User:Finell/My Sandbox

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Contents 1 Golden ratio and related articles 1.1 Introduction 1.2 History 1.3 Geometry 1.4 Aesthetics 1.5 Math questions 1.6 Pyramids 1.7 Notes 1.8 Research notes 1.9 References 2 Euclid 3 Mark Barr 4 Luca Pacioli 5 Theremin 6 Manchester 7 Toolserver Table of Contents 8 Magnus' toys 8.1 PrepBio 8.2 Reference generator 9 Templates 9.1 Citation 9.1.1 Book 9.1.2 Journal 9.1.3 Web 9.1.4 Encyclopedia 10 Software update history?

[edit] Golden ratio and related articles

[edit] Introduction

Elements.^[1]

Livio..^[2]

[edit] History

An original entry was based on the Rouse History of Mathematics

[edit] Geometry

http://www.1911encyclopedia.org/Dodecahedron: DODECAHEDRON (Gr. SccSerca, twelve, and Spa, a face or base), in geometry, a solid enclosed by twelve plane faces. The "ordinary dodecahedron" is one of the Platonic solids (see Polyhedron). The Greeks discovered that if a line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a cube and dodecahedron inscriptible in the same sphere. The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are Archimedean solids (see Polyhedron). In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones. The "rhombic dodecahedron," one of the geometrical semiregular solids, is an important crystal form. Many other dodecahedra exist as crystal forms, for which see Crystallography.

[edit] Aesthetics

This section would benefit from more references, preferably from books on art and design rather than books on the golden ratio, many of which have a promoting or debunking POV. However, the use of averages to address this subject is, to use a word that I have only recently learned, twaddle.

• Suppose the arithmetic mean aspect ratio of some statistically significant sample of paintings was φ, but the closest individual aspect ratio was 1.9. Suppose all the aspect ratios were significantly higher or lower than φ (perhaps dual bell curves equidistant from φ), but happened to average φ. Would that support the proposition that a golden ratio was aesthetically pleasing? No, the analysis would prove the opposite, and the mean would be a misleading artifact.

• Suppose the median aspect ratio of some sample of paintings was φ, but the next closet ratio was 1.9. Same question, same answer.

• Finding a mode aspect ratio at or very near φ could support the proposition that many artists chose it, but further analysis would be required to draw any meaningful conclusion. What does the rest of the distribution look like? Is it statistically normal? Is the mode near the center of the range of values or nearer an extreme? What other aspect ratios appear with relatively high frequencies, and how are they distributed?

• Suppose (although it clearly is not the case) that Leonardo, Raphael, Rembrandt, Durer, Titian, Caravaggio, Rubens, Van Dyck, Velazques, Vermeer, Ingres, and Corot used golden rectangle canvasses for 1/3 (or alternatively 2/3) of their paintings. Would any statistical mean, no matter how far from φ, be a refutation of the statement, "Many masters chose golden rectangle canvasses for a significant percentage of their paintings"?

I don't think that anyone is saying that all or most canvasses are golden rectangles. Further, there are other compositional reasons for choosing the aspect ratio of a canvas, the natural scale of the subject depicted being a primary one. Many paintings were commissioned to be hung in a particular space, so the dimensions of that space would be relevant to the artist's choice of dimensions. Some canvases are square or round for formal reasons, so they would pull down a mean or median. (By the way, in some of the perceptual studies, the subjects' preferences showed a secondary spike for an aspect ratio of 1 [a square] with the mode at or near φ, and the distribution was not statistically normal.) So a statistical average does not prove or disprove anything in this context.

An adult of average height can easily drown in a swimming pool with an average depth of 4 feet.

Finell (Talk) 06:12, 3 October 2006 (UTC)

[edit] Math questions

I have some math questions for the real mathematicians around here. The questions are not rhetorical: if I knew how to do or show these things myself, I would.

1. Deriving φ from the general case

The mathematical derivations of φ that I have seen, including ours, proceed from a special case involving φ, 1, and related terms. Is it possible to demonstrate that the general case is necessarily true:

2. versus

Why are we using \varphi rather than \phi in our formulae? Isn't \phi cleaner looking and more recognizable to more of the general public? Most everywhere else I look, plain old \phi is used.

