Sangaku Saturday #13

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.

Been a busy bee today, so here are some animals from the Expo 70 Commemoration Park.

Japan Weekend coming up!

This weekend, in fact! Every April, Strasbourg hosts some ekiden running races, and a festival of Japanese culture on the side. Taiko drums, shamisen, martial art demos including kyûdô and aikidô, Japan-inspired artists, food... and games like shôgi and mah-jong, the latter of which I will be partaking in as a member of the Strasbourg club. So if perchance you are in Strasbourg this weekend, pop by!

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.

Sangaku Sunday #7

We're back with a new problem from Miminashi-yamaguchi-jinja! This is going to be more ambitious than the first one, though it won't be much harder from a geometry standpoint - the main tool will still be Pythagoras's theorem. But we really need to set the stage for this one.

Consider an isosceles triangle, with two circles whose diameters are on the height from the apex, tangent to each other, and so that the top circle passes through the apex and the bottom circle is tangent to the base. We seek to draw one more circle on either side, which is tangent to the first two, and tangent to two sides of the triangle.

Details and first questions below the cut.

The triangle is given: it is an isosceles triangle SNN'. For the sake of simplicity, let's shrink or blow up the figure so that the height SO is equal to 1 (for a configuration with height h, we will just need to multiply all the lengths by h). The length of the base NN' is therefore the fixed parameter of the problem, and, as the figure is symmetric with respect to SO, we only need to set the length ON as our parameter: set ON = b. Hence, we are working in the right triangle SON.

The problem involves finding the three circles that fit the configuration in SON. Let these circles have respective centres A, B and C, and respective radii p, q and r. The radii are the unknowns of our problem, and we need to find three independent relations between them to solve. From the sketch, it looks like there should be only one solution.

The first relation is obvious: 2*(p+q) = 1, as the diameters of the first two circles form the height SO. This is also very easy to solve: if we have p, then q = 1/2 - p.

A second relation must start to involve r. For this, project the centre of the third circle onto SO and ON, calling these projections P and Q respectively. Now we get to two questions for you to munch on.

1: Prove that

2: Get the lengths AC and PA. Deduce another expression for PC, and prove that

With that, we just need another equation to find p, and we'll be done.

Hikone Sawayama: base

Walking North along the railway from Hikone station, one reaches the base of the hiking trail up Sawayama. After passing Nagabayashi Inari-jinja, a typical shrine dedicated to the shintô deity of prosperity with its succession of red torii gates, several temples appear, featuring monuments to two historical figures of Hikone, Ishida Mitsunari and Ii Naomasa. More on them when we reach the top.

This is Ryôtan-ji Sanmon, the "gate to the mountain" which leads us to the grounds of Ryôtan temple and starting the short, sharp climb. As we begin, we are met with more popular Japanese deities: the Shichi-Fukujin, or Seven Lucky Gods.

Apparently Ryôtan-ji has a fantastic zen garden, but we missed it.

A few pictures of Bastille Day fireworks... at least whatever got above the roofline.

MiniWorld Lyon

Looking for a cool place to go with @teamroquette on the hottest day of my trip to Lyon, we opted for... Lyon. But the miniature version, housed in the MiniWorld diorama park!

MiniWorld Lyon was surprisingly impressive at every level. The sets are huge and the details are amazing. We spent hours there and didn't catch everything - there are 4 Wallies (Waldos) in the whole park and I only found two. But to show the level of dedication, see that traffic jam going into Fourvière tunnel on the left? It goes all the way in, as far as the turn...

And it's like this all the way through the park. The main exhibit is divided into four zones (each with a Wally): generic city, mountain, countryside and Lyon.

This exhibit is on a 20-minute day/night cycle, and every hour, Mini Lyon holds a replica of Lyon's Fête des Lumières held in December, which includes light shows projected on buildings, such as those on Place des Terreaux.

The current temporary exhibit is called Japan Mania, with dioramas from Japanese pop culture. A few Japanese elements have been added to the main exhibit too, including something familiar...

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.

Suzuka Circuit

April became Formula 1 month for Suzuka last year, but back in 2018, it was the venue for a Super GT test weekend. I took the opportunity to enjoy the circuit in a much calmer atmosphere, though the weather was very changeable on the day (I got drenched walking down to Inô station afterwards!).

Opened in 1962, the track is very much enjoyed by drivers for its large variety of corners (the Esses, hairpin, chicane, the double-apex sweeper at Spoon, the dauntingly fast 130R...), and has an unusual figure-of-8 shape, crossing over itself - the bridge is before this hairpin, just out of shot on the left. On a test day like this, most grandstands are open to all, offering the viewer a similar variety of angles and vantage points.

The paddock was also open for the relatively few fans to walk around and have a chance to meet the drivers (James Rossiter pictured above). But even then, 2018 was the year Jenson Button was racing, and his garage got a lot of attention!

Despite the weather which turned miserable in the afternoon, the teams didn't shy away from running. There were even a couple of Safety Car training moments: rolling restart, and full SC procedure with class separation.