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Home > Category Index for Science Quotations > Category Index T > Category: Tetrahedron

Tetrahedron Quotes (4 quotes)

[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits.
Presidential Address to the Chemical Society (16 Apr 1936), Journal of the Chemical Society (1936), 533.
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Are the atoms of the dextroacid (tartaric) grouped in the spirals of a right-hand helix or situated at the angles of an irregular tetrahedron, or arranged in such or such particular unsymmetrical fashion? We are unable to reply to these questions. But there can be no reason for doubting that the grouping of the atoms has an unsymmetrical arrangement with a non-superimposable image. It is not less certain that the atoms of the laevo-acid realize precisely an unsymmetrical arrangement of the inverse of the above.
Leçons de Chemie (1860), 25.
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Surely the claim of mathematics to take a place among the liberal arts must now be admitted as fully made good. Whether we look at the advances made in modern geometry, in modern integral calculus, or in modern algebra, in each of these three a free handling of the material employed is now possible, and an almost unlimited scope is left to the regulated play of fancy. It seems to me that the whole of aesthetic (so far as at present revealed) may be regarded as a scheme having four centres, which may be treated as the four apices of a tetrahedron, namely Epic, Music, Plastic, and Mathematic. There will be found a common plane to every three of these, outside of which lies the fourth; and through every two may be drawn a common axis opposite to the axis passing through the other two. So far is certain and demonstrable. I think it also possible that there is a centre of gravity to each set of three, and that the line joining each such centre with the outside apex will intersect in a common point the centre of gravity of the whole body of aesthetic; but what that centre is or must be I have not had time to think out.
In 'Proof of the Hitherto Undemonstrated Fundamental Theorem of Invariants', Collected Mathematical Papers (1909), Vol. 3, 123.
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The smallest particles of matter were said [by Plato] to be right-angled triangles which, after combining in pairs, ... joined together into the regular bodies of solid geometry; cubes, tetrahedrons, octahedrons and icosahedrons. These four bodies were said to be the building blocks of the four elements, earth, fire, air and water ... [The] whole thing seemed to be wild speculation. ... Even so, I was enthralled by the idea that the smallest particles of matter must reduce to some mathematical form ... The most important result of it all, perhaps, was the conviction that, in order to interpret the material world we need to know something about its smallest parts.
[Recalling how as a teenager at school, he found Plato's Timaeus to be a memorable poetic and beautiful view of atoms.]
In Werner Heisenberg and A.J. Pomerans (trans.) The Physicist's Conception of Nature (1958), 58-59. Quoted in Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory (2001), Vol. 2, 12. Cited in Mauro Dardo, Nobel Laureates and Twentieth-Century Physics (2004), 178.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 70 -
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- 50 -
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- 40 -
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- 30 -
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Richard Feynman
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- 20 -
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- 10 -
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