-
Ramsay, O.B.1
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35
-
-
34250759365
-
-
J. Buckingham, Chasing the Molecule, Sutton Publishing, 2004, pp. 75-76 plus Chap. 14.
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J. Buckingham, Chasing the Molecule, Sutton Publishing, 2004, pp. 75-76 plus Chap. 14.
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36
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34250692099
-
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For instance, in 1898 Nature published a series of letters in response to a previous article by F. R. Japp entitled Stereochemistry and Vitalism that summarized Pasteur's work and refers to asymmetric molecules and asymmetry. A detailed analysis of this correspondence can be found in M. Gardner, The New Ambidextrous Universe, 3rd ed., W. H. Freeman, New York, 1990, pp. 141, 144.
-
For instance, in 1898 Nature published a series of letters in response to a previous article by F. R. Japp entitled "Stereochemistry and Vitalism" that summarized Pasteur's work and refers to asymmetric molecules and asymmetry. A detailed analysis of this correspondence can be found in M. Gardner, The New Ambidextrous Universe, 3rd ed., W. H. Freeman, New York, 1990, pp. 141, 144.
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37
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34250715950
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E. L. Eliel, Stereochemistry of Carbon Compounds, McGraw-Hill, New York, 1962, pp. 9-10: An asymmetric molecule lacks both simple and alternating axes of symmetry, whereas a dissymmetric molecule lacks an alternating axis of symmetry (it may or may not be asymmetric).
-
E. L. Eliel, Stereochemistry of Carbon Compounds, McGraw-Hill, New York, 1962, pp. 9-10: "An asymmetric molecule lacks both simple and alternating axes of symmetry, whereas a dissymmetric molecule lacks an alternating axis of symmetry (it may or may not be asymmetric)."
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38
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34250784060
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By the late 1860s it was known that lactic acid from sour milk was optically inactive, while the so-called sarcolactic acid from muscle tissue, which has similar properties, was optically active. No chemical resolution of milk lactic acid was attempted, and therefore it was never determined whether an enantiomer of sarcolactic acid might be present in milk. See O. B. Ramsay, Stereochemistry, Heyden, London, 1981, pp. 78-80.
-
By the late 1860s it was known that lactic acid from sour milk was optically inactive, while the so-called sarcolactic acid from muscle tissue, which has similar properties, was optically active. No chemical resolution of milk lactic acid was attempted, and therefore it was never determined whether an enantiomer of sarcolactic acid might be present in milk. See O. B. Ramsay, Stereochemistry, Heyden, London, 1981, pp. 78-80.
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39
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34250730291
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W. Thomson Kelvin, Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light, C. J. Clay, London, 1904.
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W. Thomson Kelvin, Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light, C. J. Clay, London, 1904.
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40
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34250759863
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15th ed, Encyclopaedia Britannica, Chicago, IL
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H. I. Sharlin, The New Encyclopaedia Britannica, Vol. 22, 15th ed., Encyclopaedia Britannica, Chicago, IL, 1990, pp. 503-505.
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(1990)
The New Encyclopaedia Britannica
, vol.22
, pp. 503-505
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Sharlin, H.I.1
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41
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34250723362
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The two scientists produced the Treatise on Natural Philosophy (1867), which traced the concept of conservation of energy to the work of Isaac Newton, and had a major influence on future physicists. The Elements of Natural Philosophy, also coauthored by Kelvin and Tait appeared in 1872.
-
The two scientists produced the Treatise on Natural Philosophy (1867), which traced the concept of conservation of energy to the work of Isaac Newton, and had a major influence on future physicists. The Elements of Natural Philosophy, also coauthored by Kelvin and Tait appeared in 1872.
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42
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34250717456
-
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Amphicheiral knots (i.e. their enantiomorphous presentations can be inter-converted by continuous deformation) had been described previously by the German mathematician J. B. Listing, who recognized that trefoil knots exist in two nonidentical mirror images, see Ref. [16].
-
Amphicheiral knots (i.e. their enantiomorphous presentations can be inter-converted by continuous deformation) had been described previously by the German mathematician J. B. Listing, who recognized that trefoil knots exist in two nonidentical mirror images, see Ref. [16].