3. Self-similarity

Can we better capture the self-similarity and self-replication that pops up wherever φ appears? For example, golden rectangles and golden triangles easily beget smaller or larger ones ad infinitum; on a line segment sectioned in extreme and mean ratio, one can readily construct 2 golden rectangles, one on the entire line segment and one on the smaller section; from a single pentagon or pentagram (all of which have φ proportions), one can easily construct larger and smaller like figures ad infinitum, and also lots of golden triangles as a by-product; any 2 intersecting diagonals of a pentagon golden section one another, while any 2 intersecting diagonals inscribe a golden triangle.

4. Limit of ratios of increasing, successive Fibonacci numbers

Is there a rigorous explanation of why φ is the limit of the ratios of increasing, successive Fibonacci numbers (likewise for similar recursive series), with the ratios alternatingly greater and less than φ? I have a hunch (but no more) that this is related to the self-similarity and self-replication.

Finell (Talk) 09:07, 9 October 2006 (UTC)

[edit] Pyramids

One of my edits deleted "remarkably", so "remarkably came back" when my edit was reverted.

Sorry for confusing the tetrahedron, but I find this whole section, including both sub-sections, confusing. It needs substantial revision, but I don't have the expertise to fix it and don't want to confuse things further by making more mistakes.

Mathematical pyramids

A geometric pyramid is not necessarily 5-sided, as erroneously stated above: it can have any number of sides; see Pyramid (geometry). It is characterized by the polygon that forms its base: e.g., triangular pyramid (tetrahedron), square pyramid, pentagonal pyramid, and so on. Also, it can either be regular or not (e.g., a rectangular pyramid). So before this sub-section starts talking about particular geometric properties of a special case (a square pyramid with unique proportions), it needs to define what it is talking about. Also, since the WP article on this subject is entitled Pyramid (geometry), I still believe that this sub-section should be headed "Geometric pyramids", both for consistency and because it is more specific than "Mathematical".

The description of the construction of this "golden pyramid" is also hard to follow. First, positing a specifically dimensioned "1 by f" golden rectangle is unnecessary; it would be clearer and more general to begin with a (any) golden rectangle, then point out the resulting proportions, as we have been doing throughout the article.

Second, I gather that after diagonally splitting the golden rectangle, the 2 halves are joined at the longer sides of the original rectangle to form an isosceles triangle with a base 2x the length of the rectangle's short side and sides equal to the rectangle's diagonal. If that is correct, it should be spelled out, and preferably illustrated.

"Such a pyramid is very close in shape to the Egyptian pyramids." Aren't all square pyramids the same shape? Does this sentence refer to the proportions?

"The central right triangle ..." To what does this refer?

The derivation of the slopes and angles should be shown (which will obviate the ^{[citation needed]} tags), and their significance to f explained.

Some hint of what and when the Rhind Papyrus is (the link is necessary but not sufficient) needs to be stated before its contents are discussed. This paragraph needs to be made both mathematically clear and accessible to the general reader. Also, this paragraph might fit better in the Egyptian sub-section: isn't the only reason for discussing this to illuminate the controversy over the Egyptian pyramids?

What is the source for these details from the Rhind? Does anyone have access to the Chace translation and commentary that I cited in a prior entry on this Talk page (I don't)? If so, it would be best to be working from a translation of the primary source rather than from the conflicting statements about it in diverse secondary treatments. Also, if we see in the Rhind itself reference to a "sacred ratio" and the context, that might be the most important find yet for the purpose of this article. Personally, I'm skeptical about this claim: from the little that I've read about ancient Egyptian math, I don't think that they would have discovered or comprehended f. On the other hand, if they thought there was something special about 5:3 or 8:5, that would be close enough to warrant mention this article.

Egyptian pyramids

Is the entire f controversy over the pyramids confined to those at Giza, or does it extend to other locales? This should be clarified.

The new first paragraph disorganizes this section even more than it was before. Now, measurements of and calculations concerning the Great Pyramid of Giza appear in the first, third, and fifth paragraphs. Obviously, this needs to be consolidated and harmonized, so it can be meaningful to the reader. Rather than saying that the angles are close to what the angles would be with a f ratio of dimensions, it would be more helpful to calculate the ratios so the reader sees how close they are or aren't to f.

In my opinion, the intervening paragraphs about Rice (which supports both sides of the controversy, unhelpfully) and Livio (which supports one) can be deleted and replaced with footnotes citing both (and possibly others) dropped from the end of this sentence: "Whether the relationship to the golden ratio in these pyramids is by design or by accident remains a topic of controversy."

