2735: Coordinate Plane Closure

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Coordinate Plane Closure

Title text: 3D graphs that don't contact the plane in the closure area may proceed as scheduled, but be alert for possible collisions with 2D graph lines that reach the hole and unexpectedly enter 3D space.

Explanation

This explanation may be incomplete or incorrect: Created by a 2D graph that has accidently become 3D (and sentient) - Please change this comment when editing this page. Do NOT delete this tag too soon. If you can address this issue, please edit the page! Thanks.

This comic is a "math notice," which is presumably a warning or reminder for mathematicians or others who interact with the field of mathematics.

Coordinate planes are used in math for drawing graphs. The joke here is that a small section has been "closed for maintenance," likening the concept of a coordinate plane to an actual physical platform used by math, which is therefore vulnerable to damage such as is shown in the comic.

The math notice advises those who are using the coordinate plane to avoid drawing any graphs in the area with the hole until the damage is patched or fixed.

The title text clarifies some of the unwanted effects of drawing a graph into the hole, stating that two-dimensional graph lines might accidentally become three-dimensional and interfere with the graphs made there.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

!!Math Notice!!

The coordinate plane will be closed Thursday between (1.5,1) and (2,1.5) to repair a hole.

If your graph uses this area, please postpone drawing until Friday or transform it to different coordinates.

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Discussion

Is there significance to the fact that the axes aren't labeled in the warning? Can I plot y = 0.75x today or not?Brossa (talk) 15:05, 8 February 2023 (UTC)

you cannot because it intersects the given square as shown in this desmos thing i whipped up in 2 seconds: https://www.desmos.com/calculator/zb9nbrl6s5 172.70.43.29 15:38, 8 February 2023 (UTC)Bumpf

I can if the forbidden coordinates are 1 ≤ x ≤1.5 and 1.5 ≤ y ≤2172.70.131.66 15:56, 8 February 2023 (UTC)

In the absence of other information, assuming horizontal x and vertical y would be conventional. --141.101.98.145 19:15, 8 February 2023 (UTC)

"Hole" is also sometimes used to mean a particular coordinate on a function which is discontinous at some point but could have a value (for example sinx/x with a hole at (0,1)). 172.70.206.92 19:18, 8 February 2023 (UTC) Randall listed 2 points, yet the cordoned off area is a square. 2 points define a line, not a square, he really should have thought of that. How is someone to know the invalid points without the diagram? Even with the diagram, we don't know whether points on the boundary are included! Is the line y=1 a valid line to draw? THESE ARE QUESTIONS THAT NEED TO BE ANSWERED RANDALL BE MATHEMATICALLY RIGOROUS NEXT TIME.

Right! A hole pops up in rational functions when there's a term that appears in the numerator AND the denominator. However, it does not mean the graph is broken; just that there is no defined y-value at the x-value of the hole. ----Theunlucky (talk) 16:55, 9 February 2023 (UTC)

One reason could simply be the alignment between the coordinates and time. Reading out the numbers without paying attention to the mathematical punctuation you can form the sentence "the coordinate plane will be closed Thursday between 1:51 and 2:15 to repair a hole", following the typical structure of such a notice to not just provide a day but a time.

Ironically, the notice makes it sound like using y=1 is fine, and the affected region is only strictly greater than y=1. That would make the region that's closed an open set, and the region that's open a closed set. 172.70.110.230 22:46, 8 February 2023 (UTC)

Right! A hole pops up in rational functions when there's a term that appears in the numerator AND the denominator. However, it does not mean the graph is broken; just that there is no defined y-value at the x-value of the hole.

🚧 DETOUR 🠕 KEEP WITHIN MINKOWSKI CONES ⛔ DO NOT ENTER Y < |X| 🚧 162.158.90.38 23:37, 8 February 2023 (UTC)

So the joke is that the coordinate plane is closed when there's damage that causes it not to be closed? Barmar (talk) 23:44, 8 February 2023 (UTC)

Aw man, I was really looking... forward... to doing math today. 172.71.222.76 11:58, 9 February 2023 (UTC)

I thought the title text was referring to the danger of lines on a 2d graph "falling through" the hole and inadvertently gaining a third dimension, which might collide with graphs at z=-1 etc. 162.158.34.75 16:14, 9 February 2023 (UTC)

