Latest Posts by merpmonde - Page 4

Three churches in Le Havre

This building very much stands out in Le Havre's rebuilt city centre, as it is far more ornate than its surroundings. It's the oldest building in Le Havre, completed in 1638, just 120 years after the founding of the town. Damage by Allied bombings but not completely destroyed, the old church was kept and restored, and, with Le Havre becoming a major town again, it got its own diocese in 1974. The church then became Notre-Dame Cathedral of Le Havre, and is now approaching 50 years in the role (anniversary in December).

As it had been decided to keep the old church, Auguste Perret, the architect in charge of the reconstruction, would build a church of his own elsewhere: the new Church of Saint Joseph, a blocky concrete structure, perfectly in sync with the rest of the urban project. Where the cathedral sticks out as its rounded, classic facade contrasts with the angular buildings around it, Saint Joseph's stands out with its tall central spire. Culminating at 107 m, the tower is inspired by lighthouses, a symbol of Le Havre's maritime nature.

Somewhere in between, other churches further away from the port also survived the war - not without damage, but restoration was chosen over replacement. In the foreground, Saint Vincent de Paul's Church was built in the 19th century in a neo-Romanesque style, its central tower reminiscent of the abbey on Mont Saint Michel.

Sangaku Saturday/Sunday is taking a week off.

Catène de Containers

To celebrate the 500th anniversary of the founding of the port on the right bank of the Seine estuary, Le Havre went big. They commissioned a sculpture from artist Vincent Ganivet... and he delivered a monument!

Standing at nearly 29 m tall, the arches are made with 36 shipping containers, representing Le Havre's half-millennium as an international trade hub. 21 in one and 15 in the other, they are arranged in a catenary shape which makes the structure self-supporting. There's stuff to satisfy a maths and physics buff in there somewhere... but I'll just concentrate on the fact that it looks cool, especially compared to its industrial and brutalist surroundings.

As a major port in Nazi-occupied France, Le Havre was bombed into oblivion by the Allies, hence most of the town centre's buildings were built at once in the late 1940s-early 1950s. The result is a very rigid, homogeneous, mineral urban environment, to which the Catène adds a welcome dash of colour.

But if nothing else (and we've established there is a lot else), it looks like it'd make a compelling Mario Kart track.

Seaside sunset at Le Havre

Enjoyed a nice weekend away with long-time-no-see friends in Normandy. The rain cleared throughout Saturday, giving us the opportunity to get out and watch the sunset from the "End of the World" beach, along the coast from Le Havre, out of view from the industrial port.

After the Sun had set, the layer of cloud on the horizon seemed to thicken, giving a very curious palette of shades of grey. There was still some light in the sky, but the ships waiting in the Channel floated against a somewhat uncanny background. The following are colour photos, I swear...

Sangaku Sunday #6

We are about to solve our first sangaku problem, as seen on the tablet shown above from Miminashi-yamaguchi-jinja in Kashihara.

First, we should conclude our discussion: what are sangaku for? There's the religious function, as an offering, and this offering was put on display for all to see, though not all fully understood the problems and their solutions. But a few people would understand, and these would have been the mathematicians of the time. When they visited a new town, they would typically stop at a temple or shrine for some prayers, and they would see the sangaku, a sample of what the local mathematicians were capable of. Whether the problems were solved or open, the visitor could take up the challenges and find the authors to discuss.

And this is where everything lined up: the local school of mathematics would have someone new to talk to, possibly to impress or be impressed by, and maybe even recruit. With the Japanese-style mathematics of the time, called wasan, being considered something of an art form, there would be masters and apprentices, and the sangaku was therefore a means to perpetuate the art.

Now, what about that configuration of circles, second from right on the tablet?

Recall that we had a formula for the radii of three circles which are pairwise tangent and all tangent to the same line. Calling the radii p, q, r, s and t for the circles of centres A, B, C, D and E respectively, we have

for the circles with centres A, B and C (our previous problem), and adapting this formula to two other systems of three circles, we get

for the circles with centres A, C and D, and

for the circles with centres B, C and E. Add these together, and use the first relation on the right-hand side, we get a rather elegant relation between all five radii:

Of course, we can get formulas for s and t,

r having been calculated previously using just p and q, which were our starting radii.