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44
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0006320651
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2nd ed, Ed, H. Gilman, Wiley, New York, Chap. 4;
-
a) R. L. Shriner, R. Adams, C. S. Marvel in Organic Chemistry, Vol. I, 2nd ed. (Ed.: H. Gilman), Wiley, New York, 1943, Chap. 4;
-
(1943)
Organic Chemistry
, vol.1
-
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Shriner, R.L.1
Adams, R.2
Marvel, C.S.3
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45
-
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34250788146
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The first of Progress in Stereochemistry, edited by W. Klyne and published by Academic Press, appeared in 1954; II (1958) and III (1962) were coedited by W. Klyne and P. B. D. De La Mare.
-
b) The first volume of Progress in Stereochemistry, edited by W. Klyne and published by Academic Press, appeared in 1954; Vol. II (1958) and Vol. III (1962) were coedited by W. Klyne and P. B. D. De La Mare.
-
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46
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34250777862
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Abstracts of Papers
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For a historical perspective:, HIST9
-
For a historical perspective: E. L. Eliel, Abstracts of Papers, 230th National Meeting of the American Chemical Society, Washington, DC, 2005, HIST9.
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(2005)
230th National Meeting of the American Chemical Society, Washington, DC
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Eliel, E.L.1
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47
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0003733338
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Benjamin, Reading, MA
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K. Mislow, Introduction to Stereochemistry, Benjamin, Reading, MA, 1965, pp. 51-52.
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(1965)
Introduction to Stereochemistry
, pp. 51-52
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Mislow, K.1
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48
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85050325851
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a) L. L. Whyte, Nature 1957, 180, 513;
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(1957)
Nature
, vol.180
, pp. 513
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Whyte, L.L.1
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49
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0037949813
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b) L. L. Whyte, Nature 1958, 182, 198;
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(1958)
Nature
, vol.182
, pp. 198
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Whyte, L.L.1
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50
-
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34250736870
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there is also an interesting posthumous paper
-
c) there is also an interesting posthumous paper: Leonardo 1975, 8, 245-248.
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(1975)
Leonardo
, vol.8
, pp. 245-248
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51
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34250730292
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An object is chiral if it cannot be brought into congruence with its mirror image by translation and rotation. Such objects are devoid of symmetry elements which include reflection: mirror planes, inversion centers, or improper rotational axes: V. Prelog, J. Mol. Catal. 1975/76, 1, 159-172 (Nobel lecture).
-
"An object is chiral if it cannot be brought into congruence with its mirror image by translation and rotation. Such objects are devoid of symmetry elements which include reflection: mirror planes, inversion centers, or improper rotational axes": V. Prelog, J. Mol. Catal. 1975/76, 1, 159-172 (Nobel lecture).
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53
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Chiral borromeates have been prepared recently, and one enantiomeric compound was isolated in the solid state: C. D. Pentecost, A. J. Peters, K. S. Chichak, G. W. V. Cave, S. J. Cantrill, J. F. Stoddart, Angew. Chem. 2006, 118, 4205-4210;
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Chiral borromeates have been prepared recently, and one enantiomeric compound was isolated in the solid state: C. D. Pentecost, A. J. Peters, K. S. Chichak, G. W. V. Cave, S. J. Cantrill, J. F. Stoddart, Angew. Chem. 2006, 118, 4205-4210;
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Angew. Chem. Int. Ed. 2006, 45, 4099-4104.
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Chem. Int. Ed
, vol.45
, pp. 4099-4104
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Angew1
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55
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34250784061
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Molecular deformations in some vibrational states will impart chirality to a molecule of methane and, as a result, at any time, individual molecules will almost always be chiral. The cancellation of two exactly mirror-image structures may only be asserted on a statistical basis; see Ref, 16] and especially the discussion on pp. 22-26
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Molecular deformations in some vibrational states will impart chirality to a molecule of methane and, as a result, at any time, individual molecules will almost always be chiral. The cancellation of two exactly mirror-image structures may only be asserted on a statistical basis; see Ref. [16] and especially the discussion on pp. 22-26.
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M. Hampe, Angew. Chem. 2006, 118, 1044-1048;
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Angew. Chem
, vol.118
, pp. 1044-1048
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Hampe, M.1
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Angew. Chem. Int. Ed. 2006, 45, 1028-1031.
