3041: Unit Circle - Revision history

AK24Ammit at 02:31, 10 February 2025

2025-02-10T02:31:12Z

172.70.160.252: /* Explanation */ Slip of the finger?

2025-01-27T11:35:30Z

‎Explanation: Slip of the finger?

172.69.194.138: /* Explanation */ Separating the unit-square diversion. Tempted to make it Trivia, as that was never directly part of the comic, but then the expanded semi-Trivia reincluded mention of the comic's circle and the title text's square-of-the-circle, again.

2025-01-27T11:10:27Z

‎Explanation: Separating the unit-square diversion. Tempted to make it Trivia, as that was never directly part of the comic, but then the expanded semi-Trivia reincluded mention of the comic's circle and the title text's square-of-the-circle, again.

172.71.178.55: /* Explanation */

2025-01-27T10:41:24Z

‎Explanation

141.101.98.248: /* Explanation */

2025-01-27T09:19:33Z

‎Explanation

172.71.158.18: /* Explanation */

2025-01-27T03:11:07Z

‎Explanation

141.101.98.55: /* Explanation / Randall is probably more* than aware. Maybe it's an intentional joke, but as "unit square" is never even mentined it probably isn't even that. Best just to explain to those who may have made their own link, unbidden.

2025-01-26T08:06:27Z

‎Explanation: Randall is probably *more* than aware. Maybe it's an intentional joke, but as "unit square" is never even mentined it probably isn't even that. Best just to explain to those who may have made their own link, unbidden.

172.71.158.22: /* Explanation */

2025-01-26T03:58:13Z

‎Explanation

172.71.155.14: /* Explanation */

2025-01-26T03:34:40Z

‎Explanation

Asdf: /* Explanation */ it was a platinum-iridium bar from 1889 to 1960

2025-01-24T21:13:17Z

‎Explanation: it was a platinum-iridium bar from 1889 to 1960

← Older revision		Revision as of 02:31, 10 February 2025
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	==Explanation==		==Explanation==
−	~~{{incomplete\|Constructed by an IMAGINARY NUMBER OF COMPASSES AND CURVED EDGES. Do NOT delete this tag too soon.}}~~
	A {{w\|unit circle}} is a mathematical concept which is a circle whose radius is one (with no units). Or put another way, the unit circle's radius is itself a unit of measure, hence the name. Thus 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.		A {{w\|unit circle}} is a mathematical concept which is a circle whose radius is one (with no units). Or put another way, the unit circle's radius is itself a unit of measure, hence the name. Thus 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.

@@ Line 17: / Line 17: @@
 The title text refers to the old geometry problem of {{w|squaring the circle}}, where one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle.
-Note that this is not the definition of a {{w|unit square}} in mathematics: a real unit square, should one ''also'' exist in the comic's context, would have edges the same length as the unit circle's radius, and not have the same area as the unit circle or the conceptual equal area square that this comic mentions. Having found a physical unit square artefact would have been as useful as this unit circle, for many purposes (it would have defined the length of the unit identically; or better, as it seems that the circle's diameter will be measured, which then needs to be halved to discover its radius, although sufficiently accurate measurement of its perimiter also reveals something about the nature of [[1292: Pi vs. Tau|pi and/or tau]]), whereas the square counterpart of the unit circle would only be useful for 'unit' purposes already specifically involving the root of pi (as length) or pi (as related to area). Though conspicuously equipped to measure the archetypal unit circle's diameter, or a square's edge-length, the expedition is not so clearly prepared to check the circumference (e.g. with a surveyor's {{w|Tape measure|steel tape}}) or directly quantify its (or ''any'' square's) area.
+Note that this is not the definition of a {{w|unit square}} in mathematics: a real unit square, should one ''also'' exist in the comic's context, would have edges the same length as the unit circle's radius, and not have the same area as the unit circle or the conceptual equal area square that this comic mentions. Having found a physical unit square artefact would have been as useful as this unit circle, for many purposes (it would have defined the length of the unit identically; or better, as it seems that the circle's diameter will be measured, which then needs to be halved to discover its radius, although sufficiently accurate measurement of its perimeter also reveals something about the nature of [[1292: Pi vs. Tau|pi and/or tau]]), whereas the square counterpart of the unit circle would only be useful for 'unit' purposes already specifically involving the root of pi (as length) or pi (as related to area). Though conspicuously equipped to measure the archetypal unit circle's diameter, or a square's edge-length, the expedition is not so clearly prepared to check the circumference (e.g. with a surveyor's {{w|Tape measure|steel tape}}) or directly quantify its (or ''any'' square's) area.
 ==Transcript==