For example, setting p=4 and q=3, we get, approximately, r=0.86, s=0.4 and t=0.37 (this is the configuration shown in the figure, not necessarily the one on the tablet - I will be able to make remarks about that on another example).

Views from Ôwakudani

As the volcano's activity isn't explosive, and there's a whole hot spring business around it, humans have been trying to tame Mount Hakone, as evidenced by the many consolidation structures seen at Ôwakudani.

These continue down the valley to contain landslides which could happen if things get more intense. Nonetheless, occasionally, a gas vent juts out, placing a distinctly natural form amongst the organised, man-made network of walls.

The yellow deposits are typically sulphur from a very pungent gas. Depending on the direction of the wind, the smell in some locations on the summit can be quite literally breathtaking.

The views, meanwhile, are figuratively breathtaking, from the striking contrasts in vegetation in the foreground to Lake Ashi and the outer mountain range of the Hakone caldera in the background.

And, of course, it is possible to see Mount Fuji from Ôwakudani. Terms and conditions apply, as always, but what little I could see on that morning gives a sense of scale to the great mountain. However, later that day, we would be treated to a much clearer view of Fuji-san.

What to do at Ôwakudani

... or what to do on the summit of an active volcano. As inauspicious as that sounds, as long as Mount Hakone's activity can be described as moderate (localised fumaroles and hot springs) and a full-blown eruption doesn't happen, and that hasn't happened in thousands of years, it's possible to settle some permanent attractions. The Ropeway is undoubtedly one of them, and the Geomuseum, housing explanations about the mountain's history and geological peculiarities, was a very pertinent addition 10 years ago.

However, the summit's biggest draw has to be its black eggs. No, black eggs aren't what you get when you raise chickens at the top of an active volcano, but it's what you get when you boil eggs in the natural volcanic spring water on Mount Hakone.

So a few restaurants have popped up in Ôwakudani to serve these curious delicacies. To be clear, it's just the shells that turn black due to the minerals in the hot spring water; they still protect the inside from those minerals, and the egg cooks perfectly normally, and the edible parts are still white and yellow. Apparently, I don't eat hard-boiled eggs.

The eggs are cooked in the steaming plant next to this fumarole further up the hill. It can be visited via a trail through some less stable ground. If I remember correctly, this trail is only open at certain times for a limited number of people at a time. Although it's only 300 metres from the main part of Ôwakudani, half a dozen shelters have been installed in case of emergency (one such concrete structure can be seen behind the steaming plant).

But how do the eggs get up there if the trail isn't always open? With their own lovely little ropeway! White eggs go up, black eggs come down, ready to be served in the restaurants!

Hakone Ropeway

The gondola lift up the Schauinsland is very good, but my favourite so far is definitely the Hakone Ropeway. After the train into Hakone, another train to Gôra, and a funicular, the last leg up the mountain is covered by this funitel, on which cars are suspended by two cables rather than one.

The Ropeway carries passengers up to Ôwakudani through the forest... at least as far as that ridge.

Mount Hakone is an active volcano and "Ôwakudani", 大涌谷, literally means "great boiling valley", featuring bright yellow sulphur deposits and gas vents. Going from lush green slopes to the mineral hellscape of the crater in an instant is a breathtaking contrast, and one of my all-time favourite moments from my travels.

The Ropeway can obviously only run when the volcano isn't too active. When I first rode it in 2016, staff handed out damp tissues for passengers to cover their nose and mouth and protect themselves against the gases. After traversing the crater, the Ropeway continues down the other side of the mountain to the North end of Lake Ashi, where one would continue a tour by boarding one of the "pirate ships" that cruise on the lake.

Schauinsland

Since it's been mentioned in the comments on the previous post, we might as well have a look at the Schauinsland, a 1284 m peak on the outskirts of Freiburg im Breisgau. Only 7 km from the Schwabentor, the base is accessible by bus, before boarding a 3.6 km gondola lift ot the summit.

