https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=DisKanis 2026-04-28T14:40:18Z User contributions MediaWiki 1.30.0 https://www.explainxkcd.com/wiki/index.php?title=3041:_Unit_Circle&diff=363312 2025-01-23T07:55:56Z

<p>DisKanis: /* Explanation */ irrational number (such as √2) are not a problem with compass&amp;straightedge. Transcendental numbers are.</p> <hr /> <div>{{comic<br /> | number = 3041<br /> | date = January 22, 2025<br /> | title = Unit Circle<br /> | image = unit_circle_2x.png<br /> | imagesize = 325x259px<br /> | noexpand = true<br /> | titletext = They're continuing to search for a square with the same area as the circle, as efforts to construct one have run into difficulties.<br /> }}<br /> <br /> ==Explanation==<br /> {{incomplete|Constructed by a COMPASS AND CURVEDEDGE. Do NOT delete this tag too soon.}}<br /> A {{w|unit circle}} is a mathematical concept which is a circle whose radius is one (with no units). When doing math problems with a unit circle, all other distances are therefore in terms of the circle's radius: a line with length 3 is three times the radius, a line of length 1/2 is half the radius, and so on. This is very useful in many geometry problems.<br /> <br /> This comic shows an expedition of some experts having located a &quot;real unit circle&quot;: a physical object which somehow is this mathematical idea. By measuring the &quot;real unit circle&quot;, mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. Doing so would be entirely pointless, as the entire purpose of the unit circle is that its radius is one unit, and it is not meant to correspond to any physical object.<br /> <br /> The title text refers to the old geometry problem of {{w|squaring the circle}}, whereupon one starts with a circle with a known area and tries to create a square with the same area, traditionally using nothing more than an idealized compass and straightedge. Such a square would have edges all measuring √π units length, and once it was proven that π is a transcendental number it was definitely proven that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who would have wished to create such a square to go along with its unit circle, but must instead rely upon finding one, under the same assumptions as they managed to find this circle. (It should be noted that a {{w|unit square}}, should one of those also exist, would have edges the same length as the unit circle's radius, and would not have the same area.)<br /> <br /> ==Transcript==<br /> {{incomplete transcript|Do NOT delete this tag too soon.}}<br /> <br /> :[In a single panel, White Hat, Ponytail, Miss Lenhart, Cueball, and Megan are standing in a field. Ponytail is holding a notebook and taking notes, Miss Lenhart is kneeling and holding her hands on a circular object with the radius marked on it, Cueball is holding a large caliper-like measuring instrument, and Megan is taking a photo with her phone sideways.]<br /> <br /> :[Caption below the panel:]<br /> :Math breakthrough: Dimensional analysts have discovered a real unit circle. Once they measure it, units can finally be added to all our geometry textbooks.<br /> <br /> {{comic discussion}}<br /> <br /> [[Category:Comics featuring Cueball]]<br /> [[Category:Comics featuring Megan]]<br /> [[Category:Comics featuring Ponytail]]<br /> [[Category:Comics featuring Miss Lenhart]]<br /> [[Category:Comics featuring White Hat]]<br /> [[Category:Math]]<br /> [[Category:Geometry]]</div>

DisKanis