Pentagons, hexagons, what's the difference...
November 3, 2017 3:21 PM   Subscribe

Maths crusader and football fan, Matt Parker, has started a campaign to fix the football image on street signs in the U.K. which are mathematically incorrect. He explains here.
posted by agatha_magatha (29 comments total) 3 users marked this as a favorite
 
Wait till he sees this impossible horror.
posted by dng at 3:25 PM on November 3, 2017 [20 favorites]


"The higher level of attention needed to understand the geometry could distract a driver's view away from the road for longer than necessary which could therefore increase the risk of an incident."

On the other hand, you have absent-minded perfectionist drivers like me who would stare an extra three seconds, thinking "That ball is mathematically impossible!" and then crash right into the car in front of me. I'm on team #fixthesign
posted by Pater Aletheias at 3:33 PM on November 3, 2017 [6 favorites]


He should show what it should look like. I used to know a guy that would rant that the deer on warning signs in Texas had their antlers on backwards. I could never remember to check though.
posted by Bee'sWing at 3:33 PM on November 3, 2017 [1 favorite]


Nice example of Euler's theory of closed polyhedra, Buckminster Fuller must spinning in grave. Another version that I was exposed to in Inorganic Chemistry was simpler (and I've never been able to find this anywhere else): for each polygon, add 6-#sides, for a closed polyhedron it will be greater than 12.
Tetrahedron; (4*(6-3))=12
Cube; (6*(6-4))=12
Octahedron; (8*(6-3))=24
Dodecahedron; (12*(6-5))=12
Soccer ball; (12*(6-5) + 20*(6-6))=12
posted by 445supermag at 3:43 PM on November 3, 2017 [1 favorite]


Always fun to google image search for bad signage. Speed Bumps Ahead When Children Are Present, Massage The Rapist, and S. Harting, indeed.
posted by axiom at 3:43 PM on November 3, 2017


As a USian with a shaky grasp of spatial reasoning, I'm way more distracted by his pronunciation of "hexagun" and "pentagun." It's "pentaGONE" you twit. (But definitely "Oregun.")
posted by basalganglia at 4:12 PM on November 3, 2017


And then there's the 3D Zebra Crosswalk in Iceland in an attempt to slow down traffic. Technically not "signage" but I felt it had some relevance when it comes to making drivers pause and stare.
posted by linux at 4:13 PM on November 3, 2017 [3 favorites]


I'm totally against all football ground location signage as it destroys the time honoured tradition of locals sending opposition fans in the wrong direction when they ask for directions.

(On a serious note there's been arguments that the UK has too many road signs to the extent that they are distracting and cause accidents)
posted by fearfulsymmetry at 4:28 PM on November 3, 2017 [2 favorites]


We don't even have football in my country and I think that graphic looks completely wrong. That's the simplest argument.

On the other hand if you want to direct drivers to the nearest star wars droid silently screaming in existential horror then A+ WOULD GRAPHIC DESIGN AGAIN 😮
posted by danny the boy at 4:38 PM on November 3, 2017


dng: the simple explanation is that the road was so slippery the car rotated from driving on the bottom of the road to the top of the road
posted by idiopath at 4:45 PM on November 3, 2017 [1 favorite]


FWIW it's not wrong so much as a deliberate simplification that's not trying to be right - most likely because simplicity of construction is a concern in designing iconography.
posted by Artw at 4:56 PM on November 3, 2017 [2 favorites]


OK, those signs are just messed up. It's fine if you want to tile a bathroom floor, not so good if you want to tile a sphere.

The pattern of white and dark hexagons is stipulated in UK law as the image for a football ground.

I don't get why they wouldn't be willing to change it. It shouldn't be that hard to redo the icon to use black pentagons and white hexagons, centered on a black pentagon, with some more black pentagon parts on the outside. Heck, the first page of google images has some decent ones.

And stipulating something mathematically incorrect just makes you look stupid as a country, like the probably apocryphal story about how the Indiana legislature passed a law making π = 3.
posted by leahwrenn at 5:01 PM on November 3, 2017


FWIW it's not wrong so much as a deliberate simplification

Except that making it out of all hexagons both looks wrong and is also more complicated than a real soccer ball by virtue of having more edges and vertices packed into the same image.
posted by Pyry at 5:08 PM on November 3, 2017


The Mozilla emoji is similarly wrong.
posted by peeedro at 5:42 PM on November 3, 2017 [1 favorite]


In common with Bryson's Theory — all British people are intimately familiar with every moderately large road within 50 miles of their home* — it took me about 3 clicks to find the place where he filmed his piece to camera, at the foot of the M32 just on the outskirts of central Bristol.

Actually watches video – Wow, I really like that he did that very simple sketch proof of why you can't tile a ball with just hexagons, and that he also shows the statutory instrument where road signs are defined. And then motivates his argument by saying "well, if we discuss it, we get people talking about geometry, and that's what actually matters". And then displays that Eldritchian horror of an elephant just to make the point.