Opened in 1930, the Schauinslandbahn was the first gondola lift built for continuous operation, with the cabins running through each end station at slow speed to turn around while letting passengers off and on. The cable car takes the riders up the hill, offering panoramic views of the Black Forest. And then there's the view from the tower at the summit... I visited in summer, but it must be fantastic in winter too.

The cable car is not the only transport infrastructure to be found on the mountain, as mines operated there until the mid-20th century, so some mining railways with preserved vehicles can be found. Some of the tunnels can be visited (though writing this post reminds me, I haven't been inside yet).

Sangaku Saturday #5

This is it, we've reached our first full sangaku problem! (At least one that I've seen on a real-life tablet.)

We set up the tools in previous posts, so I'll let you work this one out by yourselves: given two circles which are tangent to each other and tangent to a same line, what can you say about the radii of the three smaller, light-coloured circles?

Freiburg's Schwabentor

The Germany city of Freiburg im Breisgau, on the transition between the Rhine valley plains and the hills of the Black Forest, was part of the Duchy of Swabia until it dissolved in the 13th century due to the ducal line going extinct. It was around this time that its "Swabian Gate" was built at the Eastern edge of the town, facing the Swabian heartland.

Like Schaffhausen's Schwabentor, it has undergone upgrades and downgrades, taken damage and been restored over time. The current illustrations on the tower include St George slaying the dragon (1903) on the outside, and a merchant with a cart (first painted in 1572) on the inside, just visible in the picture below.

Freiburg's Altstadt has many gorgeous, colourful houses decorated with trompe-l'oeil facades. An effort has also been made to preserve the little rivers in the streets, known as Bächle. Local superstition says that anyone who accidentally steps in a Bächle will marry a local - unusual to see a place that values clumsiness!

Schaffhausen's Schwabentor

Schaffhausen has a great preserved historical centre. One of the entries to this would have been the Schwabentor, the Gate of Swabia, and indeed, it faces North, towards the southwestern area of Germany. Built in 1361, it burned down in 1932, and a couple of curious features were added to it during restoration.

As I took photos, a local woman in a car stopped at the red light and told me to "keep my eyes open". What? "Lappi tue d'Augen uf, that's what it says on the tower". I noticed it just after crossing back over.

When the tower was restored in the 1930s ("Renoviert 1933" is just visible above the relief), a road junction had appeared before it, and this sign was added to warn people walking around near the Schwabentor.

Another addition are the clocks, each surrounded by a painting which are clearly 20th-century works. Carl Roesch's tableaux are called Kosmos on the South side, Kreislauf ("Cycle") on the North side, and they depict our lives in the vastness of space, and subject to the inexorable march of time, and Death can be seen at the top of the clock above: modern style it may be, but the symbols are classics.

Sangaku Saturday #4

In the previous info post, we went over the debate on the religious aspect of sangaku, and the fact that the absence of prayers on these tablets was more puzzling to some than the mathematics. As such, the tablets are not ema prayer tablets, but donations, which usually don't feature prayers on them. Case in point, some consecrated sake and French wine seen at Meiji-jingû in 2016.

Beyond wishing for good fortune and health, such donations serve two very worldly purposes: to contribute to the life and prestige of the shrine or temple (having a famous contributor makes the shrine famous by association), and to advertise the donor in return, as their name is on display. See this large torii at Fushimi Inari Taisha paid for by TV Asahi (テレビ朝日).

With that in mind, Meijizen's cynical comment from 1673 that sangaku aim "to celebrate the mathematical genius of their authors" may not far from the truth. The authors of sangaku are looking to gain notoriety through the publicity that the shrine or temple provides. But was the bemused Meijizen the target audience?

More on that in a couple of weeks. Below the cut is the solution to last week's problem.

The solution to the first problem (below the cut in this post) is the key. Name K, L and M the intersections of the three circles with the horizontal line. Then, by using that previous result,

Indeed, as in that problem, we can construct three right triangles, ABH, ACI and BCJ and apply Pythagoras's theorem in each.

Now, it suffices to note that KL = KM + LM, so

or, dividing by 2*squareroot(pqr), we get the desired result:

Inverting and squaring this yields the formula for r:

This gives us the means to construct this figure on paper using a compass and a marked ruler. Having chosen two radii p and q and constructed the two large circles (remember that AB=p+q) and a line tangent to both, placing M and C is done after calculating the lengths IK=CM=r and IC=KM=2*sqrt(pr).

