218:"The law of least action … demands that the somewhat rigid crustal portion of the earth keep in contact with the lessening interior with the least possible readjustment of its surface. … a shrinking sphere tends by the law of least action to collapse into a tetrahedron, or a tetra-hedroid, a sphere marked by four equal and equidistant triangular projections; and the earth with its three about equal and equidistant double continental masses triangular southward with three intervening depressed oceans triangular northward, its northern ocean and southern continent, with land everywhere antipodal to water, realizes the tetrahedroid status remarkably.“
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its area. As we traverse the set in order of increasing number of faces, we find that k increases for each member; it is 0.0227 for a tetrahedron and 0.0940 for a sphere. Thus the tetrahedron is the regular solid with the largest surface area for a given volume, and makes a reasonable endpoint for a
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theory is now generally accepted to explain the dynamic nature of the Earth's surface; the tetrahedral shape plays no special role in modern theories. Explanations of details such as water to land ratios, the precise shape of continents and their sizes continue to be developed.
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theory that land masses moved great distances over the Earth's history. Wegener was also at first met with hostile reactions. By the mid-1920s Holmes had developed theories on what could cause the drift. The
67:, is now of historical interest only, being finally refuted by that same Holmes (see reference 7). It attempted to explain apparent anomalies in the distribution of land and water on the Earth's surface:
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512:(September 22, 1928). "Theory of Continental Drift: a Symposium on the Origin and Movement of Land Masses, both Inter-Continental and Intra-Continental, as proposed by Alfred Wegener".
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This is suggesting that a cooling spherical Earth might have shrunk to form a tetrahedron, with its vertices and edges forming the continents, and four oceans (
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43:. Although it was a historically interesting theory in the late 19th and early 20th century, it was superseded by the concepts of
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126:(20 sides), the sphere can be considered to have an infinite number of sides. All six regular solids share many symmetries.
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Vestiges of the molten globe, as exhibited in the figure of the earth, volcanic action and physiography
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Now, for each regular solid, we may relate its surface area and volume by the equation:
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413:. Vol. 56, no. 6. American Philosophical Society. pp. 445–472.
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110:(four equilateral triangles); progressing through the hexahedron or
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The north pole is surrounded by water, the south pole by land.
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To understand its appeal, consider the "regular solids": the
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Exactly opposite the Earth from land is almost always water.
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in 1875. It was still popular in 1917 when summarized as:
407:"Tetrahedral Deformations and Intercontinental Torsions"
355:. Anmol Publications PVT. Limited. pp. 109–113.
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106:. The solid with the lowest number of sides is the
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63:This idea, described as ‘"ingenious" by geologist
71:More than 75% of the Earth's land area is in the
466:(June 6, 1925). "The Origin of the Continents".
94:occupies about one third of the Earth's surface.
561:University of California Museum of Paleontology
556:"Plate Tectonics: The Rocky History of an Idea"
440:University of California Museum of Paleontology
167:{\displaystyle V=k\times A\times {\sqrt {A}}}
27:attempting to explain the arrangement of the
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411:Proceedings, American Philosophical Society
202:Illustration of Tetrahedral hypothesis by
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381:. APH Publishing. 2004. pp. 84–85.
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16:Obsolete theory of continent locations
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353:Encyclopedia of nature of geography
181:is a characteristic of each solid,
51:. The theory was first proposed by
78:Continents are roughly triangular.
39:by referring to the geometry of a
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210:The theory was first proposed by
565:. University of California. 2006
444:. University of California. 2006
378:Principles of Physical Geography
245:(1880–1930) had proposed in his
318:Principles of physical geology
81:Oceans are roughly triangular.
1:
435:"Alfred Wegener (1880-1930)"
190:shrinking spherical Earth.
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25:obsolete scientific theory
649:Obsolete geology theories
403:Benjamin Kendall Emerson
102:and the 5-member set of
284:. London: E. Stanford.
347:A. Z. Bukhari (2005).
276:William Lowthian Green
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212:William Lowthian Green
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204:William Lowthian Green
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53:William Lowthian Green
21:tetrahedral hypothesis
594:The Tetrahedral Earth
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597:. Forgotten Books.
526:1928Natur.122..431H
480:1925Natur.115..873H
349:"Continental Drift"
290:1875vmge.book.....G
73:northern hemisphere
322:. Nelson. p.
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604:978-1-60506-415-4
520:(3073): 431–433.
474:(2901): 873–874.
420:978-1-4223-7253-1
388:978-81-7648-731-3
362:978-81-261-2443-5
333:978-0-17-448020-4
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228:Atlantic Ocean
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608:. Retrieved
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567:. Retrieved
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628:|work=
589:Edna Kenton
124:icosahedron
108:tetrahedron
47:and modern
41:tetrahedron
659:Tetrahedra
643:Categories
259:References
116:octahedron
33:continents
630:ignored (
620:cite book
610:August 4,
569:August 4,
448:August 4,
314:(1965) .
206:from 1875
155:×
149:×
55:in 1875.
563:web site
442:web site
405:(1917).
278:(1875).
122:and the
542:4138562
522:Bibcode
496:4066330
476:Bibcode
298:3571917
286:Bibcode
194:History
601:
540:
514:Nature
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468:Nature
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118:, the
114:, the
100:sphere
59:Theory
37:oceans
23:is an
538:S2CID
492:S2CID
177:where
29:Earth
632:help
612:2010
599:ISBN
571:2010
450:2010
415:ISBN
383:ISBN
357:ISBN
328:ISBN
294:OCLC
234:and
112:cube
90:The
35:and
19:The
530:doi
518:122
484:doi
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31:'s
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187:A
183:V
179:k
160:A
152:A
146:k
143:=
140:V
75:.
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