Hikone Sawayama: Base

I promised more impressive views from the hills above Toba, and here they are. They're not very hard to reach: the Hiyoriyama circuit is only a couple of kilometres long around the station and involves climbing around 50 m. Hinoyama is further away, further South and a little higher.

The views of the coastline at Toba were good enough for Hiroshige to use in his Famous Views from the Sixty-Odd Provinces to illustrate Shima province (though there wasn't much else, I presume, Shima province was tiny, it was just Toba and the neighbouring town of Shima - also Shima is 志摩 and not 島 "island").

Beyond the islands near Toba, lies the mainland again, the Southern part of Aichi prefecture across the Ise Bay (Minamichita and Tahara), which the car ferry in the above picture traverses.

As any jagged coastline should, Shionomisaki has a lighthouse. Many were built across Japan during the modernisation of the Meiji era, and Kushimoto town has two.

After passing through the shrine in this picture, a trail continues to the left to a cape out of frame. People from the nearby port of Koza would go out there to watch for the arrival of pods of whales when their migration was due, and return home to basically say that hunting season had begun.

As such, Shionomisaki has always had a bit of a lookout role. And, according to the Akari no Moribito story, this guy below will be looking out for us against the forces of darkness in the future! The project has aimed to give all of Japan's main lighthouses a character, complete with a voice actor! I don't understand much, but on the surface, I think it's neat.

Another short one today, just a couple of Christmas decorations from Strasbourg. The "tree of cathedrals" was, as far as I can remember, new for last year in front of the station, and is back again this year. I definitely should talk at length about the cathedral at some point... Not to worry, normal nerdy and rambling service will soon be resumed.

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for "Multi Amenity eXpress", was the second and so far last double-decker high-speed type operated by JR East, and was withdrawn in 2021.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).

The CFTR's steam train

In a serious rain shower, the Chemin de Fer Touristique du Rhin's train stops at Volgelsheim station, where the association that maintains the line has its museum. The train itself is made up of former Austrian carriages built in the 1920s with what I suspect were 2nd and 3rd class seating.

The locomotive is a T3 tender built around 1900 at Graffenstaden, just South of Strasbourg, for the Alsace-Lorraine Railways. At the time, the region was under Imperial German control, hence the Eagle logo and German inscription "Elsaß-Lothringen" above the number. The association has two of these, nicknamed Berthold and Theodor. These are supported by small Diesel engines; on our trip, one of these hauled the train to the depot, where the extent of the association's work is on display. The active engines are maintained here, while others are being restored.

Peut-être un jour? - To run again one day?

The town of Breisach, on the other side of the Rhine and therefore in Germany, is visible, and a boat carries passengers across the river from near the depot.

The conference went well, as far as I can tell, so here are a couple of low-sun views of Kashihara's preserved Edo-period area, Imai-chô, as an outro. The first building seems to be operating as an art gallery (maybe?), while the other is a neat little temple. Both are on the same street, 大工町筋, which Google Translate says could be Daiku-chô suji or Daiku-machi suji... or it could be something else, I don't remember reading the name myself on site.

Different place next.

To build or not to rebuild? The case of Heijô-kyô

In 710, the Imperial court moved from Kashihara to Nara. Just over 80 years later, the capital once again changed location, settling in Kyôto where it would stay for a millennium. The palace in Nara was abandoned, and in the 1000 years that followed, the grounds were used for menial things. However, a few structures have been rebuilt in recent years, such as the main audience hall in the background, which was completed in time for Heijô-kyô's 1300th anniversary.

Besides a museum housing artefacts from its 8th-century heyday, the palace is seen here hosting some art exhibits, and a play is underway, just visible in the above photo. Of course, I didn't understand a word of it...

This view of the Suzaku South gate shows how recently interest was given to the site: by the time excavations had begun, a railway was already running through it! This is the Kintetsu line, opened in 1914. As such, trains between Ôsaka and Nara pass directly through this historic site.

The trains the E10 will replace

Following the announcement of a new Shinkansen type due to enter service on the Tôhoku Shinkansen in 2030, let's have a quick look at the oldest trains on the line, that will be replaced.

The E2 is the oldest high-speed train type that JR East owns, and many examples have already been retired. Built for the slower Jôetsu route to Niigata, they operate the Yamabiko and all-stop Nasuno services.

The E10s will also replace E5 sets. This sounds unreal to me, the E5 is the pinnacle of Shinkansen, still the only train running at 320 km/h in Japan (coupled with the E6, when the couplings work), and still young, having been introduced in 2011! Granted, by 2030, the first E5s will be nearly 20 years old, but they're probably not going to disappear completely in one go.

Photos taken at Utsunomiya station (as far North as I've ever been in Japan).

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).

More views of Schonach

A quick post today as I don't have much time... So here are some views around the ski jumping hill and cross-country skiing venue for this weekend's Schwarzwaldpokal.