Japan's rail speed record holder: 300X

Sticking with the Tôkaidô Shinkansen and the SCMaglev & Railway Park, this is the (highly abridged) story of the fastest conventional train in Japan.

Following privatisation and sectorisation in the 1980s, and seeing France and Germany take the lead in the high-speed train department, the three JR companies that had Shinkansen lines set about catching up to offer 300 km/h services where they could. The aerodynamics and sheer weight of the venerable 0 Series and its derivatives weren't going to cut it, so each company designed a prototype train to test new technologies.

JR Tôkai's solution was 300X, officially Shinkansen Class 955 - numbers starting with 9 are trains not open to the public, either prototypes or work trains like Class 923 "Doctor Yellow". Launched two years after JR West's WIN350 and JR East's STAR21, it featured two radically different end cars. The more elegant one, in my opinion, is on display at JR Tôkai's museum in Nagoya, while the other is preserved at JR Group's research centre in Maibara. The intermediate cars have all been scrapped.

The three prototypes took turns to hold the national rail speed record, and, 300X being the last, it took the record last, and holds it to this day. We mentioned the fact that the Tôkaidô Shinkansen still had too many relatively tight turns, but the Maibara to Kyôto stretch is the best part, and that's where this train hit 443 km/h in 1996. This video may, or may not, be that run, but it still looks very fast - note the unusually large, "flying saucer" pantograph cowlings.

Unless JR East decide to go completely bonkers with their ALFA-X prototype, it's unlikely that the record is going to be beaten any time soon. It's not in the spirit of these trains, they are pure test beds and run quite extensively with the aim of increasing service speeds. Records also require special preparation of the tracks, which is why the French TGVs made their 1990 and 2007 record runs before the opening of a brand new line.

But JR Tôkai have gone much faster with their Maglev programme, which holds the world speed record for passenger trains outright with 603 km/h. Behind 300X at the museum is a predecessor of that record holder, MLX01, the first Maglev train to clock over 500 km/h. Again, this is not (just) showboating, the lengthy test programme's main aim is to prove that consistent service at very high speed with this technology is feasible, so that the Maglev Chûô Shinkansen can achieve this when it opens (if Yamanashi-ken can agree on a route).

Wow, I basically forgot the Nishi-Kyushu Shinkansen in my run-down at the end! But yes, it is a complicated situation, with a stretch of line isolated from the rest of the network (there's that gauge difference explained above), and Saga-ken disagreeing on how to build the connection to the main Kyushu line. No clear plan yet apparently. :(

60 Years of the Tokaido Shinkansen!

On 1 October 1964, a railway line like no other opened. Connecting Tôkyô and Ôsaka, paralleling an existing main line, the Tôkaidô New Trunk Line had minimal curves, lots of bridges, zero level crossings. Striking white and blue electric multiple units, with noses shaped like bullets some would say, started zooming between the two cities as at the unheard-of speed of 210 km/h.

This was the start of the Shinkansen, inaugurating the age of high-speed rail.

The trains, with noses actually inspired by the aircraft of the time, originally didn't have a name, they were just "Shinkansen trains", as they couldn't mingle with other types anyway due to the difference in gauge between the Shinkansen (standard gauge, 1435 mm between rails) and the rest of the network (3'6" gauge, or 1067 mm between rails). The class would officially become the "0 Series" when new trains appeared in the 1980s, first the very similar 200 Series for the second new line, the Tôhoku Shinkansen, then the jet-age 100 Series. Yes, the 200 came first, as it was decided that trains heading North-East from Tôkyô would be given even first numbers, and trains heading West would have odd first numbers (0 is even, but never mind).

Hence the next new type to appear on the Tôkaidô Shinkansen was the 300 Series (second from left), designed by the privatised JR Tôkai to overcome some shortcomings of the line. Indeed, the curves on the Tôkaidô were still too pronounced to allow speeds to be increased, while all other new lines had been built ready for 300 km/h operations. But a revolution in train design allowed speeds to be raised from 220 km/h in the 80s to 285 km/h today, with lightweight construction (on the 300), active suspension (introduced on the 700 Series, left) and slight tilting (standard on the current N700 types).

