Japan's First Concorso D'Eleganza

Sangaku Saturday #3

Another problem this week, adding to the configuration we looked at previously.

Specifically, given two circles tangent to each other and tangent to a same line - these circles have respective centres A and B, and respective radii p and q -, we want to construct the circle tangent to both of the original circles, and tangent to the line beneath them.

Can you prove that the radius of this third circle, denoted r, satisfies

and deduce a formula for r as a function of p and q?

Help below the cut, answers next week.

Hint. Name K, L and M the intersections of the circles with the line below, and use the previous result on each pair of circles to get the lengths KL, KM and LM. One of these lengths is the sum of the two others.

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.

After that news post, back to Thann, for this view of the Thur valley and the Vosges mountains. On the day of my visit, I climbed here first, before continuing along a ridge to the Grumbach summit and down to the Grumbach pass, before circling back down to Engelbourg Castle which I posted about first. A nice hike, not too difficult - most of the climbing is done when you've reached the Roche Albert viewpoint. There's something to be said about why it's called "Albert's Rock", but I'll save that for another time.

The things people write on clocks...

Craignez la dernière - Eglise Notre-Dame de Croaz-Batz, Roscoff

Literally, this means "fear the last". OK, but the last what? Well, you're looking at the sundial for the time, which here, in French, would be "12 heures", so the full saying is inferred to be "craignez la dernière heure" - "fear thy final hour". Reminding people of their own mortality was an important part of medieval-Renaissance Christian discourse, as we saw with the ages of Man passing before Death among the automatons on the Astronomical Clock in Strasbourg Cathedral, built around the same time as this church in Roscoff.

Die Zeit eilt, Die Zeit heilt - Rathaus St. Johann, Saarbrücken

I've only got a close-up of one, but the tower of the historic town hall in Saarbrücken has at least two clocks, each with a message. The meaning of "die Zeit eilt" is similar to "time flies", and could be linked to what we saw above: be aware of what time you may have left. The second clock cleverly adds one letter to that to make "die Zeit heilt": "time heals".

"How to use this sundial" - Piazza della Borsa, Trieste

In the ground in front of the Chamber of Commerce in Trieste is a sundial, but conspicuously, the hand is missing. That is because you are the hand! Taking astronomy into account, one should stand in a slightly different place depending on the season, and apply corrections to the minutes to get official time. It was cloudy when I saw this, so I'm afraid I don't have a nice picture of the sundial in action. The instructions are in Italian on the left side of the base.

Can't read my, can't read my, No you can't read my 岡 face!

I sighted this Vectron at Karlsruhe: a Dual Mode, which can move either with its Diesel engine or getting its energy from the overhead wires (German 15 kV AC only for now). However, it only delivers a third of the power of a standard all-electric Vectron, and is therefore not designed for main line hauling, and is expected to be more at home near sorting yards. Deutsche Bahn have also bought some of these as ICE rescue locomotives, serving when a train breaks down.

For Vectron!

Produced since 2010 by Siemens, the Vectron is a modular locomotive platform with various engine options - AC electric, quad-voltage for use across Europe, "last-mile Diesel" option for parking, Diesel motors, dual mode/hybrid... It hauls both freight and passenger trains. But the main reason I've wanted to mention the Vectron is...

this Mitchell and Webb sketch!

This is from series 3 of That Mitchell and Webb Look, which was aired in 2009. The Siemens Vectron was officially launched in 2010, so it's fair to say that the name appearing in both is a coincidence. However, when I see a Vectron, it reminds me of this sketch, so it's harder for me to take this train seriously!

But it is serious business, as it is one of the most common locos in continental Europe. Only Iberia (due to using a different gauge) and France (because if it ain't Alstom, they'll oust 'em) don't see much of them. The examples shown here are from Germany, Switzerland and Slovakia, and were all pictured in the same area of Germany. The quad-voltage version in particular allows companies to carry freight all over Europe, they're virtually borderless.

Yet here I am, still snickering at the name, by Vectron's beard!

Climbing Toba Hinoyama

The road (and I guess that is the only downside: it is a road all the way) to the top of Hinoyama starts with the welcoming entrance to Jôan-ji temple.

After some 800 m uphill, past a rather large resort hotel, a chance for a break appears: a viewpoint with a camera stand (which may have been the first time I noticed one! very handy for group shots, though I was alone of course), and an art garden called Medaka no Gakkô, or the school of rice fish. Not knowing that at the time (I looked it up for this piece!), I didn't notice the fish, but I did notice the art and the wisteria in full bloom.

Most of the climbing is done at this point, and it's only another 300 m to the entrance to the shrines at the top of Hinoyama. Shrines, plural, and of various sizes, as the modest Hakuryû Inari-jinja sits next to the grander Toba branch of Kotohira-gû.

On the right, at the bottom of the stairs of Kotohira-gû, one finds the donors' board, and an inviting path... to the views shown in the previous post.

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.

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

Palais Universitaire de Strasbourg

In 1870, a broad coalition of German nations waged a war against France. Napoleon III's Second French Empire fell swiftly, and the Second German Reich formed on the back of this victory, with a Kaiser at its head. Germany annexed Alsace and Moselle, and had particularly grand plans for Strassburg, the capital of the region. While the city centre on the island was repaired after heavy shelling, the Germans decided to develop around it. To the North, the Neustadt, "New Town", was built, with, at its core, a wide avenue with a palatial residence for the Kaiser at one end, and a University Palace at the other, the storefront of a brand new campus complex. It's still part of the university today, with classrooms and all.

Completed in 1884 in a neo-Renaissance style as a monument to Germany's newfound power, the Palace is richly decorated with statues, ranging from effigies of Germania and Argentina - no relation, the Roman settlement at Strasbourg was called Argentoratum -, and historical figures of German science and thought: below, theologist Martin Luther, mathematician Gottfried von Leibniz, astronomer Johannes Kepler and educator Johannes Sturm. Though probably not a direct response, the Eiffel Tower would provide a similar list of French greats a few years later.

France regained Alsace following World War I, and would de-germanify several buildings in the Neustadt area. The home of Germania insurances became the Gallia building, and the effigy of Germania, restored below, was removed from the University Palace. A similar process would be undertaken in 1945, after Alsace was once again be annexed by Germany in 1940 - the University Palace would need de-nazifying.

However, a few symbols remain as a reminder of the Nazi oppression. In the grand hall, called the Aula, a subtle swastika appears among the geometric patterns on the floor. It sits in a corner, as lonesome as it is loathsome. I thought I had a picture of that swastika, but looking through my folders, I don't appear to have taken photos of the interior at all. I seem to remember thinking "nah, it's weird to take pictures of Nazi swastikas". It's still weird, right?