2748: Radians Are Cursed - Revision history

82.132.245.209: /* Explanation */

2025-11-25T19:17:45Z

‎Explanation

109.147.4.117: /* Explanation */

2025-11-25T12:11:05Z

‎Explanation

FaviFake: /* Explanation */

2025-03-02T13:01:38Z

‎Explanation

FaviFake: Updated category name

2023-05-23T15:13:38Z

Updated category name

Xurkitree10: /* Transcript */

2023-04-25T05:20:03Z

‎Transcript

Xurkitree10: /* Explanation */

2023-03-29T17:58:10Z

‎Explanation

172.71.242.191: we don't have to stick to utf-8

2023-03-20T12:40:21Z

we don't have to stick to utf-8

Asdf: /* Transcript */ category

2023-03-17T04:29:19Z

‎Transcript: category

162.158.102.140: 2713 is to be paired with 2717 not 0058

2023-03-16T11:20:23Z

2713 is to be paired with 2717 not 0058

Leduyquang753: /* Transcript */ Added explicit descriptions of the colored texts.

2023-03-13T07:26:17Z

‎Transcript: Added explicit descriptions of the colored texts.

@@ Line 18: / Line 18: @@
 The fourth and final fact states that because it was determined in earlier facts that a radian is equal to the radius of the unit circle as well as 57.3°, then the radius of the unit circle must be equal to 57.3°. This is usually not how degrees are supposed to work, because they are a measure of angle, not length. Hence, this fact is labeled "cursed" by Randall, leading to the comic's title. (However, since the radian is also an angular measure, the second fact could be viewed as equally cursed.)
-The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog:  http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument, but—in a reference to comic [[1827: Survivorship Bias]]—Randall claims you can't argue with results. As the previous comic says, however, if you stick with it, you can argue with anything.
+The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog:  http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument, but — in a reference to comic [[1827: Survivorship Bias]] — Randall claims you can't argue with results. As the previous comic says, however, if you stick with it, you can argue with anything.
 Randall has alluded to Plait's angular area tip previously [https://what-if.xkcd.com/109/ in his own blog What If?], in a post that examined the chances of hitting various celestial objects with a laser blast aimed at random from Earth's surface.

@@ Line 18: / Line 18: @@
 The fourth and final fact states that because it was determined in earlier facts that a radian is equal to the radius of the unit circle as well as 57.3°, then the radius of the unit circle must be equal to 57.3°. This is usually not how degrees are supposed to work, because they are a measure of angle, not length. Hence, this fact is labeled "cursed" by Randall, leading to the comic's title. (However, since the radian is also an angular measure, the second fact could be viewed as equally cursed.)
-The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog:  http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument.
+The title text is referring to {{w|Phil Plait}}'s claim about the size of the sky, which was published on his blog:  http://www.badastronomy.com/bitesize/bigsky.html. Dimensional analysis utilizes the rationale that both sides of an equation need to have the same unit. Radius typically refers to a length, which has SI units of meters. The surface area has SI units of square meters. The units of Phil Plait's "angular area" is as the title text mentions, {{w|square degrees}}. Thus the comic's {{w|dimensional analysis|dimensional analysts}} (not a profession, but instead the adherents of the mathematical technique) are said to be angered by this argument, but—in a reference to comic [[1827: Survivorship Bias]]—Randall claims you can't argue with results. As the previous comic says, however, if you stick with it, you can argue with anything.
 Randall has alluded to Plait's angular area tip previously [https://what-if.xkcd.com/109/ in his own blog What If?], in a post that examined the chances of hitting various celestial objects with a laser blast aimed at random from Earth's surface.