Examples of five generations of train used on the Tôkaidô Shinkansen are preserved at JR Tôkai's museum, the SCMaglev & Railway Park, in Nagoya, with the N700 prototype lead car outdoors. It's striking to see how far high-speed train technology has come in Japan in 60 years. The network itself covers the country almost end-to-end, with a nearly continuous line from Kyûshû to Hokkaidô along the Pacific coast (no through trains at Tôkyô), and four branch lines inland and to the North coast, one of which recently got extended.

東海道新幹線、お誕生日おめでおう！

60 Years of the Tokaido Shinkansen!

On 1 October 1964, a railway line like no other opened. Connecting Tôkyô and Ôsaka, paralleling an existing main line, the Tôkaidô New Trunk Line had minimal curves, lots of bridges, zero level crossings. Striking white and blue electric multiple units, with noses shaped like bullets some would say, started zooming between the two cities as at the unheard-of speed of 210 km/h.

This was the start of the Shinkansen, inaugurating the age of high-speed rail.

The trains, with noses actually inspired by the aircraft of the time, originally didn't have a name, they were just "Shinkansen trains", as they couldn't mingle with other types anyway due to the difference in gauge between the Shinkansen (standard gauge, 1435 mm between rails) and the rest of the network (3'6" gauge, or 1067 mm between rails). The class would officially become the "0 Series" when new trains appeared in the 1980s, first the very similar 200 Series for the second new line, the Tôhoku Shinkansen, then the jet-age 100 Series. Yes, the 200 came first, as it was decided that trains heading North-East from Tôkyô would be given even first numbers, and trains heading West would have odd first numbers (0 is even, but never mind).

Hence the next new type to appear on the Tôkaidô Shinkansen was the 300 Series (second from left), designed by the privatised JR Tôkai to overcome some shortcomings of the line. Indeed, the curves on the Tôkaidô were still too pronounced to allow speeds to be increased, while all other new lines had been built ready for 300 km/h operations. But a revolution in train design allowed speeds to be raised from 220 km/h in the 80s to 285 km/h today, with lightweight construction (on the 300), active suspension (introduced on the 700 Series, left) and slight tilting (standard on the current N700 types).

Examples of five generations of train used on the Tôkaidô Shinkansen are preserved at JR Tôkai's museum, the SCMaglev & Railway Park, in Nagoya, with the N700 prototype lead car outdoors. It's striking to see how far high-speed train technology has come in Japan in 60 years. The network itself covers the country almost end-to-end, with a nearly continuous line from Kyûshû to Hokkaidô along the Pacific coast (no through trains at Tôkyô), and four branch lines inland and to the North coast, one of which recently got extended.

東海道新幹線、お誕生日おめでおう！

A few details from Singen Stadtpark

This bridge is not particularly big or special, but it cost YES Marks in the early 1920s, as post-WWI Germany went through a phase of hyperinflation.

Sangaku Saturday #3

Another problem this week, adding to the configuration we looked at previously.

Specifically, given two circles tangent to each other and tangent to a same line - these circles have respective centres A and B, and respective radii p and q -, we want to construct the circle tangent to both of the original circles, and tangent to the line beneath them.

Can you prove that the radius of this third circle, denoted r, satisfies

and deduce a formula for r as a function of p and q?

Help below the cut, answers next week.

Hint. Name K, L and M the intersections of the circles with the line below, and use the previous result on each pair of circles to get the lengths KL, KM and LM. One of these lengths is the sum of the two others.

Moissac: home to the world's best grapes (IMO)

Located on the river Tarn in southwestern France, Moissac is most famous for its grapes, specifically Chasselas. This green, sweet and thin-skinned grape is just marvellous, my personal favourite, and Chasselas de Moissac season is a sure sign that Autumn is nearly here.

When I saw that Moissac wasn't too far from where I was living at the time, of course I had to visit, and as the photos demonstrate, it was well worth the trip on a sunny, unseasonably warm early November day (I ate lunch on the terrace at the restaurant, that's insane for November!).

