3264: 720 Ollie

2026-06-27T19:11:54Z

Rborchert: FIxed a typo - change "most be rotated" to "must be rotated"

{{comic
| number = 3264
| date = June 26, 2026
| title = 720 Ollie
| image = 720_ollie_2x.png
| imagesize = 257x325px
| noexpand = true
| titletext = This discovery was key to his demonstration of regular/goofy symmetry violation, which won him gold in the theory portion of the X Games.
}}

==Explanation==
{{incomplete|This page was created by a spin-½ boson. Don't remove this notice too soon.}}

{{w|Tony Hawk}} tells Cueball that doing a single 360° spin causes him to land backward rather than forward. This is unexpected, since a 360° turn in the xy plane is a full revolution, meaning that it should normally return Tony Hawk to his original position rather than perform a half-rotation (normally the result of a 180° spin). As repeating this would reverse his reverse, doubling this to a 720° spin is what finally allows him to land forward. Normally, revolving 360*n degrees, for any whole number (n=0, n=±1, n=±2, etc) should leave him pointing the same range as before, but for him he returns to the same orientation if n is even, but he lands with the opposite orientation if n is odd.

The caption reveals that this is because Tony Hawk is a spin-½ fermion. Spin-½ fermions have the unusual property that they must be rotated through two full turns before returning to their original configuration. This explains the paradox, but is unusual because spin-½ particles are normally very small, only occurring in quantum physics rather than Newtonian physics. Since Tony Hawk is not a subatomic particle,{{Citation needed}} it is unclear how his skateboard tricks could be described only by quantum physics.

A '''{{w|fermion}}''' is a classification of particles (or groups of particles) whose intrinsic angular momentum (aka "spin") is half-integer multiple of the ''reduced Planck constant''; the behavior of these objects' spin is described via spinors, a type of complex vector. This is in contrast to '''bosons''', whose spin is an integer multiple of the reduced Planck constant, and described by the normal Euclidean vectors you know and love.{{Citation needed}}

Tony Hawk is an American skateboarder credited with inventing the 720, a trick (under normal circumstances) involving two full mid-air rotations. Since Hawk invented it in 1985, larger {{w|Aerial (skateboarding)|mid-air rotations}} have been invented (up to 1260, three and a half rotations), and according to the comic they can have even stranger quantum properties.

The title text is a riff on the Nobel Prize-winning discovery of {{w|CP violation}}, (something that may have been on [[Randall]]'s mind, recently, due to the [[3263: Baryon Asymmetry|prior comic]]'s subject matter/anti-matter). The {{w|Footedness#Goofy stance vs. regular stance|regular/goofy styles of riding a skateboard}} could be considered as a physical quality of the "skateboarder particle", as values of charge and parity are of subatomic ones. The {{w|X Games}} are a prestigious 'street-sport' event that includes competitions in skateboarding as well as other related board- and bike-disciplines. The parallel is made between being able to win a gold medal for impressive skateboarding skills (and demonstrating new tricks, in the process, as Tony Hawk has been known to do) and earning the gold Nobel Prize medal for a scientific achievements in Physics or one of the other established prize categories. So far, nobody has done both of these. But, if this comic is entirely true, perhaps Tony Hawk could be the first to do so.

Skateboarding is also the subject of [[296: Tony Hawk]].

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}
:[Tony Hawk and Cueball are talking. Tony Hawk is holding his skateboard. An image, above the heads of Tony Hawk and Cueball, depicts Tony Hawk doing two 360-degree turns on a skateboard]

:Tony Hawk: Something weird I've noticed is that if I do a 360 ollie, I land backward. I have to do a 720 to land going forward.

:Caption: Tony Hawk discovers that he's a spin-½ fermion.

{{comic discussion}}<noinclude>
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring real people]] 
[[Category:Sport]]
[[Category:Skateboard]]

2740: Square Packing

2023-02-22T06:01:54Z

Rborchert: /* Explanation */

{{comic
| number = 2740
| date = February 20, 2023
| title = Square Packing
| image = square_packing_2x.png
| imagesize = 326x295px
| noexpand = true
| titletext = I also managed to improve the solution for n=1 to s<0.97, and with some upgrades I think I can hit 0.96.
}}

==Explanation==
{{incomplete|Created by a HYDRAULIC PRESSED SQUARE - This appears to be referring to a specific puzzle that merits explanation before going into description of the comic. Do NOT delete this tag too soon.}}
The {{w|Square packing in a square|square packing problem}} is a type of geometry problem. The goal is to find the smallest possible "outer square" that will fit N "inner squares" that are each 1 unit wide and 1 unit tall. In the comic N=11, leading to its name of "The N=11 Square Packing Problem," and s is the length of the outer square's sides.

A few days before this comic's post, a web page [https://erich-friedman.github.io/packing/squinsqu/ ''Squares in squares''] gained interest on social media platforms such as [https://twitter.com/KangarooPhysics/status/1625436240412540928 Twitter] and [https://news.ycombinator.com/item?id=34809023 Hacker News]. For many values of N, that page depicts the best known solutions, some of them known to be optimum. The one for N=11 (best known but not proven to be optimum) is shown on the left here; its general arrangement was found by Walter Trump in 1979 and slightly improved by Gensane et al. in 2004.<ref>Gensane, T., Ryckelynck, P. – ''Improved dense packings of congruent squares in a square''. Discrete Comput Geom 34, pages 97–109 (2005). https://doi.org/10.1007/s00454-004-1129-z</ref>

Munroe claims to have found a more efficient solution for this N=11 case, by physically deforming the squares involved in the best-known solution with a {{w|hydraulic press}}. The size of the resulting bounding square is indeed smaller, but the "solution" isn't actually one because the inner shapes have countless wrinkles and are no longer squares. Geometrical shapes in packing problems are not conventionally assumed to be deformable in this manner.{{citation needed}}

The title text mentions the same approach "improved" the solution for 1 unit square, whose optimum solution is obviously that unit square itself with s=1. Munroe remarks that if he had "some upgrades", presumably a more powerful hydraulic press, he could get the resulting square to be even smaller.

The humorous implication behind the comic and the title text is that rather than the shapes being mathematical, abstract shapes, they are actually physical squares, constructed of some extremely strong, but not completely incompressible material. It is not obvious what material that might be: even using a hydraulic press, its volume can only be reduced to 0.97 or 0.96 times its starting volume. (The fact that the squares exist in a 2D universe in the problem statement, but are being crushed presumably by a 3D hydraulic press is not addressed, either).

This is perhaps a related joke to [[2706: Bendy]], but now with squares and compressed areas instead of triangles and extended lengths.

‎<references />

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[11 squares optimally packed inside a square arrangement]
:Previous best
:s<3.877084
:(Gensane, 2004)

:[11 deformed squares crushed together to pack them into a smaller square arrangement]
:New record
:s<3.40

:[Caption below the panel:]
:I've significantly improved on the solution to the n=11 square packing problem by using a hydraulic press.

{{comic discussion}}
[[Category:Math]]
[[Category:Geometry]]

explain xkcd - User contributions [en]

3264: 720 Ollie

2740: Square Packing