The Amazing Mathematics of the World’s Most Watched Object, Princeton University Press, 2025, 130 p, including 4 p Credits, i p Preface, i p Translator’s Note. Translated from the French LA PETITE HISTOIRE DU BALLON DE FOOT, (Odile Jacob, 2023,) by Teresa Lavender Fagan.

The translator’s note at the beginning informs us the history of both names for the game played with the titular object is fascinating but she has chosen to call the game football rather than soccer (as is only proper.) There was only one lapse.

This book could almost have been designed for me A football fan (well, a fan of the Sons of the Rock, so arguably not football) with a scientific background and therefore a grounding in maths. How could a discussion of the mathematics surrounding the football not interest me? Nevertheless it wasn’t a book I sought out; indeed I was unaware of its existence until I unwrapped it as a birthday present.

Amazingly (to me at least, I discovered it in this book) the rules of football state about the construction of the ball only that it must be made of a suitable material – but without specifying what constitutes suitability! (It must also be spherical and lie within a certain circumference and weight range with internal pressure between 1.6 and 2.2 atmospheres at sea level.)

The book starts with the familiar Telstar ball, dating from the 1970 World Cup and containing twelve black pentagonal panels, twenty white hexagons and requiring ninety seams. It is impossible (despite the illustrations on UK road signs which indicate football grounds) to construct a sphere only from hexagons, or indeed solely from pentagons. In this regard the logo for the (so-called) Champions League is incorrect. The actual ball has five-pointed stars surrounding curved hexagons, three stars around each hexagon. The logo, in places, has four.

In terms of geometry the Telstar is in fact a truncated icosahedron (ie one with its points cut off) and then inflated to [near] sphericality. It is also extremely symmetrical, ensuring stability in flight, but the pattern for cutting out the panels is very complicated.

The balls for more recent World Cups are truncated versions of other Platonic solids. Teamgeist (2006) was a truncated octahedron, the Jabulani (2012) a truncated tetrahedron with eight panels which weren’t flat, the Brazuca (2014) a truncated cube! (Albeit that last had curved panels.) 2022’s Al Rihla was based on an icosidodecahedron.

So much for geometry. The other criterion considered here is drag. It is the interaction between drag and gravity that determines a football’s flight. Without drag the ball’s flight would be inherently unpredictable and, due to turbulence, slow down too quickly! The ninety seams on the Telstar ensured sufficient drag. The Jabulani’s fewer seams and relative smoothness made it seemingly erratic. (Drag reduces with smoothness.) French goalkeeper Hugo Loris called the Jabulani a catastrophe. More modern footballs like the Al Rihla, as a close-up photograph demonstrates, are dimpled (in a similar way to golf balls) so as to reduce drag.

This is an excellent book for those interested in both football and maths but I think its explanations, not to mention the copious illustrations and diagrams, are sufficiently clear to pose no barrier to the maths-phobic.

Pedant’s corner:- “The horizon is a straight line” (It isn’t; it’s actually slightly curved,) “the English government” (there is no such thing. [there is a UK government, though],) uses English plurals (rather than Greek) for the Platonic solids.

The Design, Meaning and Symbolism of World Football’s Most Famous Club Badges, Bloomsbury Sport, 2018, 255 p. First published by Pintxo Förlag, Sweden, 2016.

This book does exactly what its subtitle suggests, exploring the history of football club crests (that is what are called badges in the UK) or club emblems used on shirts, programs and stationery.

The contents are divided by country. There are 27 English club emblems discussed in detail, 12 each from Spain, Italy and Germany, 9 from France, 20 from the rest of Europe, 6 US clubs, 3 Australian and 5 South American. The entries give a potted history of the badge and (some of) its variations – many clubs have not kept a history of the changes – that club’s date of founding, its present stadium and capacity, its nicknames plus names of selected historic players, along with illustrations and descriptions of the relevant badge’s evolution.

As an addendum 126 “notable crests” are illustrated with the relevant badge, founding date, stadium and capacity, nicknames and country.

Sadly, despite its historical importance as the first outright winner of the Scottish League* and its badge depicting an elephant with a castle on its back Dumbarton FC’s striking emblem is not included. I note that Coventry City’s badge also has an elephant and castle and is given as one of the notable crests.

Manchester United’s historic players’ list contains Bobby Charlton and George Best but does not include Denis Law (though he appears with Derek Dougan in a photo on the Wolverhampton Wanderers pages) Sunderland’s list misses out Len Shackleton (I know a Mackem whose favourite, oft-repeated, football tale relates to him.)  Tottenham’s omits Danny Blanchflower. I first supposed the author is perhaps too young to be aware of these illustrious forebears but Charlie Buchan is in Sunderland’s list and he predates Shackleton by twenty plus years.

One of Aberdeen’s nicknames – along with ‘the Dons’ and ‘the Reds’ – is said to be ‘the Dandies’. I must confess that I had never heard of this though it does appear on the club’s Wikipedia page.

This is an agreeably idiosyncratic way of discovering something of the histories of the various clubs discussed.