The heart of the town is its 11th-century Romanesque abbey. The monks there had a vineyard to tend to (what else?), and as the railways and tourism developed in the 19th century, Moissac envisioned becoming a "uval resort", in the same vein as thermal or seaside resorts, only with grapes as the centre theme. A full uval complex didn't come to fruition, but the local grapes began to be transported out of the region for the rest of France to appreciate. Cheers!

A potential unfulfilled: the Intercity 225

As I had some time to wander around before catching the Eurostar back to France, I checked out the trains at King's Cross station. To my slight disappointment, there wasn't a huge amount of variety on display: Azuma, Azuma, Azuma... They're nice trains, don't get me wrong (built by Hitachi, using the same base as JR Kyushu's 885 series), but that's all there was. Still, I decided to check out all the platforms, and, at the far end, hidden behind an Azuma, there it was.

The star in train books during my childhood was the Intercity 125 or High Speed Train (HST), a 125 mph-capable Diesel-powered set, which, I think, still holds the world record for the fastest Diesel passenger service. I would have loved to see one when visiting England, but this was just as good. In fact, I had seen it out of the window while riding into London, taken a crappy photo and thought "oh well, never mind", only to see it had followed us in.

In the early 90s, the Intercity 225 was touted as the next big thing: all-electric, capable of running at 225... km/h (that's 140 mph, using different units was admittedly a bit disingenuous), designed to receive a tilting mechanism later on, completing the Advanced Passenger Train's redemption arc. What could go wrong?

Not long after the introduction of the Intercity 225, Britain's railways were privatised, with the typical lack of ambition for service that it brings. No private company was going to invest in the infrastructure and upgrades to allow the train to reach its full potential; meanwhile France and Germany were expanding their 250-300 km/h networks. Instead, these trains were limited it to 125 mph - the same as the HST, just on electrified lines. Worse still, it was one of these sets that met with the consequences of the privatised rail maintenance's culture of corner-cutting and outsourcing, on a broken rail at Hatfield in 2000.

From the outside looking in, I'm left with a bitter sense of "what could have been" for this train. Perhaps a rail fan from the UK could say more about what they feel the Intercity 225's legacy would be. At least its successor, the Azuma, has the fact that it's bi-mode (Diesel and electric) to shout about.

Still great to see one and its "so 90s" design in the flesh! LNER have also given the trains their original livery back, except with a burgundy main body colour instead of the original graphite grey, while the locomotive was in a special commemorative livery for the Battle of Britain Memorial Flight.

For more on the Intercity 225: Ruairidh MacVeigh's video

Sangaku Sunday #2

As the tags in a reblog by @todayintokyo indicated, I waffled about what we'll do in this series in the first post without really defining its main object!

Sangaku are wooden tablets on display at Shintô shrines or Buddhist temples in Japan, featuring geometry problems and their solutions, usually without proof. They started appearing in the Edo period, a particular time for the Japanese people and Japanese scientists. The votive role of these tablets has been debated as far back as the Edo period, as indicated by Meijizen who wrote in 1673:

"There appears to be a trend these days, of mathematical problems on display at shrines. If they were true votive tablets (ema), they should contain a prayer of some sort. Lacking that, one wonders what they are for, other than to celebrate the mathematical genius of their authors. Their meaning eludes me."

I feel the debate on their religious role is overrated. If you look at some food offerings at shrines today, I don't think you'll find a prayer on the bottle of tea or pack of rice, as the prayer is made at the time of offering. It likely is the same for sangaku tablets, which went on display with other offerings. But, as Meijizen hinted, they did have another purpose.

Until we expand on that, below the cut is the solution of last weekend's problem.

Place the point H on the line between A and C1 so that the distance between A and C1 is equal to r2. As the lines (AC1) and (BC2) are both perpendicular to the line (AB), they are parallel, and since AH=BC2=r2, HABC2 is a parallelogram with two right angles: it's a rectangle.