@@ Line 15: / Line 15: @@
 This comic shows an expedition of some experts ([[White Hat]], [[Ponytail]], [[Miss Lenhart]] (the mathematician), [[Cueball]] and [[Megan]]) having located a "real unit circle": a physical object which somehow is this mathematical idea. Cueball is holding a set of {{w|Calipers#Vernier caliper|vernier calipers}}, precise instruments used to provide an exact measurement of the unit circle.  By measuring the "real unit circle", mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. The notion of defining a unit in terms of an actual physical object is actually quite reasonable, as the meter was {{w|Metre#Timeline|officially defined as a length of a specific platinum–iridium bar}} from 1889 to 1960 and the kilogram was defined by the mass of a {{w|International_Prototype_of_the_Kilogram|specific physical object}} until 2019. Doing so with the unit circle would be entirely pointless, however, as the entire purpose of the unit circle is to define mathematical relationships, which can be generalized to any unit, rather than being restricted to a given length.
-The title text refers to the old geometry problem of {{w|squaring the circle}}, where one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle. (Note that this is not the definition of a {{w|unit square}} in mathematics: a real unit square, should one ''also'' exist in the comic's context, would have edges the same length as the unit circle's radius, and not have the same area as the unit circle or the conceptual equal area square that this comic mentions.)
+The title text refers to the old geometry problem of {{w|squaring the circle}}, where one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle.
 ==Transcript==

@@ Line 15: / Line 15: @@
 This comic shows an expedition of some experts ([[White Hat]], [[Ponytail]], [[Miss Lenhart]] (the mathematician), [[Cueball]] and [[Megan]]) having located a "real unit circle": a physical object which somehow is this mathematical idea. Cueball is holding a set of {{w|Calipers#Vernier caliper|vernier calipers}}, precise instruments used to provide an exact measurement of the unit circle.  By measuring the "real unit circle", mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. The notion of defining a unit in terms of an actual physical object is actually quite reasonable, as the meter was {{w|Metre#Timeline|officially defined as a length of a specific platinum–iridium bar}} from 1889 to 1960 and the kilogram was defined by the mass of a {{w|International_Prototype_of_the_Kilogram|specific physical object}} until 2019. Doing so with the unit circle would be entirely pointless, however, as the entire purpose of the unit circle is to define mathematical relationships, which can be generalized to any unit, rather than being restricted to a given length.
-The title text refers to the old geometry problem of {{w|squaring the circle}}, where one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle. (Note that this is not the definition of a {{w|unit square}} in real mathematics: a real unit square, should one also exist, would have edges the same length as the unit circle's radius, not have the same area as the unit circle.)
+The title text refers to the old geometry problem of {{w|squaring the circle}}, where one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle. (Note that this is not the definition of a {{w|unit square}} in mathematics: a real unit square, should one ''also'' exist in the comic's context, would have edges the same length as the unit circle's radius, and not have the same area as the unit circle or the conceptual equal area square that this comic mentions.)
 ==Transcript==

@@ Line 15: / Line 15: @@
 This comic shows an expedition of some experts ([[White Hat]], [[Ponytail]], [[Miss Lenhart]] (the mathematician), [[Cueball]] and [[Megan]]) having located a "real unit circle": a physical object which somehow is this mathematical idea. Cueball is holding a set of {{w|Calipers#Vernier caliper|vernier calipers}}, precise instruments used to provide an exact measurement of the unit circle.  By measuring the "real unit circle", mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. The notion of defining a unit in terms of an actual physical object is actually quite reasonable, as the meter was {{w|Metre#Timeline|officially defined as a length of a specific platinum–iridium bar}} from 1889 to 1960 and the kilogram was defined by the mass of a {{w|International_Prototype_of_the_Kilogram|specific physical object}} until 2019. Doing so with the unit circle would be entirely pointless, however, as the entire purpose of the unit circle is to define mathematical relationships, which can be generalized to any unit, rather than being restricted to a given length.
-The title text refers to the old geometry problem of {{w|squaring the circle}}, whereupon one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle. (Note that this is not the definition of a {{w|unit square}} in real mathematics: a real unit square, should one also exist, would have edges the same length as the unit circle's radius, not have the same area as the unit circle.)
+The title text refers to the old geometry problem of {{w|squaring the circle}}, where one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle. (Note that this is not the definition of a {{w|unit square}} in real mathematics: a real unit square, should one also exist, would have edges the same length as the unit circle's radius, not have the same area as the unit circle.)
 ==Transcript==

