A Quick Post In Response To Ferrari's Second Consecutive Overall Win At Le Mans, With A Few Sights From

Japan's biggest shimenawa: Izumo Taisha Kagura-den

We've seen larger and larger sacred ropes in our previous posts, and here's the largest of all: the shimenawa adorning the Kagura-den at Izumo Taisha. It is 13.5 m long and weighs 5 tons!

Shimenawa ropes are made with hemp or rice straw. This shot shows just how densely packed Izumo Taisha's shimenawa is - it's almost like a tree trunk, truly an impressive and imposing feature.

Here and in previous examples, we can see folded paper shide streamers, another symbol of sacred items in Shinto, on the first picture. Knots also appear, particularly on the ropes on the Meoto Iwa at Futami, as paper would not fare well by the sea... These ropes and streamers indicate a demarcation line between our world and the realm of kami spirits.

The Kagura-den is a hall just outside the main compound of Izumo Taisha, to the West. It was built to house kagura rituals, traditional dances which retell the stories of the early gods. As Izumo, formerly in Iwami province, is one of the most ancient shrines in Japan, Iwami Kagura is one of the major forms of the dance.

As a bonus, here's a train decorated with characters of Iwami Kagura.

Golden Week has begun in Japan, and this quick succession of public holidays ends with Children's Day on 5 May. It's for this occasion that the koinobori, or carp streamers, are brought out. Here are some flying over Asuka-gawa in Kashihara during my visit in 2018, with Unebi-yama, at the base of which Kashihara-jingû is located, in the background below.

My part of France is also on school break. With my homework done, it's time to get out and about again for my own Golden Week!

Everything is ready for Tuesday! How this particular configuration works, as well as the one below, will be covered - we can talk about it on here too afterwards if anyone's interested.

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?...

On the JR Nara line

Uji city and the the building on the 10-yen coin can be accessed by train from Kyôto by going roughly a third of the way to Nara. Other famous sites near the line are Fushimi Inari Taisha (Inari stop), and the studios of Kyoto Animation, famous for the music and sports anime K-On and Free! (Kohata stop).

The most recent type on the route is the 221 Series, and it's already getting on a bit, introduced in 1989. It won one of the Japan Railfan Club's two main new train design awards, the Laurel Prize, the following year. The 221 is used on the fastest Miyakokji Rapid services, which do the Kyôto to Nara run in under 45 minutes.

Green 103 Series sets can also be seen. This is the oldest type still in active JR service (if not, it's close), as it was introduced in 1963. In 2016, when I first visited Japan, I was living near Paris, and some Métro and suburban lines were running trains of a similar age, if not older, and these were atrocious in hot weather - no air conditioning, and ventilation only provided by opening windows! The RATP MP 59 used on Métro line 11 was stinky to boot; it was withdrawn just before the Games, no wonder! Point is, the 103 doesn't have air con either, but is at least trying...

Rheinfall: a second look

The weather improved greatly throughout my day at Schaffhausen, and I'd read that the falls are lit up at night, so I decided to give it a second look. And this was the view from the scenic Neuhausen Rheinfall station when I got back:

The falls roughly face West, so the evening is actually the best time to photograph them as the sunlight hits them directly.

Also, the boats stop at 6:30 in the summer, so we get a clearer view of the pool below, and no-one standing on the rock in the middle.

The trail on the Laufen side remains open though, so people can still see the falls up close, as described in the previous post.

The bridge on the far left of the top picture and at the back of the second picture is a rail bridge carrying the line from Neuhausen (central) to Schloss Laufen. It's no doubt one of the most spectacular in Europe, and it doubles up as a footbridge, allowing people to walk alongside some Swiss Dostos.

Oh, and they do light up the falls at night.

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!

Sangaku Saturday #13

Last week, we uncovered this configuration which is also a solution to our "three circles in a triangle" problem, just not the one we were hoping for.

This is something that happens in all isosceles triangles. Draw the inscribed circle, with centre B, and the circle with centre C, tangent to the extended base (ON) and the side [SN] at the same point as the first circle is. Then it can be proved that the circle with centre A, whose diameter completes the height [SO] as our problem demands, is tangent to the circle with centre C.

But that's not what I'm going to concentrate on. Despite this plot twist, we are actually very close to getting what we want. What the above configuration means is that, returning to the initial scaled situation with SO = h = 1 and ON = b, we get

Knowing a solution to a degree 3 equation is extremely powerful, as we can factor the polynomial and leave a degree 2 equation, which has simple formulas for solutions. So, to finish off, can you:

1: prove that

2: solve the equation 2x²-(s-b)x-1 = 0, and deduce the general formulas for p, q and r that fit the configuration we are aiming for;

3: test the formulas for an equilateral triangle, in which s = 2b.

This last question is the one the sangaku tablet claims to solve.

Engelbourg: the castle with the hole!

A less glamorous variation of the 10 yen coin photo, but I did say back in March that this place made me crave Polo mints!

More seriously, I returned to Thann this weekend with two Japanese people working in France this year. The timing was impeccable, as there had been some snowfall in the previous days, giving us some spectacular views from the summit.

Also, just in time for the start of the Christmas market! Getting into the festive mood early this year... and no need for fake snow! At least, that was the case yesterday. Today, the weather got much warmer and it's probably all gone.

February 2020 was weird

In my mind, visiting Oberkirch mid-February 2020 as my last outing before lockdown in Europe. Actually, that's not true - late February I went to Western France and Paris... but this was indeed my last solo excursion. I went for the carnival, which did take place, but Covid was very much on the horizon at that point. So there's something special about looking back at seeing people at the castle, enjoying the views and nature while it was still possible.

Also in Portsmouth harbour in August 2012, also not powered by aircraft engines: the Italian Navy's training ship Amerigo Vespucci.

As explained in Oceanliner Designs' video on the ill-fated Kobenhavn, even after steam had become the prime mover of the world's warships, navies still valued sailors who could operate a fully-rigged sailing ship. Hence training vessels were still built with sail in mind, and are still in use in that capacity today, such as France's Belem, built in 1896, which recently carried the Olympic torch from Greece to Marseille, and Italy's Amerigo Vespucci, built in 1930, which also carried the Olympic torch for the Rome games in 1960, and is basically on a perpetual world tour.

Funnels are clearly visible on this side view, as, like most sailing ships today, other engines are provided, at least for safety when the wind cannot be used. In fact, the Amerigo Vespucci's Diesel engines received a serious upgrade not long after these photos were taken in 2012.

Speaking of 2012, that was the year the replica of the Bounty sank in a hurricane. It too was a sailing ship with Diesel back-ups, and Brick Immortar has a full video on the incident, which includes one of the daftest quotes I have ever heard - I struggle to believe the narrators could say it with a straight face -, with the captain claiming, in the context of sailing near a hurricane, that "a ship is safer at sea than in port."