So the length we want, AB, is equal to HC2. The triangle HC1C2 has a right angle at the vertex H, so we can use Pythagoras's theorem:

HC1² + HC2² = C1C2²

In this equality, two lengths are known: C1C2=r1+r2, and

HC1 = AC1-AH = r1-r2 (assuming r1>r2, if not just switch the roles of r1 and r2)

Thus, HC2² = (r1+r2)²-(r1-r2)² = 4 r1 r2 after expanding both expressions (e.g. (r1+r2)² = (r1+r2)x(r1+r2) = r1² + 2 r1 r2 + r2²).

Taking the square root yields the result.

Where I grew up (initially): Great Chesterford

Going back to Great Chesterford with my current eyes was quite interesting. I hadn't realised (as no 6-year-old would) how pretty the village centre was, with many charming houses and thatched cottages. The nearest town, Saffron Walden, is even better, but I'd need to go back and visit properly. This time, we just passed through there to go to the shops - and pick up a bunch of biscuits and sweets I remember from my childhood!

Said sweets and biscuits are very nice, of course, but also a tad underwhelming. I remember feeling disappointed by the size of Party Rings the last time I bought some, and I had a similar sense of underwhelming when passing near the school. The wall along the street was much higher in my memory, as was the hill at the back of the playground - in my mind, it was a proper hill! But take into account the fact that I was so much smaller back then, and it all checks out, really!

The old school building itself was apparently built by a single person between 1845 and 1849. Chesterford has a very rich history, dating back to Roman times (and if nothing else on the topic, I remember dressing up as a Roman at school once), and the church dates back to the 13th century. The village's biggest claim to fame is probably having been the home of Germaine Greer, a feminist author from the 1970s, for a few decades.

The Reality Checkpoint

In the middle of Parker's Piece (no relation to the Thunderbirds character) in Cambridge, stands a lamppost. The only lamppost on the common, a beacon and a reference for anyone walking there at night. A bit like the lamppost in Narnia. A lot like the lamppost in Narnia in fact, as it serves as a boundary marker between the university and the town, two worlds with distinct notions of reality. That's one theory behind the name, the Reality Checkpoint.

Another theory suggests one should use the checkpoint to assess their clarity when going back from the pub, and this view certainly calls reality into question... Not to worry, the Ferris Wheel is just being dismantled.

This ornate lamppost has been restored in recent years, and improved with a Dinky Door. Well, I say "improved", but the note on the door says "on holiday, please check reality yourself"!

I mentioned a train accident that was local to the Strasbourg area - here's an air crash on Mont Sainte Odile that truly shocked the Alsace region. There is a memorial on the mountain, I should visit and pay respects some day.

First time in the Channel Tunnel!

Hard to believe, given that I have family on both sides of the Channel, that this month was the first time I used the Tunnel! For a long time, I've lived on the Western side of France and travelled in a car, so going to Calais to catch the shortest ferry links or LeShuttle never made sense compared to a relaxing six-hour crossing from a port in Normandy. Now I live in Eastern France and don't use a car, so the train is a no-brainer, and finally, I took the Eurostar from Lille to London.

On paper, the trip is amazing: just 90 minutes, roughly 30 on the French high-speed line, 30 in the tunnel, and 30 on High Speed 1 in England. Buuuuut... you need to get to the departure station around 60 minutes early for security and border checks, there's not a lot to do in the densely populated waiting area, and once on the train, I found it quite hard to relax in the hard, narrow seats under rather harsh lighting. While the ride was quick and operations felt reliable, the comfort of some regional trains has won me over more swiftly. That said, I've also been underwhelmed by the German ICE 3 (BR 407), which is the same Siemens Velaro D model as the Eurostar e320.

The Channel Tunnel turned 30 this year, with the French high-speed line connected to it upon opening and TGV-derived stock at the ready (now called the Eurostar e300, left), while the UK finished their high-speed line to London in 2007 (plaque at St. Pancras, right). Since then, it's been possible to go from London to Paris or Brussels in under two and a half hours (not counting security before boarding).

And there I was, starting to think I'd be riding the Seikan Tunnel before the Channel Tunnel!

Arashio-beya

The quickest way to witness some sumo wrestling is probably to watch a morning practice session in a stable (though we'd probably use the word "club" in Europe). Arashio-beya in Tôkyô is one such stable, with the nearly-daily practice watchable from the street.