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Chem. Int. Ed
, vol.45
, pp. 1028-1031
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Angew1
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Eds, W. J. Lough, I. W. Wainer, Blackwell, Oxford
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b) L. D. Barron, Chirality in Natural and Applied Science (Eds.: W. J. Lough, I. W. Wainer), Blackwell, Oxford, 2002, pp. 53-86;
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(2002)
Chirality in Natural and Applied Science
, pp. 53-86
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Barron, L.D.1
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0003976534
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2nd ed, Cambridge University Press, Cambridge
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c) L. D. Barron, Molecular Light Scattering and Optical Activity, 2nd ed., Cambridge University Press, Cambridge, 2004, pp. 38-52.
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(2004)
Molecular Light Scattering and Optical Activity
, pp. 38-52
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Barron, L.D.1
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Clarendon Press, Oxford
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a) G. Priest, Contradiction, Clarendon Press, Oxford, 1987;
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(1987)
Contradiction
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Priest, G.1
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64
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J. Polanyi, Queen's Quart. 2000, 107, 31-36. I thank Roald Hoffmann for providing this quotation in his lecture Honesty to the Singular Object, which he gave, for example, in Lindau, Germany, in June 2006
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J. Polanyi, Queen's Quart. 2000, 107, 31-36. I thank Roald Hoffmann for providing this quotation in his lecture "Honesty to the Singular Object", which he gave, for example, in Lindau, Germany, in June 2006.
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65
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Stereochemistry of Organic Compounds
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E. L. Eliel, S. H. Wilen, Stereochemistry of Organic Compounds, Wiley, New York, 1994, p. 5.
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(1994)
Wiley, New York
, pp. 5
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Eliel, E.L.1
Wilen, S.H.2
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In a broad sense asymmetric (or asymmetrical) means lacking symmetry, mis-proportionated, or simply unequal. The latter is the common use of asymmetry in biological sciences: not equal in quantity, size, rank, value, etc, see Section 6 of this essay, In physics, the terms asymmetric, antisymmetric, and nonsymmetric as applied to wave functions follow the sense attributed in logic, that is, a relation never holding between a pair of values x and y when it holds between y and x
-
In a broad sense asymmetric (or asymmetrical) means lacking symmetry, mis-proportionated, or simply unequal. The latter is the common use of asymmetry in biological sciences: not equal in quantity, size, rank, value, etc. (see Section 6 of this essay). In physics, the terms asymmetric, antisymmetric, and nonsymmetric as applied to wave functions follow the sense attributed in logic, that is, a relation never holding between a pair of values x and y when it holds between y and x.
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67
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Most examples of stereodifferentiating reactions can likewise be labeled mirror-image symmetry breaking (not chiral symmetry breaking) processes. See: a) D. M. Walba, Top. Stereochem. 2003, 24, 457-518;
-
Most examples of stereodifferentiating reactions can likewise be labeled "mirror-image symmetry breaking" (not chiral symmetry breaking) processes. See: a) D. M. Walba, Top. Stereochem. 2003, 24, 457-518;
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68
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b) M. Ávalos, R. Babiano, P. Cintas, J. L. Jiméez, J. C. Palacios, Tetrahedron: Asymmetry 2004, 15, 3171-3175.
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(2004)
Tetrahedron: Asymmetry
, vol.15
, pp. 3171-3175
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Ávalos, M.1
Babiano, R.2
Cintas, P.3
Jiméez, J.L.4
Palacios, J.C.5
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69
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E. L. Eliel, S. H. Wilen, Stereochemistry of Organic Compounds, Wiley, New York, 1994, Chap. 6, especially pp. 153-155.
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E. L. Eliel, S. H. Wilen, Stereochemistry of Organic Compounds, Wiley, New York, 1994, Chap. 6, especially pp. 153-155.
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70
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Retournons à Pasteur!; for an extended commentary, see: K. Mislow
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Mislow alludes to a previous exhortation by
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Mislow alludes to a previous exhortation by F. M. Jaeger: Retournons à Pasteur!; for an extended commentary, see: K. Mislow, Top. Stereochem. 1999, 22, 27.
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