2042: Rolle's Theorem - Revision history

Caralice: fix formatting

2025-03-22T08:13:54Z

fix formatting

172.71.30.171: /* Removed various errors, mistakes and other issues in pursuit of greater brevity */

2025-01-09T16:28:52Z

‎Removed various errors, mistakes and other issues in pursuit of greater brevity

Solomon: add link to https://www.reddit.com/r/math/comments/pgj3og/are_there_any_theoremsobjects_involving_company/

2023-05-31T00:58:05Z

add link to https://www.reddit.com/r/math/comments/pgj3og/are_there_any_theoremsobjects_involving_company/

Jacky720: rv

2022-05-04T21:08:53Z

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Ex Kay Cee Dee at 20:21, 4 May 2022

2022-05-04T20:21:16Z

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Davidy22: Reverted edits by X. K. C. D. (talk) to last revision by Lettherebedarklight

2022-05-04T02:10:11Z

Reverted edits by X. K. C. D. (talk) to last revision by Lettherebedarklight

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X. K. C. D. at 23:38, 3 May 2022

2022-05-03T23:38:10Z

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Lettherebedarklight: /* Explanation */ the bbc link refuses to work, so wikipedia it is

2021-10-11T13:58:49Z

‎Explanation: the bbc link refuses to work, so wikipedia it is

162.158.106.126: /* grammar edits */

2018-09-18T04:15:43Z

‎grammar edits

172.68.51.130: added "tangent"

2018-09-15T09:50:20Z

added "tangent"

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 ==Explanation==
-In mathematics, a {{w|differentiable function}} is a function that is "smooth" everywhere, without any sudden breaks or pointy "kinks" or similar. The derivative of such a function is a new function that represents the "slope" or "rate of change" of the original. The function in this comic curves up from point (a) until a point above (c), smoothly turns around, and then curves down from (c) to (b). As a result, the derivative of this function is positive from (a) to (c), and then is negative from (c) to (b). At (c) itself, the function is "flat": the more one zooms in, the more horizontal it looks. The function is moving neither up nor down, so the derivative is neither positive nor negative, but zero. This is what ''f'(c) = 0'' means, as ''f''' is a common notation for the derivative of the function ''f'' in {{w|differential calculus}}.
+In mathematics, a {{w|differentiable function}} is a function that is "smooth" everywhere, without any sudden breaks or pointy "kinks" or similar. The derivative of such a function is a new function that represents the "slope" or "rate of change" of the original. The function in this comic curves up from point (a) until a point above (c), smoothly turns around, and then curves down from (c) to (b). As a result, the derivative of this function is positive from (a) to (c), and then is negative from (c) to (b). At (c) itself, the function is "flat": the more one zooms in, the more horizontal it looks. The function is moving neither up nor down, so the derivative is neither positive nor negative, but zero. This is what ''f'(c) = 0'' means, as ''f<nowiki>'</nowiki>'' is a common notation for the derivative of the function ''f'' in {{w|differential calculus}}.
 A {{w|theorem}} in mathematics is a statement that has been ''proven'' from former accepted statements, like other theorems or {{w|axiom}}s. This comic references {{w|Rolle's theorem}}. The theorem essentially states that, if a smoothly changing function has the same output at two different inputs, then it must have one or more turning points in between, as the derivative is zero at each one. As a special case, should the function remain flat between the two inputs, then its derivative is actually zero for every point between the inputs. To [[Randall]], this is obvious. However, the proof of this theorem is not as obvious as the result.

@@ Line 14: / Line 14: @@
 The seeming triviality of the theorem, coupled with the honour bestowed on the theorem namer, leads Randall to make a comparison to attendees of art museums who look at abstract art pieces and perceive only an apparent technical simplicity in the work. Such a visitor might exclaim "My child could paint that!". However, such works of art typically are seen as having value from attributes other than the painterly difficulty in achieving the piece. For example, an artist's work in this style may be lauded for its visionary qualities, or the emotions expressed through the choice of colours or textures. One such artist is {{w|Jackson Pollock}}. The 'clueless' visitor does not see these aspects and believes their child could imitate the piece. Randall suggests he experiences a similar feeling looking at Rolle's Theorem and noting only the obvious correctness without acknowledging the complicated nature of the proof, or other hidden aspects of the theorem.
-In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. (See [https://www.reddit.com/r/math/comments/pgj3og/are_there_any_theoremsobjects_involving_company/ "Are there any theorems/objects involving company names."] on r/math.) Furthermore, "Rolle's" sounds like "Rolls", a common abbreviation for the {{w|Rolls-Royce Motor Cars|Rolls Royce}} brand implying possible sponsorship by the British car manufacturer. The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.
+In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, even the legendary {{w|Proclus}} admits that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. (See [https://www.reddit.com/r/math/comments/pgj3og/are_there_any_theoremsobjects_involving_company/ "Are there any theorems/objects involving company names."] on r/math.) The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.
-Randall implies that there are many seemingly easy theorems like this. For instance the Dirichlet's box principle, also known as the {{w|Pigeonhole principle}}, that states that if you have more objects than containers, you're going to have to put at least two objects in one container.
+Randall implies that there are many seemingly easy theorems like this. For instance the Dirichlet's box principle, also known as the {{w|Pigeonhole principle}}, which states that if you have more objects than containers, you're going to have to put at least two objects in one container.
 ==Transcript==

