{"id":1467,"date":"2020-05-01T17:09:49","date_gmt":"2020-05-01T22:09:49","guid":{"rendered":"http:\/\/fortmarinus.com\/blog\/?p=1467"},"modified":"2020-05-01T17:23:35","modified_gmt":"2020-05-01T22:23:35","slug":"a-rotation-by-one-turn-is-1","status":"publish","type":"post","link":"http:\/\/fortmarinus.com\/blog\/1467\/","title":{"rendered":"A Rotation by One Turn is 1"},"content":{"rendered":"

In Michael Hartl\u2019si<\/a><\/sup> Tau Manifestoii<\/a><\/sup>iii<\/a><\/sup>, he addresses a criticism of the Tau formulation which points out that the \\tau-form of Euler\u2019s equation only relates 4 fundamental constants (e, i, circle constant, and 1), while the \\pi-form relates 5 (despite needing to be re-arranged to do so). In response, he jokingly tacks on a trivial \u2018+0\u2019 to the \\tau-form to put it on par with the \\pi-form.<\/p>\n\n\n\n\n
\n

Re-arranged Pi form<\/span><\/p>\n

e^{i\\pi}+1 = 0<\/p>\n<\/td>\n

\n

Trivially Modified Tau form<\/span><\/p>\n

e^{i\\tau} = 1 + 0<\/p>\n<\/td>\n<\/tr>\n

\n

Full Pi form<\/span><\/p>\n

e^{i\\pi} = (-1 + 0i)<\/p>\n<\/td>\n

\n

Full Tau form<\/span><\/p>\n

e^{i\\tau} = (1 + 0i)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

However, all joking aside, e^{i\\tau} is a complex number which evaluates to the complex number (1 + 0i). Thus, it is not trivial to represent the zero, in fact, it is thoroughly correct to do so. Conversely, the cleverly re-arranged \\pi-form is even uglier than previously thought, as it breaks up its own complex number evaluation (-1 + 0i) and places half of it on either side of the equation.<\/p>\n

Both forms properly include a zero, but the modified \\pi-form\u00a0breaks the symmetry of the solution, while the \\tau-form maintains its symmetry without modification.<\/p>\n

Now, as a disclaimer on the \\pi-\\tau debate, I believe that the debate is not about choosing a constant or a symbol that makes equations look prettier; this is utterly secondary and wholly counterproductive. The debate is about the proper definition of the fundamental circle constant. Which, is\u00a0\\tau, obviouslyiv<\/a><\/sup>.<\/p>\nReferences:

  1. https:\/\/www.michaelhartl.com\/<\/a> [↩<\/a>]<\/li>
  2. https:\/\/hexnet.org\/files\/documents\/tau-manifesto.pdf<\/a> [↩<\/a>]<\/li>
  3. https:\/\/tauday.com\/tau-manifesto<\/a> [↩<\/a>]<\/li>
  4. https:\/\/www.imdb.com\/title\/tt8228288\/<\/a> [↩<\/a>]<\/li><\/ol>","protected":false},"excerpt":{"rendered":"

    In Michael Hartl\u2019si Tau Manifestoiiiii, he addresses a criticism of the Tau formulation which points out that the -form of Euler\u2019s equation only relates 4 fundamental constants (e, i, circle constant, and 1), while the -form relates 5 (despite needing to be re-arranged to do so). In response, he jokingly tacks on a trivial \u2018+0\u2019 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[9],"tags":[],"_links":{"self":[{"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/posts\/1467"}],"collection":[{"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/comments?post=1467"}],"version-history":[{"count":33,"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/posts\/1467\/revisions"}],"predecessor-version":[{"id":1500,"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/posts\/1467\/revisions\/1500"}],"wp:attachment":[{"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/media?parent=1467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/categories?post=1467"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/fortmarinus.com\/blog\/wp-json\/wp\/v2\/tags?post=1467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}