@@ Line 11: / Line 11: @@
 ==Explanation==
 {{incomplete|Constructed by an IMAGINARY NUMBER OF COMPASSES AND CURVED EDGES. Do NOT delete this tag too soon.}}
-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.
+A {{w|unit circle}} is a mathematical concept which is a circle whose radius is one (with no units). Or put another way, the unit circle's radius is itself a unit of measure, hence the name. Thus 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.
 This comic shows an expedition of some experts ([[White Hat]], [[Ponytail]], [[Miss Lenhart]] (the mathematician), [[Cueball]] and [[Megan]]) having located a "real unit circle": a physical object which somehow is this mathematical idea. Cueball is holding a set of {{w|Calipers#Vernier caliper|vernier calipers}}, precise instruments used to provide an exact measurement of the unit circle.  By measuring the "real unit circle", mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. The notion of defining a unit in terms of an actual physical object is actually quite reasonable, as the meter was {{w|Metre#Timeline|officially defined as a length of a specific platinum–iridium bar}} from 1889 to 1960 and the kilogram was defined by the mass of a {{w|International_Prototype_of_the_Kilogram|specific physical object}} until 2019. Doing so with the unit circle would be entirely pointless, however, as the entire purpose of the unit circle is to define mathematical relationships, which can be generalized to any unit, rather than being restricted to a given length.

@@ Line 13: / Line 13: @@
 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.
-This comic shows an expedition of some experts ([[White Hat]], [[Ponytail]], [[Miss Lenhart]] (the mathematician), [[Cueball]] and [[Megan]]) having located a "real unit circle": a physical object which somehow is this mathematical idea. Cueball is holding a set of {{w|Calipers#Vernier caliper|vernier calipers}}, precise instruments used to provide an exact measurement of the unit circle.  By measuring the "real unit circle", mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. The notion of defining a unit in terms of an actual physical object is actually quite reasonable, as the meter was {{w|Metre#Meridional_definition|officially defined as a fraction of the size of the Earth}} until 1960 and the kilogram was defined by the mass of a {{w|International_Prototype_of_the_Kilogram|specific physical object}} until 2019. Doing so with the unit circle would be entirely pointless, however, as the entire purpose of the unit circle is to define mathematical relationships, which can be generalized to any unit, rather than being restricted to a given length.
+This comic shows an expedition of some experts ([[White Hat]], [[Ponytail]], [[Miss Lenhart]] (the mathematician), [[Cueball]] and [[Megan]]) having located a "real unit circle": a physical object which somehow is this mathematical idea. Cueball is holding a set of {{w|Calipers#Vernier caliper|vernier calipers}}, precise instruments used to provide an exact measurement of the unit circle.  By measuring the "real unit circle", mathematicians could then provide its measurement in whatever ordinary unit they choose, such as centimeters or inches, to textbooks which describe the unit circle. The notion of defining a unit in terms of an actual physical object is actually quite reasonable, as the meter was {{w|Metre#Timeline|officially defined as a length of a specific platinum–iridium bar}} from 1889 to 1960 and the kilogram was defined by the mass of a {{w|International_Prototype_of_the_Kilogram|specific physical object}} until 2019. Doing so with the unit circle would be entirely pointless, however, as the entire purpose of the unit circle is to define mathematical relationships, which can be generalized to any unit, rather than being restricted to a given length.
 The title text refers to the old geometry problem of {{w|squaring the circle}}, whereupon one starts with a circle with a known area - for a unit circle, π - 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 measuring √π units in length, and once it was proven that π is a transcendental number, it was definitively known that squaring a circle is impossible. This causes problems for the comic's team of mathematicians, who wished to create such a square to go along with its unit circle but must instead rely upon finding one, presumably using the same approach they used to find this circle. (Note that a {{w|unit square}}, should one also exist, would have edges the same length as the unit circle's radius, and would not have the same area as either of the others.)

3041: Unit Circle - Revision history

AK24Ammit at 02:31, 10 February 2025

172.70.160.252: /* Explanation */ Slip of the finger?

172.69.194.138: /* Explanation */ Separating the unit-square diversion. Tempted to make it Trivia, as that was never directly part of the comic, but then the expanded semi-Trivia reincluded mention of the comic's circle and the title text's square-of-the-circle, again.

172.71.178.55: /* Explanation */

141.101.98.248: /* Explanation */

172.71.158.18: /* Explanation */

141.101.98.55: /* Explanation */ Randall is probably *more* than aware. Maybe it's an intentional joke, but as "unit square" is never even mentined it probably isn't even that. Best just to explain to those who may have made their own link, unbidden.

172.71.158.22: /* Explanation */

172.71.155.14: /* Explanation */

Asdf: /* Explanation */ it was a platinum-iridium bar from 1889 to 1960

141.101.98.55: /* Explanation / Randall is probably more* than aware. Maybe it's an intentional joke, but as "unit square" is never even mentined it probably isn't even that. Best just to explain to those who may have made their own link, unbidden.