My RSS reader picked this comic up at exactly midnight UTC on Feb 8, which stood out to me because usually they seem to be posted later in the day. Danielp82 (talk) 04:02, 10 February 2023 (UTC)

This comic reminded me of Complex Analysis, where we integrate in circles around singularities of complex functions (aka holes). See Cauchy integral formula. Maybe we should mention that in the explanation. 172.71.154.39 07:29, 10 February 2023 (UTC)

The beauty of the Wiki is that you can add it yourself, if you think you can word it relevently. Or anyone who now wants to. (Whoever does, note that {{w|Cauchy's integral formula}}, or an altered text version like your {{w|Cauchy's integral formula|Cauchy integral formula}}, would be the prefered wikilink format to use.) 141.101.98.151 08:08, 10 February 2023 (UTC)

I made the unfortunate but defensible change from "airmen" to "air missions". The FAA re-consecrated "NOTAM" to the gender-neutral (and execrable) form on 2 Dec 2022. The "airmen" form may still be in use by ICAO or nations other than the US. Der57 (talk) 10:52, 10 February 2023 (UTC)

Don't you think it's uncharacteristic of Randall to deviate from the normal math practice of placing the x coordinate first before the y coordinate when not explicitly identifying them? Furthermore, each coordinate is backwards from the convention of smaller number first, then larger? This is so out of step for him I think he did it deliberately and we're missing a subtle joke... Paso Dan (talk) 16:38, 10 February 2023 (UTC)

What are you talking about. He lists the number as (X, Y) completely normal with X on the lower axis and Y on the one going up and so does the numbers he gives follow normal style. Also he starts with the number that comes first on the x-axis. See no reason to start with another, and this is also relevant for making it look like he is given a time period. Seems to me you must have made a mental mistake when you wrote this? --Kynde (talk) 17:35, 10 February 2023 (UTC)

Yeah, like Kynde said, he's using standard notation... the region (1.5, 1), x = 1.5 and y = 1, and (2, 1.5), x = 2 and y = 1.5... X first, then Y, standard. He even plots those points, with dotted lines denoting a square "cordoned" off... And when sorted, graph points usually go left-to-right (so, ascending order by X), which he did. NiceGuy1 (talk) 05:42, 11 February 2023 (UTC)

I get what Paso Dan is saying, and it was my impression as well. Indicating that the coordinate plane is closed between two points (A,B) and (C,D) doesn't by itself tell you whether the closure is along the line between those two points, or a circle with a diameter running from (A,B) to (C,D), or some other 2-D shape. The diagram indicates a square with corners at (A,B) and (C,D) and sides parallel to the axes, but that information isn't in the text. If on the other hand it's interpreted as a closure for the region where x is between 1.5 and 2 and y is between 1 and 1.5, you get a full description of the closed area. --Brossa (talk) 17:36, 18 February 2023 (UTC)

Two points are capable of defining an axis-aligned rectilinear quadrilateral, or a diamondoid (if you decide to use the convention of a 45-degree skew), or an arbitrarily-rotated square (defining one of the long diagonals). Pretty much any other quadrilateral (or other shape) needs further pre-agreed presumptions or more points of definition. A circle can be defined by three (non-colinear, non-identical) edge-points, or an oval (even skewed) by, at the very least, a third value/coordinate in different manners.

(Oh, ok, you could assume a circle defined by just two points (diametrically opposed), the circumscircle to the arbitrary square, above, or even the circle that is inscribed to it. Or "centre and point on radius". From that stage you could indicate further polygon that can be circumscribed thusly, oriented either constantly to the axes or to the direction defined by the (initial) radial point. So your toolkit can feature a "drawShape(coord1,coord2)" for all kinds of areas, one for each possible kind and treatment.)

Yet, in the absence of any detail other than "this defines an area", two surface coordinates almost certainly will be best assumed to defibe a rectangle (or a graticule, given latitude/longitude coords) and two 3D coords ones a cuboid/whatever. 172.69.79.185 20:27, 18 February 2023 (UTC)

Finally, I get an explanation why I've seen so many mentions of "China balloon" lately (and the picture of the moon with a silhouette on it, like the one I saw with X-Wings photoshopped flying off to it, didn't even realize they were related). :) I didn't feel like Googling it, figuring it would come to my attention eventually. LOL! NiceGuy1 (talk) 05:35, 11 February 2023 (UTC)