Hormone Is Apparently Short For ホルモン焼き, Horumon-yaki, A Dish That Originated In Ôsaka. It

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.

Schwarzwaldpokal!

Finally, as someone who used to watch a lot of it, I've been to a ski jumping event in person! And it wasn't just jumping, it was nordic combined, which sees a jump followed by cross-country skiing; the same people, doing both. It happened today at Schonach, in the Black Forest, next to Triberg and all those cuckoo clocks.

The hill was built in October 1924, and is therefore celebrating its 100th anniversary, hence the big "100" on the knoll. Much younger is the concept of the Womens' Nordic Combined World Cup - it only exists since 2020! Ski jumping has been the final frontier for women in winter sport, so it was great to see men and women compete.

The longest jump of the day was 102 m, twice, for Norway's Jarl Magnus Riiber and Austria's Thomas Rettenegger. In the womens' contest, Germany's Maria Gerboth took the lead with 95 m.

The competitions follow the Gundersen format, in which the jump comes first, and the gaps in points after that equate to time handicaps at the start of the cross-country race. Above left are the time penalties for some in the womens' race, and right, the start, with the top three starting almost together, while the others must wait. The race is effectively a pursuit, with the athlete crossing the line first being the winner.

In the end, Norway were unbeatable today. Despite starting with a 25-second handicap, Ida Marie Hagen took the lead of the womens' 4 km race in the middle of the first lap and didn't look back, celebrating her upcoming win in the final corner (left picture)! Nathalie Armbruster got the host nation's only podium of the day, ahead of the Kasai twins from Japan.

The mens' race was longer, at 10 km, and required more effort management. On the final lap, Jarl Magnus Riiber lost his long-held lead to Jens Luras Oftebro (right picture), who would defeat Austria's Johannes Lamparter in the final sprint to the finish.

All in all, a great day. Fresh in the morning, especially with the hill in shade, which also made photos more difficult, nice in the sunshine in the afternoon, the races were easy to follow (it was surprising how much of the cross-country course we could see), the atmosphere was really pleasant, and I wasn't going it alone for a change!

A quick post in response to Ferrari's second consecutive overall win at Le Mans, with a few sights from the manufacturer's home town, Maranello. Everything here is Ferrari: their road car factory with the classic entrance gate (above), the more modern F1 team base, the Fiorano test track, the Scuderia museum, the statues to founder Enzo Ferrari and the Prancing Horse, a park featuring Ferrari's most famous road car models...

Yep, everything is Ferrari here. Except, well, this store front apparently. It's rather gutsy to show off a Lambo badge here, but then again, historically, middle fingers to Ferrari was what Ferrucio Lamborghini was all about!

Hikone Sawayama: summit & castle

It's not about what is there today, as much as it's about what was there. Sawayama was the original location of Hikone Castle, and it is quite possibly the most important castle in Japan to have been completely lost, as it was the castle of Ishida Mitsunari, the leader of the Western Army which lost the battle to unite Japan following the death of Toyotomi Hideyoshi. There are so few traces of the castle, no obvious tell-tale structures... This small altar may trace its roots back to the days of the castle, or maybe not, but this is just about it.

Sawayama Castle was thoroughly dismanted after 1600 following the defeat of Ishida, as the new lord of the area, Ii Naomasa, appointed by the victorious Tokugawa clan, relocated the castle to a smaller hill closer to Lake Biwa. Hikone Castle, which still stands today, basically recycled the materials from Sawayama, and the view of the "new" castle complex and the lake is the main draw for hikers today.

The summit offers good views of the mountains on the other side too, with the industrial complexes near Maibara, most noticeably Fujitec and their 170 m-tall elevator test tower, in the foreground.

