Expo 70 Japanese Garden

I'm a bit low on inspiration and time today (work starting to pile up), so here's a train in the snow from the recent trip to Mulhouse and Thann. The train itself is a bi-mode Regiolis B84500 set, waiting at Mulhouse as the Sun sets.

Port du Crouesty

We start the new year where we left off in the last, on Presqu'île de Rhuys, but one year later. Or should that be two? The previous post was from the stormy 2013-2014 New Year celebrations, whereas this covers the calmer 2014-2015 change with most of the same friends, and our walk around the tip of the peninsula and Port du Crouesty.

These aren't the best photos given the relatively low light, but also this was before my current camera. Still, point it towards the sunset and the result isn't too bad.

I failed to mention this in the original post, but Meiji-jingû is also a high point of sumo culture. Newly promoted yokozuna, the highest rank in the sport, perform their first ring entry dance there, before their first tournament at that level. This would be their first appearance with the "horizontal rope" (that's what yokozuna means), in the shimenawa style, around their waist.

That's just happened, with the 74th yokozuna making his debut.

NHK WORLD

Hoshoryu performs first ring-entering ceremony as yokozuna | NHK WORLD-JAPAN News

About 3,500 people gathered at Meiji Jingu shrine in Tokyo on Friday to see sumo yokozuna grand champion Hoshoryu perform his first ring-ent

The New Year shrine visit: Meiji-jingû

A common New Year ritual in Japan is to go to a shrine, possibly a large one, a visit known as 初詣, hatsumôde. NHK reported that Meiji-jingû in particular was very busy. Of course, I would avoid that, so here we are with a more tranquil time, closer to the Autumn festival.

Meiji-jingû was, as its name suggests, founded to enshrine the spirit of Emperor Meiji after his death. The first Emperor of the post-Edo period presided over sweeping societal reforms, such as the abolishment of classes like the samurai, as Japan re-opened to the rest of the world and sought to catch up. The Imperial attachment is symbolised by the Chrysanthemum crests on the torii.

One of the things that can be wished for at Meiji-jingû is a happy marriage and family life, particularly at this dedicated spot with two camphor trees planted in 1920, linked with sacred rope - these are called "married trees", 夫婦楠 Meoto Kusu.

The train to Kushimoto: a JR West 283-series Kuroshio express. The sets are getting on a bit, they were introduced in 1996 and the livery could do with a refresh, but the "dolphin nose" is distinctive, and I, for one, really like it. They're also quite rare, only 4 sets exist.

The Kisei Main Line is essentially the coastal route from Nagoya to Wakayama. The full trip around the Kii peninsula takes 8 hours by express train, with a change required at Shingû or Katsuura, but it's definitely scenic as it gets very close to the sea (photo between Kii-Tahara and Koza).

Retired: the E4 and 700 Shinkansen

While we were on the topic of trains which will soon be retired, here are two that are out of service today, that I got to see in 2016. These are the 700 Series and the E4 Max Series.

The E4 Max, which stands for "Multi Amenity eXpress", was the second and so far last double-decker high-speed type operated by JR East, and was withdrawn in 2021. With a top operating speed of 240 km/h, they were mainly used on the Jôetsu line between Tôkyô and Niigata. They featured some "commuter" class rooms with 3+3 seating, and two E4 Maxes coupled together could carry a total of over 1600 passengers, the highest capacity for a high-speed service.

But of course, all people will talk about is the very distinctive conk. I didn't take as many pictures of trains at the time, so I didn't walk around to get a better view of this unique vehicle.

The original 700 Series was the first Shinkansen model that JR Tôkai and JR West cooperated on, for joint service on the Tôkaidô and San'yô lines between Tôkyô, Ôsaka and Hakata. Combining knowledge acquired by each company with the 300 and 500 Series, it has formed the basis of new models since then.

To be precise, the 700s which are now retired are the white and blue, 16-car sets, withdrawn in March 2020. Covid caused the cancellation of the type's celebratory final run on the Tôkaidô line. Eight-car trains painted in grey and branded "Hikari Rail Star" can still be found on the San'yô Shinkansen, as well as JR West's Doctor Yellow inspection train (JR Tôkai's set was recently retired).