@@ Line 14: / Line 14: @@
 The seeming triviality of the theorem, coupled with the honour bestowed on the theorem namer, leads Randall to make a comparison to attendees of art museums who look at abstract art pieces and perceive only an apparent technical simplicity in the work. Such a visitor might exclaim "My child could paint that!". However, such works of art typically are seen as having value from attributes other than the painterly difficulty in achieving the piece. For example, an artist's work in this style may be lauded for its visionary qualities, or the emotions expressed through the choice of colours or textures. One such artist is {{w|Jackson Pollock}}. The 'clueless' visitor does not see these aspects and believes their child could imitate the piece. Randall suggests he experiences a similar feeling looking at Rolle's Theorem and noting only the obvious correctness without acknowledging the complicated nature of the proof, or other hidden aspects of the theorem.
-In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. Furthermore, "Rolle's" sounds like "Rolls", a common abbreviation for the {{w|Rolls-Royce Motor Cars|Rolls Royce}} brand implying possible sponsorship by the British car manufacturer. The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.
+In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. (See [https://www.reddit.com/r/math/comments/pgj3og/are_there_any_theoremsobjects_involving_company/ "Are there any theorems/objects involving company names."] on r/math.) Furthermore, "Rolle's" sounds like "Rolls", a common abbreviation for the {{w|Rolls-Royce Motor Cars|Rolls Royce}} brand implying possible sponsorship by the British car manufacturer. The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.
 Randall implies that there are many seemingly easy theorems like this. For instance the Dirichlet's box principle, also known as the {{w|Pigeonhole principle}}, that states that if you have more objects than containers, you're going to have to put at least two objects in one container.

@@ Line 12: / Line 12: @@
 A {{w|theorem}} in mathematics is a statement that has been ''proven'' from former accepted statements, like other theorems or {{w|axiom}}s. This comic references {{w|Rolle's theorem}}. The theorem essentially states that, if a smoothly changing function has the same output at two different inputs, then it must have one or more turning points in between, as the derivative is zero at each one. As a special case, should the function remain flat between the two inputs, then its derivative is actually zero for every point between the inputs. To [[Randall]], this is obvious. However, the proof of this theorem is not as obvious as the result.
-The seeming triviality of the theorem, coupled with the honour bestowed on the theorem namer, leads Randall to make a comparison to attendees of art museums who look at abstract art pieces and perceive only an apparent technical simplicity in the work. Such a visitor might exclaim "My child could paint that!". However, such works of art typically are seen as having value from attributes other than the painterly difficulty in achieving the piece. For example, an artist's work in this style may be lauded for its visionary qualities, or the emotions expressed through the choice of colours or textures. One such artist is [http://www.bbc.co.uk/guides/zqhgr82 Jackson Pollock]. The 'clueless' visitor does not see these aspects and believes their child could imitate the piece. Randall suggests he experiences a similar feeling looking at Rolle's Theorem and noting only the obvious correctness without acknowledging the complicated nature of the proof, or other hidden aspects of the theorem.
+The seeming triviality of the theorem, coupled with the honour bestowed on the theorem namer, leads Randall to make a comparison to attendees of art museums who look at abstract art pieces and perceive only an apparent technical simplicity in the work. Such a visitor might exclaim "My child could paint that!". However, such works of art typically are seen as having value from attributes other than the painterly difficulty in achieving the piece. For example, an artist's work in this style may be lauded for its visionary qualities, or the emotions expressed through the choice of colours or textures. One such artist is {{w|Jackson Pollock}}. The 'clueless' visitor does not see these aspects and believes their child could imitate the piece. Randall suggests he experiences a similar feeling looking at Rolle's Theorem and noting only the obvious correctness without acknowledging the complicated nature of the proof, or other hidden aspects of the theorem.
 In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. Furthermore, "Rolle's" sounds like "Rolls", a common abbreviation for the {{w|Rolls-Royce Motor Cars|Rolls Royce}} brand implying possible sponsorship by the British car manufacturer. The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.

@@ Line 16: / Line 16: @@
 In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. Furthermore, "Rolle's" sounds like "Rolls", a common abbreviation for the {{w|Rolls-Royce Motor Cars|Rolls Royce}} brand implying possible sponsorship by the British car manufacturer. The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.
-Randall implies that there are many seemingly easy theorems like this. For instance the Dirichlet's box principle, also known as the {{w|Pigeonhole principle}}, that states that if you have more objects than containers, you're going to have to put at least two objects in one container
+Randall implies that there are many seemingly easy theorems like this. For instance the Dirichlet's box principle, also known as the {{w|Pigeonhole principle}}, that states that if you have more objects than containers, you're going to have to put at least two objects in one container.
 ==Transcript==

@@ Line 25: / Line 25: @@
 :Rolle's theorem states that any real, differentiable function that has the same value at two different points must have at least one "stationary point" between them where the slope is zero.
-:[The graph shows a sine like curve in blue intersecting the x-axis at points "a" and "b" marked in red while in the middle a point "c" has a vertical dashed green line to the apex and on top also in green f'(c)=0 is drawn with a horizontal line.]
+:[The graph shows a sine like curve in blue intersecting the x-axis at points "a" and "b" marked in red while in the middle a point "c" has a vertical dashed green line to the apex and on top also in green f'(c)=0 is drawn with a horizontal tangent line.]
 :[Caption below the frame:]