C'est avec grand plaisir que je présenterai le mardi 16 avril à la Maison Universitaire France-Japon de Strasbourg une conférence sur la géométrie pendant la période d'Edo, avec en support le sangaku de Kashihara. Entre grande Histoire et petits calculs. Lien vers les détails 4月16日(火)、ストラスブール市の日仏大学会館に江戸時代の算額についてコンファレンスをします。楽しみにしています！ Looking forward to giving a conference on Edo-period geometry on 16 April at Strasbourg's French-Japanese Institute. Expect a few posts about Kashihara around then. Has it really been 6 years?...

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).

Fort National, Saint Malo

Work is starting to pile up on my end, so I have to make this a quick one.

This is Fort National, a building we saw in the post on MV Bretagne. It was built in the late 17th century by Vauban - one of many, many, many projects he designed for Louis XIV's grand plan to fortify the French border. It was called Fort Royal, a name which would stick for little more than a century, before the Revolution banished any mention of royalty. It became Fort Républicain, then Fort Impérial under Napoleon, and finally Fort National after Napoleon III's Empire was defeated by Prussia in 1870. This regular name changing was derided by a local nickname, "Fort Caméléon", but it also give a glimpse into France's political history.

The rock on which the fort sits, known as Îlette (the small island), has quite a sorry history. Before Vauban, it was apparently used as an execution ground by local lords, and during World War II, the occupying Nazis used it as a prison during Allied bombings - fully expecting the fort to be bombed.

Today, the fort is privately owned, but visits are allowed on occasions.

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!

French and German cross-border railcars

Just on the French side of the border, Wissembourg station sees French TERs arriving from Haguenau and Strasbourg, meeting German Regionalbahn from Landau and Neustadt. When a French service doesn't cross the border itself, SNCF and DB services are often synced up, giving us the chance to see both companies' cross-border efforts side by side.

The B 85500 is a brand-new bi-mode (electric and Diesel) multiple unit from the Alstom Régiolis family. While not the first international Régiolis - a tri-voltage electric version runs between Évian and Geneva -, the B 85500 adds autonomous Diesel power. With 30 units on order, it aims to revive and/or intensify cross-border routes into Germany. I was under the impression there was a bit of a gathering at the front end of the train, maybe local politicians marking the type's first visit to Wissembourg?

On the German side meanwhile, we have a standard railcar for what DB regard as a relatively low-density non-electrified regional route, which was closed to passengers for over 20 years between 1975 and 1997. The BR 628/928 (628: power car, 928: trailer car) is a 1980s design. Besides the lack of low floor, there's not a lot wrong with them, and they have comfortable, current DB Regio interiors. More recent types have been used, and if a plan to electrify Landau and Winden stations to allow charging of battery-EMUs goes ahead, there could soon be the latest trains on the German side of Wissembourg station too.

Which brings us to our "I beg your pardon" of the week:

A year ago, I was taking off for Japan

No such five-week adventure this year, but I have the chance to relive the smell and taste of Japan courtesy of Yuki, Kazu, Asaka and Maiko who I met in Paris last month, and who gave me a lot to eat and drink! So, to mark the anniversary, I decided it was time to have nice things...

Kitsune udon with nori, ebi and yuzu senbei

The kitsune udon floored me. The smell of the soup base was enough to transport me, I couldn't get enough of that savoury scent.

Matcha KitKat, dried nattô and konbucha

I hadn't tried nattô in Japan, but I'd read it had a bit of a reputation. So I was a little apprehensive trying the nattô morsels, but a little less so when I read that dried nattô is actually milder than the real thing. And I like it! And so do colleagues I've shared it with!

The konbucha is... interesting. First, do not confuse with kombucha. I know, I know, it's very confusing. This konbucha is kelp tea, a tea made with algae, combined with plum and extra salt. It kind of tastes like the sea, only milder... It's pleasant in its own way, though I'd probably make the next one less strong.

And if you want to run through last year's voyage, I did a travel blog here, but I'll also go through some places here at a leisurely pace (I've already reviewed Kushimoto, Hikone Sawayama and Nagahama -to name what I can remember- from that trip here).