On some days, wrestlers may come out to meet the spectators and pose for some photos. This happened on the day I was there.

While researching for this post, it appeared that these two wrestlers may be among the stable's most successful. Arashio-beya was founded in 2002, and has had four wrestlers reach the top division as sekitori. Their first one is retired and now manages the stable, and their second was Wakatakakage, who won their first major tournament in March 2022 - and who probably is pictured left (I'm confident it is him based on other photos, but I'm couching it slightly just in case I'm wrong). Wakatakakage is the youngest of three brothers who all wrestle for Arashio-beya, and one of his brothers is the third sekitori from the stable. The fourth and most recent is Kôtokuzan, probably pictured right.

For someone who knows absolutely nothing about sumo, looking back at that morning, it's neat to think I was in the presence of people who would fulfill their ambitions.

Sangaku Saturday #1

In this series, I'll try to put something up every Saturday or Sunday (depending on my plans and/or your time zone), either with a puzzle, a solution or some historical info on sangaku. If people find this interesting (and editing maths on this probably will be), we can work step by step to solving full sangaku problems.

Let's start with a puzzle, one of the most basic tools of the genre. Two circles, with radii r1 and r2, are tangent to each other and tangent to a same line.

This means that the distance between C1 and C2 is equal to r1+r2, the distance between C1 and A is r1, and the distance between C2 and B is r2. Moreover, the lines (AC1) and (AB) are perpendicular, and the lines (BC2) and (AB) are perpendicular.

Can you prove that the distance between A and B is equal to

???

Hints below the cut, questions possible in the reply section.

Take your time, I intend to show the solution next weekend.

Hints. Place the point H on the line between A and C1 so that the distance between A and H is equal to r2. Then the triangle HC1C2 is a right triangle with two sides of known length. A famous theorem gets the third length, which is equal to AB.

Walking in on the Nagoya Basho

While I saw Tokyo's sumo arena out of sumo season, I stumbled on an active sumo tournament last summer. July is the month of the Nagoya Basho, and the flags of the various participating sekitori (officially ranked wrestlers, all the names on the flags ending with the character zeki, 関) welcomed not only the spectators, but also the visitors to Nagoya Castle. That's quite the entrance!

I did see one or two sumo wrestlers out and about, and made nothing of it until I noticed the flags. That's when I put everything together regarding what a man at the subway had asked. "Sumô? Sumô?" That's literally all he said, no other attempt to clarify. Yes, I know what sumo is, but it seemed unlikely to me that was what he was talking about - we were, after all, just standing in the subway tunnels waiting for a heavy shower to pass, the topic didn't fit the context and what I knew, I was just going to the castle. So I just stuck to looking a bit dim, like I didn't understand (which, to be fair, I was, and didn't).

As a footnote, the Nagoya Basho will no longer be held inside the castle walls from 2025. It moves to a brand new arena just to the North.

Ryôgoku Kokugikan

It's sumo season in Tokyo! Though, to be fair, it's sumo season three months per year, as this arena, the Kokugikan in Ryôgoku, on the East bank of the Sumida-gawa two stops from Akihabara on the Chûô-Sôbu line, hosts half of the year's six major tournaments.

It wasn't open when I visited Tokyo, so I didn't see inside, but even then, there are apparently, and unsurprisingly, a lot of sumo-related places to visit in Ryôgoku, like Ekô-in temple... and I missed them all! Well, apart from the odd statue.

I went to Ryôgoku area without a real plan, I wandered around and found some interesting places I'll get to another time, but one thing I think I planned was to try the "lunch of champions", the classic stew for sumo wrestlers: chankonabe, or chanko for short. It was rich and copious, as you'd expect, and, as I remember, I didn't quite finish it.

Approaching 100 posts - yes I know, this one's adding to it, but with asks and reblogs possible on Tumblr, I consider the companion Instagram to be a more reliable publication counter, not to mention I have plans for content that will only be on Tumblr (sangaku solving). I also need to clean up some tags before the task gets too daunting, with the aim to get some major themes rolling and provide direct links to them in the menu bar.

Thanks for likes left so far, I hope you'll enjoy what's next!