I mean, I'm not saying there's anyone at the DfT stubbornly sitting there saying "well, we want footballs to look like honeycomb" rather than "lets leave it as that silly Blockbusters board in a circle we did in 20 minutes one afternoon", but I guess it's going to take a while for it to percolate through to make an actual change.

*Incidentally, if you're looking for memorable laybys just outside Warminster, I recommend going for a swim here.
posted by ambrosen at 6:44 PM on November 3, 2017 [3 favorites]


I once told my son that those were puntagons interspersed among the hexagons, because soccer and punt.

He came home from school very angry with me a few weeks later.

Worth it.
posted by Pogo_Fuzzybutt at 7:25 PM on November 3, 2017 [2 favorites]


Oh man, the image in that first link. I made my pilgrimage to Anfield this August and walked from Lime Street. Seeing the signage to the stadium was great...until it turned into maybe you are walking towards the local enemy? It took some wandering to make sure I was on the red track.

BTW: The Everton Library is a building that casually screams, "I am totes haunted."

Long story short: I made it, got drunk, and enjoyed a 4 nil win at home.
posted by robocop is bleeding at 7:44 PM on November 3, 2017


Maybe after Parker succeeds in fixing the soccer signs he can come to the US and make sure the skulls in our poison labels have the proper number of teeth
posted by ejs at 8:42 PM on November 3, 2017 [1 favorite]


Matt Parker with more football geometry.
posted by onya at 11:17 PM on November 3, 2017


A significant proportion of the population don't even know what the current signs mean. 20% not recognising the national speed limit sign is surprising.

My bugbear is signs covered by overgrown trees and hedges. If we have spent the money designing, making and erecting the sign at least make sure people can see it.
posted by 92_elements at 2:27 AM on November 4, 2017


Someone should tell the Eden Project that their domes are mathematically impossible.
posted by Flashman at 6:44 AM on November 4, 2017 [1 favorite]


They have pentagons interspersed between the hexagons, albeit only a few (you can see a couple of the pentagons in that picture).

The Eden Project Domes: Each dome actually has two web layers, one with hexagonal and pentagonal panels and one with triangular panels. The total Eden structure uses 625 hexagons, 16 pentagons and 190 triangles.
posted by dng at 7:35 AM on November 4, 2017 [2 favorites]


I coloured all the pentagons visible in that picture of the Eden Project, and there really aren't very many.
posted by ambrosen at 11:30 AM on November 4, 2017 [1 favorite]


How bizarre that that's what they went with, the current sign doesn't read as a football to me at all.
posted by lucidium at 5:29 PM on November 4, 2017


The signs are fine. What's wrong is him thinking they're intended to depict balls, when clearly they're just snapshots of the bathroom floors at the stadiums.
posted by flabdablet at 2:04 AM on November 5, 2017


Probably because it's on a bunch of signs already, and replacing signage is probably not cheap, and if you replaced signs for technically-impossible-but-still-identifiable objects, you start opening a can of worms.

It wouldn't be that difficult to create a new design and require that all new signs use it. It's the sign for football stadium, not a poison warning label - very little downside to having two in use until the old signs are completely replaced (unless you are a Vogon, that is).

...and yet no one's going around saying "This depiction of a pedestrian is impossible! How does the head stay floating above the body! And how does one pedestriate without feet!"...

A better analogy would be if the sign for person had three legs, or six fingers: the ball design is wrong for no other reason except the person (or committee, more likely) designing it didn't know what they were doing. The floating head / blocky trunk makes the sign easier to read while somewhat skipping over the what-does-a-normal-person-look-like minefield , the invalid geometry ball doesn't offer any real advantage.
posted by Dr Dracator at 2:22 AM on November 5, 2017


the ball design is wrong for no other reason except the person (or committee, more likely) designing it didn't know what they were doing

Maybe.

Or perhaps it's just that when you put the pentagons in where they're supposed to go, then project the result onto the flat surface of a sign, the resulting 2D mesh invokes the idea of a football even less successfully than the existing design.

Frankly I refuse to worry about this until after we've solved the problem of school children making drawings that feature red hexagonal STOP signs.
posted by flabdablet at 3:49 AM on November 5, 2017


Wait till he sees this impossible horror.

My mother brought me up to think of that one as impossible as well. I accepted her scornful snort without question until the day I saw that very skid pattern left indelibly on a road surface in fresh black rubber (not mine, thank goodness).

Hint: consider the tracks drawn by a car's rear wheels as it spins after going out of control at high speed on a slippery surface.
posted by flabdablet at 3:58 AM on November 5, 2017


Has anyone even used one of those Telstar balls since the eighties?
posted by Sys Rq at 6:42 AM on November 5, 2017


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