2042: Rolle's Theorem

2018-09-06T00:51:22Z

Howtonotwin: /* Explanation */ Clarify and consolidate into fewer paragraphs

{{comic
| number = 2042
| date = September 5, 2018
| title = Rolle's Theorem
| image = rolles_theorem.png
| titletext = I mean, if it's that easy to get a theorem named for you ... "a straight line that passes through the center of a coplanar circle always divides the circle into two equal halves." Can I have that one? Wait, can I auction off the naming rights? It can be the Red Bull Theorem or the Quicken Loans Theorem, depending who wants it more.
}}

==Explanation==
{{incomplete|Go a little bit more into the explanation. Do NOT delete this tag too soon.}}

In mathematics, a {{w|differentiable function}} is a function that is "smooth" everywhere, without any sudden breaks 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}}.

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.

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. It is interesting to note that this theorem: even if it 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}}.

==Transcript==
:[A single framed picture shows a colored x-y-graph with a text above:]
:'''Rolle's Theorem'''
:From Wikipedia, the Free Encyclopedia

: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.

:[Caption below the frame:]
:Every now and then, I feel like the math equivalent of the clueless art museum visitor squinting at a painting and saying "c'mon, my kid could make that."

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Line graphs]]
[[Category:Math]]
[[Category:Wikipedia]]

Talk:2016: OEIS Submissions

2018-07-06T20:15:30Z

Howtonotwin:

"All integers which do not appear in the example terms of another OEIS sequence" there is no paradox: it's pecified *another* sequence
[[Special:Contributions/162.158.154.133|162.158.154.133]] 17:52, 6 July 2018 (UTC)

I am so sorry that this comment is not related to the strip, but is the scaling for the explanation way off? Previously the scaling of the whole website was stretched, but now it is a bit too cramped for me. It happens to the previous strips too.Boeing-787lover 18:10, 6 July 2018 (UTC)

Is it too much of a stretch to mention that Chris Hemsworth stars in the movie ''Blackhat'', which is also a nickname for an XKCD character? [[User:John at work|John at work]] ([[User talk:John at work|talk]]) 19:31, 6 July 2018 (UTC)

The Sub 59 one is also a paradox, it specifies that it should include all of the author's accepted submissions, so it would have to be on it's own list itself in order to be accurate? [[Special:Contributions/172.68.58.233|172.68.58.233]] 19:47, 6 July 2018 (UTC)
:No, it would not be paradoxical. If it is accepted, then the sequence contains its identification number. If it is not accepted, that number is not in the sequence. The sequence changes depending on its own status, but there is no contradiction. This is different from e.g. the set of sets that don't contain themselves. If that set contained itself, it shouldn't contain itself, and if it didn't contain itself, it should contain itself. Both alternatives are logically impossible, so the set itself is impossible. There is nothing impossible about submission 59. [[User:Howtonotwin|Howtonotwin]] ([[User talk:Howtonotwin|talk]]) 20:15, 6 July 2018 (UTC)

explain xkcd - User contributions [en]

2042: Rolle's Theorem

Talk:2016: OEIS Submissions