2042: Rolle's Theorem

2018-09-05T21:41:27Z

Verket:

{{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|differentiable function}} is a function whose derivative exists at each point in its domain. The derivative represents the slope of the corresponding graph which must be ''smooth'' in any point without any abrupt breaks or similar. In the case of this comic the slope starts with a positive value at point (a), then decreases until it reaches zero at point (c), and then smoothly turns to a negative value towards point (b). Only the area for positive x- and y-values are considered as the relevant domain.

To [[Randall]] it's trivial that a line starting with a slope upwards but then turning downwards to the same level must have, at one point in the middle, a slope of zero.

This comic references the theorem in calculus {{w|Rolle's theorem}}, which is intuitively obvious but harder to prove than they seem.

At the title text Randall mentions a line together with a ''coplanar'' circle. This simply means that those both 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 diagonal which divides it into two equal parts.

It is interesting to note that the theorem mentioned in the title text is already taken: even if this theorem 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]]

1881: Drone Training

2017-08-25T22:21:37Z

Verket: /* Explanation */

{{comic
| number = 1881
| date = August 25, 2017
| title = Drone Training
| image = drone_training.png
| titletext = The joke will be on him in a few weeks when animal control shows up and takes custody of his Roomba.
}}

==Explanation==
{{incomplete|A simple comic, anything missing?}}
In this comic, [[Black Hat]] enters a pet store run by [[White Hat]]. He wants to buy something to help him train his drone, which keeps flying into the wrong rooms. This is absurd as drones are not living creatures like dogs or cats, which can be trained to do tricks, or stay in the correct areas (inside his property). He also wants a shock collar for his {{w|Roomba}}, which would train it to stay inside or at least on his lawn.

{{w|Cat repeller}} are devices or substances for training cats or repelling them from furniture or other areas. The Wikipedia page lacks the spray but you easily can create it at home as shown here: [http://www.instructables.com/id/Friendly-but-Effective-Cat-Repellent/ Friendly (but Effective) Cat Repellent], Black Hat is probably wasting some money when he buys it in a shop.

Roomba is a branch of autonomous robotic vacuum cleaners and controlling it by electric shocks from a {{w|Shock collar|shock collar}}, normally used for dogs, is more than questionable. Those collars are legal in the US but they are banned in many European countries and others. A Roomba was previously mistaken for a dog in [[1558: Vet]].

Knowing Black Hat, he might be poking fun at either people's assumptions that modern robots are more advanced than they actually are, or possibly at White Hat's various inaccurate claims. It is also possible, however, that he just wants to terrify people with the idea of robot abuse/conditioning. There is also a chance that he genuinely believes he can force robots to obey him via inflicting suffering, and would prefer doing so to just using a remote control on the drone, a Roomba Virtual Wall, or an ordinary vacuum rather than a Roomba.

The title text may mean one of three things: The endeavor will become a total flop when the Roomba probably gets rid of the collar and terrorizes the neighborhood. As a result dogcatchers from the {{w|Animal control service|animal control service}} will arrest this "wild animal". Or animal control services will confiscate the Roomba to save it from its abusive owner. Or, at least, White Hat also owns a Roomba and it will be taken into custody because it has not been trained with a shock collar.

==Transcript==
:[Black Hat stands in front of a store counter facing White Hat who stands behind.]
:Black Hat: My drone keeps flying into the wrong rooms. Do you have anything to discourage it?
:White Hat: Sir, this is a pet store.

:Black Hat: Yeah, I was thinking one of those spray bottles for cats.
:White Hat: I don't think you can train a drone.

:[White Hat hands a spray bottle over the counter.]
:Black Hat: Eh, they say that about cats, too. Plus, these days they probably all come with deep learning or whatever. Drones, I mean. Maybe cats too.
:White Hat: Fine, here's a bottle.

:Black Hat: Do you sell a shock collar that can fit around a Roomba?
:White Hat: I'm going to have to ask you to leave.

{{comic discussion}}

[[Category:Comics featuring Black Hat]]
[[Category:Comics featuring White Hat]]
[[Category:Artificial Intelligence]]

explain xkcd - User contributions [en]

2042: Rolle's Theorem

1881: Drone Training