Introductory sentence

Until I saw the above explanation of the intro sentence, I did not realize that it was confined only to the single specific instance of geometric pyramid described. So my changing its meaning and resulting inaccuracy in rewriting it was unintentional. However, as the sentence stands, I don't think that the intro sentence says anything meaningful. Therefore, I am taking the liberty of deleting it without replacing it. My edit summary will NOT say, "Deleted pointless sentence".

Finell (Talk) 17:34, 18:37, 20 September 2006 (UTC)

[edit] Notes

1. ^ Euclid, Elements, Book 6, Definition 3
2. ^ Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books, p. 6. ISBN 0-7679-0815-5. 

[edit] Research notes

Paulos, John Allen. Beyond Numeracy. New York: Alfred A. Knopf, 98–101. ISBN 0-394-58640-9. 

"Not surprisingly, the Parthenon in Athens can be framed by a golden rectangle, as can many of the smaller areas within it. Much other Greek art madu use of the proportions of the golden rectangle, as have subsequent works from da Vinci to Mondrian and Le Corbusier." p. 99

"The golden rectangle and the static harmony it exemplifies is typical of classic Greek geometry ...." p. 101

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Devlin, Keith (1994). Mathematics: The Science of Patterns. New York: Scientific American Library. ISBN 0-7167-5047-3. 

"Mathematical patterns sometimes reflect visual patterns that the human eye finds particularly aesthetic. One famous example of such mathematical pattern is the golden ratio. p. 108

"According to the Greeks, the golden ratio is the ideal proportion for the sides of a rectangle that the eye finds most pleasing. The rectangular face of the front of the Parthenon has sides whose ratio is in this proportion, and it may be observed elsewhere in Greek architecture." p. 108

Penrose discovered his tiling in 1974. p. 167 Dimensions are ratios of 1/φ, 1, and φ. pp. 167–69. Penrose tiling has local 5-fold symmetry, but the infinate tiling of the plane does not. p. 169.

Quasicrystal alloy Al_5.1Li₃Cu has 5-fold symmetry in the 5 rhombic facesthat meet at a single point, forming a starlike shape. Likewise, quasicrystal material Al₆₅Co₂₀Cu₁₅ has local 5-fold symmetry. p. 169.

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[edit] References

Excellent bibliography here: http://www.research.att.com/~njas/sequences/A001622

Euclid [c. 300 BC] (David E. Joyce, ed. 1997). Elements. Retrieved on 2006-08-30.  Citations in the text are to this online edition.

Hemenway, Priya (2005). Divine Proportion: Phi In Art, Nature, and Science. New York: Sterling. ISBN 1-4027-3522-7. 

Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements (3 vols.), 2nd ed. [Facsimile. Originally published: Cambridge University Press, 1925], New York: Dover Publications. ISBN 0-486-60088-2 (v. 1), ISBN 0-486-60089-0 (v. 2), ISBN 0-486-60090-4 (v. 3). 

Heath, Thomas L. (1981). A History of Greek Mathematics (2 vols.), [Reprint. Originally published: Oxford: Clarendon Press, 1921], New York: Dover Publications. ISBN 0-486-24073-8 (v. 1), ISBN 0-486-24074-6 (v. 2). 

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To order from library

Cook, Theodore Andrea (1979). The Curves of Life. New York: Dover Publications, 420. ISBN 0-48623-701-X. 

Heath, Thomas L. (1981). A History of Greek Mathematics (2 vols.), [Reprint. Originally published: Oxford: Clarendon Press, 1921], New York: Dover Publications. ISBN 0-486-24073-8 (v. 1), ISBN 0-486-24074-6 (v. 2). 

PADOVAN, RICHARD. 1999. Padovan: Proportion, Science, Philosophy, Architecture. London: E & F Spon; USA and Canada: Routledge.

HAMBIDGE, JAY. 1926. The Elements of Dynamic Symmetry. Rpt. 1953, New York: Dover.

"". 

[edit] Euclid

Mathematician and historian W. W. Rouse Ball remarked that despite the criticisms, "the fact that for two thousand years it was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose."^[3]

Euclid [c. 300 BC] (David E. Joyce, ed. 1997). Elements. Retrieved on 2006-08-30.  Citations in the text are to this online edition.

Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements (3 vols.), 2nd ed. [Facsimile. Original publication: Cambridge University Press, 1925], New York: Dover Publications. ISBN 0-486-60088-2 (vol. 1), ISBN 0-486-60089-0 (vol. 2), ISBN 0-486-60090-4 (vol. 3).  Heath's translation of the text plus extensive historical research and detailed commentary throughout the text.

