![\"\"](\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Hyperboloid-Ruled-Surface-Fig2.jpg\")
When our daughter-in-law made wheat shocks as center-pieces for hers and our son\u2019s fall-themed wedding reception, I naturally could not help pointing out the age-old observation that they represented a hyperboloid of one sheet. This was naturally greeted with the usual groans, but the thought stayed with me as I realized I had never proved this mathematically to myself. And so I did.<\/p>\n
See the Hyperboloid as Ruled Surface<\/a>.<\/p>\n (Updates 10\/9\/2020, 9\/19\/2022) Spinning Rod Demo, Spinning Umbrella (Update 10\/9\/2020) Spinning Rod Demo<\/strong><\/p>\n It dawned on me after watching the following the surprising video, that the demonstration was actually showing the generation of a hyperboloid ruled surface and the vertical plastic sheet was just a hyperbolic cross-section of the surface.\u00a0 It looks like his mathematical derivation is similar to mine.<\/p>\n From Futility Closet: Throwing a Curve<\/a>, 9 October 2020:<\/p>\n \u201cIn 2009, mathematician Jeff Chyatte and his colleagues at Maryland\u2019s Montgomery College built a mathematical sculpture: An inclined rod is connected at its center to a horizontal arm, which is connected to a rotating vertical axis. As the axis rotates, the rod passes through a vertical plane.<\/p>\n What shape does the rod cut in the plane? Perhaps surprisingly, it\u2019s a hyperbola. See the video above<\/a> for an explanation. Chyatte\u2019s sculpture was displayed at Washington\u2019s Touchstone Gallery with the title \u201cTheorem.\u201d<\/p>\n (\u201cJust Passing Through,\u201d Math Horizons<\/em> 16:4 [April 2009], 16.)\u201d<\/p>\n (Update 9\/19\/2022) Spinning Umbrella<\/strong><\/p>\n Here is another, more dramatic example<\/a>. When our daughter-in-law made wheat shocks as center-pieces for hers and our son\u2019s fall-themed wedding reception, I naturally could not help pointing out the age-old observation that they represented a hyperboloid of one sheet. This was naturally greeted with the usual groans, but the thought stayed with me as I realized I had never proved […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[40,80],"class_list":["post-587","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-analytic-geometry","tag-differential-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/587","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=587"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/587\/revisions"}],"predecessor-version":[{"id":2884,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/587\/revisions\/2884"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n<\/strong><\/p>\n![\"\"](\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/10\/Hyperboloid-Ruled-Surface-Spinning-Rod.jpg\")
<\/p>\n![\"\"](\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/09\/Hyperboloid-Ruled-Surface-Umbrella.jpg\")
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