Editing Superellipse (section)

== History ==
The general Cartesian notation of the form comes from the French mathematician [[Gabriel Lamé]] (1795&ndash;1870), who generalized the equation for the ellipse.

[[File:MeliorSuperEllipse.svg|thumb|176px|The outer outlines of the letters 'o' and 'O' in Zapf's Melior typeface are described by superellipses with ''n'' = {{nowrap|log(1/2) / log (7/9)}} ≈ 2.758]]

[[Hermann Zapf]]'s [[typeface]] [[Melior (typeface)|Melior]], published in 1952, uses superellipses for letters such as ''o''. <!--Many web sites say Zapf actually drew the shapes of Melior by hand without knowing the mathematical concept of the superellipse, and only later did Piet Hein point out to Zapf that his curves were extremely similar to the mathematical construct, but these web sites do not cite any primary source of this account.-->  Thirty years later [[Donald Knuth]] would build the ability to choose between true ellipses and superellipses (both approximated by [[cubic spline]]s) into his [[Computer Modern]] type family.

[[File:Sergels torg.jpg|thumb|The central fountain of Sergels Torg is outlined by a superellipse with ''n'' = 2.5 and ''a''/''b'' = 6/5.]]

The superellipse was named by the [[Denmark|Danish]] poet and scientist [[Piet Hein (Denmark)|Piet Hein]] (1905–1996) though he did not discover it as it is sometimes claimed. In 1959, city planners in [[Stockholm]], [[Sweden]] announced a design challenge for a [[roundabout]] in their city square [[Sergels Torg]]. Piet Hein's winning proposal was based on a superellipse with ''n'' = 2.5 and ''a''/''b'' = 6/5.<ref name=gardner>{{Citation | last=Gardner | first=Martin | author-link=Martin Gardner | chapter=Piet Hein’s Superellipse | year=1977 | title=Mathematical Carnival. A New Round-Up of Tantalizers and Puzzles from Scientific American | location=New York | publisher=[[Vintage Press]] | pages=[https://archive.org/details/mathematicalcarn00gard/page/240 240–254] | isbn=978-0-394-72349-5 | chapter-url-access=registration | chapter-url=https://archive.org/details/mathematicalcarn00gard/page/240 }}</ref> As he explained it:
{{blockquote|''Man is the animal that draws lines which he himself then stumbles over. In the whole pattern of civilization there have been two tendencies, one toward straight lines and rectangular patterns and one toward circular lines. There are reasons, mechanical and psychological, for both tendencies. Things made with straight lines fit well together and save space. And we can move easily &mdash; physically or mentally &mdash; around things made with round lines. But we are in a straitjacket, having to accept one or the other, when often some intermediate form would be better. To draw something freehand &mdash; such as the patchwork traffic circle they tried in Stockholm &mdash; will not do. It isn't fixed, isn't definite like a circle or square. You don't know what it is. It isn't esthetically satisfying. The super-ellipse solved the problem. It is neither round nor rectangular, but in between. Yet it is fixed, it is definite &mdash; it has a unity.''}}

[[File:The_Local_logo.png|thumb|The Local's logo, based on Stockholm's Sergels Torg, with the L representing the glass obelisk]]

Sergels Torg was completed in 1967.  Meanwhile, Piet Hein went on to use the superellipse in other artifacts, such as beds, dishes, tables, etc.<ref name=bbc>[https://www.bbc.co.uk/dna/h2g2/A1053884 ''The Superellipse''], in ''The Guide to Life, The Universe and Everything'' by [[British Broadcasting Corporation|BBC]] (27 June 2003)</ref>  By rotating a superellipse around the longest axis, he created the [[superegg]], a solid egg-like shape that could stand upright on a flat surface, and was marketed as a [[novelty item|novelty toy]].

In 1968, when negotiators in [[Paris]] for the [[Vietnam War]] could not agree on the shape of the negotiating table, Balinski, [[Kieron Underwood]] and Holt suggested a superelliptical table in a letter to the [[New York Times]].<ref name=gardner/>  The superellipse was used for the shape of the 1968 [[Estadio Azteca|Azteca Olympic Stadium]], in [[Mexico City]].

The second floor of the original [[World Trade Center (1973–2001)|World Trade Center]] in New York City consisted of a large, superellipse-shaped overhanging balcony.

[[Waldo R. Tobler]] developed a [[map projection]], the [[Tobler hyperelliptical projection]], published in 1973,<ref>{{Citation | last=Tobler | first=Waldo | title=The hyperelliptical and other new pseudocylindrical equal area map projections | journal=Journal of Geophysical Research | volume=78 | issue=11 | pages=1753–1759 | year=1973 | doi=10.1029/JB078i011p01753 | postscript=. | bibcode=1973JGR....78.1753T | citeseerx = 10.1.1.495.6424 }}</ref> in which the [[Meridian (geography)|meridians]] are arcs of superellipses.

The logo for news company [[The Local]] consists of a tilted superellipse matching the proportions of Sergels Torg. Three connected superellipses are used in the logo of the [[Pittsburgh Steelers]].

In computing, mobile operating system [[iOS]] uses a superellipse curve for app icons, replacing the [[rounded corner]]s style used up to version 6.<ref>{{cite web |last1=Mynttinen |first1=Ivo |title=The iOS Design Guidelines |url=http://iosdesign.ivomynttinen.com/}}</ref>