*Neither is that of the first winners of the (English) Football League, Preston North End, though that too is fairly distinctive.

Pedant’s corner:- The author is Swedish and the book’s first publication was in Sweden so it is perfectly understandable that some infelicities should occur. No translator is listed so the author may have performed that function himself.  I noted a misplaced comma, “the claret and blue colours was the main motive” (the claret and blue colours were the main motif,) “the 1997 Champions’ League sinal” (final,) “forceably relegated” (forcibly,) “(1963/640” (1963/64,) “the Ukraine” (just ‘Ukraine’.) Arguabaly (Arguably,) “one star resembles ten titles” (one star represents ten titles.)

We visited Carlisle on the way down to Barrow-in-Furness, mainly to have a look at a second hand book shop in the town centre. As I recall I didn’t buy any books.

As we travelled on to south Cumbria we passed Brunton Park, home of Carlisle United FC, and I stopped to photograph it – or what I could gain access to. (There was some work going on at the ground.)

External view of stands:-

Statue outside club shop on Warwick Road:-

The plaque on the statue commemorates 100 years of the club:-

View of stands from the road round the side of the stadium:-

Pitch and stands (photographed through a fence):-

Further round I was able to get a less obstructed view of the pitch and stands:-

At the time the club was still in the English Football League but it has since been relegated to the National League.

Maybe I’m a jinx.

Much underrated Scottish footballer, and Nottingham Forest legend, John Robertson died on Christmas Day.

He was never the most athletic looking of men (which probably led to that underrating) but he was described by Brian Clough, the manager who got the most out of him, as “the Picasso of our game” and by his Nottingham Forest teammate John McGovern as “having more ability than Ryan Giggs.” Forest coach Jimmy Gordon rated him as “a better player than Tom Finney and Stanley Matthews.”

He is one of the few Scotsmen to win two European Cups, providing the assist for the winning goal in his first in 1979 and scoring the winner himself in the second a year later.

He also scored a winner for Scotland against England at Wembley. In 1981: Scotland have only won once there since.

John Neilson Robertson: 20/1/1953 – 25/12/2025. So it goes.

I mentioned Furness Rovers FC in yesterday’s post. They have several teams in different age groups and play games at Wilkie Road which lies right beside Barrow AFC’s Holker Street ground.

Wilkie Road club house:-

Wilkie Road pitch from entrance:-

North End, Wilkie Road. Penalty shoot out in progress. Holker Street (Barrow AFC) in background:-

Hollker Street is to the left of this shot:-

As can be seen from this shot Wilkie Road is not completely fenced off:-

Holker Street is the home stadium of Barrow AFC, currently playing in the fourth tier of English football

This is the ground viewed from the west. A Furness Rovers game is in the foreground.

From west showing entrance building:-

Entrance to Holker Street (off Wilkie Road.) It seems to be sponsored as the SO Legal Stadium:-

Pitch viewed from northwest. Note temporary stand addition:-

Holker Street from northeast (stitch of two photos.) Again note temporary stand extension:-

A view of the stand from before these additions is here.

The ground from northeast:-

Mosset Park is home to Forres Mechanics FC, who play in the Highland League. The ground lies right by the A 95.

We happened to pass it on our trip up north in July 2024, so of course I had to stop to photograph it.  It looks tidy enough but I’ve not been inside.

Mosset Park, Forres:-

This football ground is home to Deveronvale Football Club who play in the Highland League.

It stands by the banks of the River Deveron, from which the club takes its name, where the river flows into the sea between the towns of Banff and Macduff.

View from the A 98:-

Closer view of stand:-

Princess Royal Park from south east:-

I missed photographing this when I visited Huntly before despite  it being very near Huntly’s War Memorial.

Christie Park is the home of Huntly FC, who play in the Highland League.

View of ground from Castle Street:-

Entrance gates/turnstiles. These have an Art Deco styling:-

Christie Park from southeast. I had to stand on a wall to get the photos from which I made this stitched picture:-

It’s a tidy ground.

In 1909 Sir Thomas Lipton, he of the tea company, organised a football tournament in Turin in thanks to the Italian Government for an honour he had been awarded. Top teams from Italy, Germany and Switzerland were invited but for some reason the invitation to a British team was given to West Auckland FC, an amateur side struggling in England’s Northern League.

I had heard of this in my youth but had forgotten about it till last June when I passed through West Auckland village in County Durham, where I stopped for a break and found this statue had been erected on the village’s green.

For, amazingly, West Auckland won the tournament, beating Switzerland’s Winterthur FC 2-0 in the final on 12/4/1909. The plaque mispells Winterthur as Winterhour.

Even more amazingly when the next tournament was played in 1911, West Auckland won it again and so got to keep the Trophy. This time they beat Juventus 6-1.

An information board at the bus stop tells the story.

Note: Renton FC have a prior claim to being the First World Football World Champions having beaten West Bromwich Albion 4-1 in 1888. Both were their domestic Cup winners at the time, the relevant national leagues not having been established yet. This was a World Championship by default as there was little football outside the UK then. Similarly, West Auckland can only really claim to have been European Champions.