@@ Line 10: / Line 10: @@
 ==Explanation==
-This comic presents a series of Math Facts, appearing to be in a sequential order.
+This comic presents a series of Math Facts, appearing to be in a sequential order. The first fact states that the {{w|unit circle}} has a radius of one, which is precisely its definition. Randall labels this fact as being "normal," complete with a large green checkmark to verify this. The unit circle is typically used in abstract contexts rather than applications with a specific length unit (such as meters). For example, the trigonometric functions cosine and sine can be define the x and y coordinates of a point on the unit circle without any additional factor.
 The second fact states that one {{w|radian}} is equal to the length of a circle's radius. This isn't actually the way that the unit is defined. Instead, radians are usually defined as the angle encompassing an arc of a circle equal in length to its radius. This comic's logic is thus somewhat erroneous. However, this fact is still labeled as also being "normal." Also, while Randall again uses the unit circle in the fact's associated diagram, any circle could theoretically be used to show the conventional definition. Under the standard definition of an {{w|angle}} as the ratio of the length of a circular arc to its radius, the radian is a dimensionless unit equal to 1.
-A correct version of the second fact would be that a radian has the same value (1) as the radius of the unit circle.
+A correct version of the second fact would be that a radian has the same value (1) as the radius of the unit circle. The third fact states that one radian is equal to 57.3°. This is indeed true (albeit rounded). The circumference of a circle is 2π radius-lengths, so the angle of a complete circle is both 2π rad and 360°. Thus 1 rad = 180/π°. This fact is again labeled "normal."
 The fourth and final fact states that because it was determined in earlier facts that a radian is equal to the radius of the unit circle as well as 57.3°, then the radius of the unit circle must be equal to 57.3°. This is usually not how degrees are supposed to work, because they are a measure of angle, not length. Hence, this fact is labeled "cursed" by Randall, leading to the comic's title. (However, since the radian is also an angular measure, the second fact could be viewed as equally cursed.)

@@ Line 46: / Line 46: @@
 [[Category:Comics with color]]
 [[Category:Comics featuring real people]] <!-- Phil Plait -->
-[[Category:Comics featuring cursed items]]
+[[Category:Comics with cursed items]]

@@ Line 27: / Line 27: @@
 ==Transcript==
 :[Title:]
 :<u>Math facts</u>

← Older revision		Revision as of 17:58, 29 March 2023
Line 10:		Line 10:

	==Explanation==		==Explanation==
−	~~{{incomplete\|Created by a DIAMETER OF 114.6 DEGREES - Please change this comment when editing this page. Do NOT delete this tag too soon.}}~~
−
	This comic presents a series of Math Facts, appearing to be in a sequential order.		This comic presents a series of Math Facts, appearing to be in a sequential order.

@@ Line 48: / Line 48: @@
 [[Category:Geometry]]
 [[Category:Facts]]
 [[Category:Comics featuring real people]] <!-- Phil Plait -->
 [[Category:Comics featuring cursed items]]

@@ Line 35: / Line 35: @@
 :[A diagram of a circle is shown with radius labeled as “1”]
-:The unit circle has a radius of one [In green] <span style="color:green>✓ Normal</span>
+:The unit circle has a radius of one [In green] <span style="color:#008000;">✓ Normal</span>
 :[The diagram now has another (unlabeled and lighter) radius at a 57.3 degree angle. The arc between the points where the radii intersect the circle is labeled as “1”]
-:One radian equals the length of a circle’s radius [In green] <span style="color:green>✓ Normal</span>
+:One radian equals the length of a circle’s radius [In green] <span style="color:#008000;">✓ Normal</span>
 :[The diagram now is completely unlabeled except for the arc, which is labeled as “57.3°”]
-:One radian is 57.3 degrees [In green] <span style="color:green>✓ Normal</span>
+:One radian is 57.3 degrees [In green] <span style="color:#008000;">✓ Normal</span>
 :[The first diagram is shown; however, the radius is labeled as “57.3°”]
-:The unit circle has a radius of 57.3 degrees [In red] <span style="color:darkred>X Cursed</span>
+:The unit circle has a radius of 57.3 degrees [In red] <span style="color:#800000;">✗ Cursed</span>
 {{comic discussion}}