Feeling rather non-committal today, so here are some flowers from the Expo '70 Commemoration Park near Osaka. This is probably going to start a mini-series because the place is huge, so more information will come later.

The Fog on the Rhine (is all mine, all mine)

After three weeks of marking, I finally managed to get out of my hole in late January. I was beckoned out by dense fog, seizing the chance to enjoy the misty atmosphere. When I reached the park that straddles the French-German border, I found it on the edge of a fog bank, with haze on one side of the footbridge and perfectly clear skies on the other.

While not among the most outstandingly beautiful parks, the Jardin des Deux Rives has things to offer on both sides of the border, and, just for that ability to hop over to another country, it ranks very high on the cool factor.

Not that the birds would know. They were just taking in the winter sunlight while they could.

The fortifications of Landau (Pfalz)

Like other towns on the edge of Louis XIV's Kingdom of France at its peak in the late 17th century, Landau, now in Germany, received the Vauban treatment, transforming the town into an up-to-date garrison and fortress: both the town's ramparts and fort, situated in the North-West corner, were built with in characteristic geometric star shape of the time.

Control of Landau alternated between France and the local lords affiliated with the Holy Roman Empire as battles and sieges between 1702 and 1713 went in favour of one then the other, and remained part of France for another century, as an enclave, until Napoleon's defeat of 1815, when it was handed to the Kingdom of Bavaria.

Today, there is little remaining of the town's ramparts, while some ruins of the fort still stand. Similarly to the Citadelle in Strasbourg, around the walls is a park, while inside is the university and a zoo. Visible in the above shot is a tower built much later than the walls, in 1910, to celebrate Otto von Bismarck - no defensive function whatsoever.

Sangaku Saturday #8

Having established that sangaku were, in part, a form of advertisement for the local mathematicians, we can look at the target demographic. Who were the mathematicians of the Edo period? What did they work on and how?

The obvious answer is that the people in the Edo period who used mathematics were the ones who needed mathematics. As far back as the time when the capital was in Kashihara, in the early 8th century, evidence of mathematical references has been uncovered (link to a Mainichi Shinbun article, with thanks to @todayintokyo for the hat tip). All kinds of government jobs - accounting, such as determining taxes, customs, or engineering... - needed some form of mathematics. Examples above: 8th-century luggage labels and coins at the Heijô-kyô Museum in Nara, and an Edo-period ruler used for surveying shown at Matsue's local history museum.

As such, reference books for practical mathematics have existed for a long time, and continued to be published to pass on knowledge to the next generation. But sangaku are different: they are problems, not handbooks.

More on that soon. Below the cut is the solution to our latest puzzle.

Recall that SON is a right triangle with SO = 1 and ON = b. These are set values, and our unknowns are the radii p, q and r of the circles with centres A, B and C. While these are unknown, we assume that this configuration is possible to get equations, which we can then solve.

1: The two circles with centres B and C are tangent to a same line, so we can just re-use the very first result from this series, so

2: Also recalling what we said in that first problem about tangent circles, we know that

Moreover, PA = AO - OP = AO - CQ = (p+2*q) - r. Thus, using Pythagoras's theorem in the right triangle APC, we get a new expression for PC:

since 2(p+q)=1 (the first relation). Equating the two expressions we now have of PC², we solve the equation for r:

again using the first relation to write 2q-1 = -2p.

It only remains to find a third equation for p to solve the problem.

Towers and trains at Oberwesel

Downstream from Bacharach and Kaub seen in the most recent posts, Oberwesel is a gorgeous town on the left-hand side of the Rhine, with many of its medieval walls and towers still standing. The railway was built alongside these walls near the river, and even goes between two towers, the Katzenturm (left) and Ochsenturm (right). Add the hills in the background, and it is certainly a spectacular train spot.

Here is another tower, the Haagsturm, in a view from the station platforms. (I just got off that train and failed to position myself in time to get the sign out of the way bottom left.) The two trains shown were the only types visible that day, as the intercity traffic was diverted to the other side of the river via Wiesbaden.

Further from the river, another section of town walls and towers runs through the hills. In the centre of the picture above, taken from the short but steep Elfenlay trail, is the Kuhhirtenturm (with raised drawbridge), with St Martin's Church rising behind it.

Oh alright, have a wider view from the Elfenlay.