Heath, Thomas L. (1981). A History of Greek Mathematics (2 vols.), [Reprint. Original publication: Oxford: Clarendon Press, 1921], New York: Dover Publications. ISBN 0-486-24073-8 (vol. 1), ISBN 0-486-24074-6 (vol. 2). 

Ball, W.W. Rouse (1960). A Short Account of the History of Mathematics, 4th ed. [Reprint. Original publication: London: Macmillan & Co., 1908], New York: Dover Publications, 50–62. ISBN 0-486-20630-0. 

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Notes

1. ^ Euclid, Elements, Book 6, Definition 3
2. ^ Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books, p. 6. ISBN 0-7679-0815-5. 
3. ^ Ball, W.W. Rouse (1960). A Short Account of the History of Mathematics, 4th ed. [Reprint. Original publication: London: Macmillan & Co., 1908], New York: Dover Publications, 50–62. ISBN 0-486-20630-0. 

[edit] Mark Barr

Cook, Theodore Andrea (1979). The Curves of Life. New York: Dover Publications, 420. ISBN 0-48623-701-X. 

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[edit] Luca Pacioli

[edit] Theremin

Strauss, D. (June 1, 2006). "Clara Rockmore". Retrieved on 2006-10-19.

• Moog, Robert (October 27, 2002). "In Clara's Words: An Interview with Clara Rockmore". Retrieved on 2006-10-19.

• Glinsky, Albert (2000). Theremin: Ether Music and Espionage. Urbana, Illinois: University of Illinois Press. ISBN 0-252-02582-2. 

• Olsen, William (Director). (1995). Mastering the Theremin [Videotape (VHS)]. Moog Music and Little Big Films.
• Martin, Steven M. (Director). (1995). Theremin: An Electronic Odyssey [Film and DVD]. MGM.
• Moog, Robert (Producer). (1998). Clara Rockmore: The Greatest Theremin Virtuosa [Videotape (VHS)]. Moog Music and Little Big Films.

[edit] Manchester

Manchester, William (1992). A world lit only by fire : the medieval mind and the Renaissance : portrait of an age. Boston: Little, Brown. ISBN 0316545317. 

Magellan: pp. 223-292

Subjects: Renaissance.

Learning and scholarship--History--Medieval, 500-1500.

[edit] Toolserver Table of Contents

Toolserver Table of Contents

[edit] Magnus' toys

Magnus' toys can be discussed at Magnus' talk page

[edit] PrepBio

PrepBio can be used to prepare a biographical entry on en.wikipedia (templates, categories, formatting etc.). Get the source of this script. For more information, see PrepBio on meta.

[edit] Reference generator

Reference generator generates a reference (footnote) using the templates for citing news on the Web, a paper in a journal, or a Web site from a form. The following is an example journal cite:

Example.^[4]

References

[edit] Templates

[edit] Citation

See Wikipedia:Citation templates

[edit] Book

{{cite book | last = | first = | authorlink = | coauthors = | editor = | others = | title = | origdate = | origyear = | origmonth = | url = | format = | accessdate = | accessyear = | accessmonth = | edition = | date = | year = | month = | publisher = | location = | language = | id = | doi = | pages = | chapter = | chapterurl = | quote = }}

[edit] Journal

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[edit] Web

Error on call to Template:cite web: Parameters url and title must be specified.

[edit] Encyclopedia

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[edit] Software update history?

Is there a place on WP that announces updates to the software on which WP runs? Was there a recent change that adds more buttons above the edit box? Finell (Talk) 18:03, 26 September 2006 (UTC)

Per the second question: there was a recent change at MediaWiki:Monobook.js, which added buttons. --Ligulem 18:20, 26 September 2006 (UTC)

Thanks. I would still appreciate, from someone, knowing where one can go to see recent changes to the software. For example, a software rev in late 2005 clobbered my signature, which used the documented Signature box trick on my User profile page. It took me quite awhile to find out what happened. Thanks again. Finell (Talk) 19:27, 26 September 2006 (UTC)

You can see the recent changes to MediaWiki by looking at the release notes in subversion. The developers keep a pretty good track of what they've updated. Hope this is what you're looking for. Shardsofmetal [ Talk • Contribs ] 22:03, 26 September 2006 (UTC)

Special:Version, which also lists the revision number from SVN. SVN root is http://svn.wikimedia.org/svnroot/mediawiki/trunk/phase3 (browsing [1]). --Ligulem 22:13, 26 September 2006 (UTC)

That is what I was looking for. Thanks. Finell (Talk) 16:24, 27 September 2006 (UTC)