Landscapes, travel, memories... with extra info.Nerdier than the Instagram with the same username.60x Pedantle Gold medallistEnglish / Français / 下手の日本語
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Latest Posts by merpmonde - Page 2
E10 Shinkansen coming soon!
The Japanese railway companies don't make prototypes for the lols. JR East's ALFA-X project will come to fruition with the E10, due to start testing in 2027 and enter commercial service in 2030.
Also of note in the announcement, is that JR East will run freight-only high speed trains, using retiring E3 Series trains (these are currently being replaced by new E8s). I remember that during the pandemic, the empty Shinkansens were used to transport fresh fish. As far as I can tell, this would be the first regular high-speed freight service since the French Post Office's TGVs which retired in 2015.
Pouancé
The small town of Pouancé is on a remarkable geographical "quadruple point", on the border of four départements! A peculiarity that dates back to the Middle Ages, when it was on the battlefront between France-affiliated Anjou and the still fiercely independent Duchy of Brittany. As such, Pouancé had a castle; its Breton counterpart was at Châteaubriant, and both towns were besieged at some point during the 15th century.
With a friend from Châteaubriant, we got to witness barriers being removed as what we guessed were maintenance or renovation works on the path around the castle were finished. The castle itself only opens during the summer, but at least we got to walk all around and get some good views of the castle, through the neighbouring park.
If you're driving into Pouancé from the West, this is how you know you've arrived:
Châteaubriant: a regional rail hard border
Rennes and Nantes, the largest cities in the Western tip of France, could have three direct rail routes connecting them. The one via Redon has always been used in this role; a second, via Laval and Angers, was ridiculously long until the high-speed line to Laval opened and 200 km/h-capable units were adapted for use on it; and a third... has been cut off at Châteaubriant.
The irony is, the Châteaubriant route would be the shortest in distance, at just over 120 km in length, in a fairly simple North-South direction. The trouble is, the line wasn't built with the traffic between the two cities in mind, is mainly single track, and has some steep inclines (1.5% is steep for a train). As such, it has always seen modest levels of traffic, and since the 1980s, it had been falling into disrepair in parts, and become abandoned in others.
The Nantes side saw a resurrection in the early 2010s: the line was electrified and, in 2014, tram-trains began operating. We've seen a tram-train on this blog before, but this service is only technically a tram-train, as it only uses a tram line parallel to the urban tram for a few kilometres inside Nantes, and only making one stop on that stretch. The Alstom Citadis Dualis (SNCF class U 53500) units are effectively regional trains in tram clothing, and are the only tram-trains in France to have onboard toilets.
But in France, local trains are managed by the administrative regions, and Nantes to Châteaubriant is under the authority of Pays de la Loire, so the electric wires, renovated stations and new trains went no higher. Worse, the line has been cut in half by a platform link, as shown above - and a photo on this webpage seems to indicate they used to be joined. So the Rennes side, managed by Bretagne region, has remained without electric power. I remember the stark contrast between the two sides of the regional border when I visited in early 2020: to Nantes, modern infrastructure and trains; to Rennes... nothing, and tracks that were starting to be overgrown!
It turns out the line was indeed closed for repair works at the time, and in 2021, Rennes to Châteaubriant reopened, with first-generation bi-mode Bombardier AGC (B 82500) sets, which only use Diesel power on this route, operating a peak-only service.
In conclusion, the Rennes-Châteaubriant-Nantes route has always been in the shadow of the slightly longer route via Redon, as the latter provided good connections to other major towns on the South Brittany coast: Vannes, Lorient and Quimper. The Châteaubriant route was never double-tracked, and today is a striking illustration of regionalisation, with different levels of investment on either side of the border, and through service now impossible.
Nijô-jô
In my experience, Nijô Castle in Kyôto is one of the most unusual in the Japanese castle landscape, in that the main focus of the conservation and tourist attraction is on a palace, the Ni-no-maru Goten, rather than a dungeon (whether reconstructed or original). It is true that, as the Tokugawa shôgun's residence in the Emperor's back yard, it was a focal point of Edo-period politics.
The palace sits behind a grand gate, decorated with lots of gold and colours. And as all noble residences from the Edo period go, there's a vast, carefully crafted garden on the side, complete with tea houses.
But all this is part of the Ni-no-maru, the area around the Hon-maru main keep. Given that the mountains around Kyôto are largely occupied by temples and shrines, there's not much of a height advantage to be gained in the city, to the point where, when the Hon-maru burned down in the 1780s, nothing was rebuilt, it was left bare!
Eerily, the Tokugawa shôgun's Kyôto castle has a similar story to the one in Edo: there was a keep, but it was destroyed during the Edo period and wasn't rebuilt, and both castle grounds were transferred to the Imperial Estate at the start of the Meiji era. It was in the 1880s that the Hon-maru palace was built, in the space the Tokugawas had left vacant.
Japan's first Concorso d'Eleganza
A Concorso d'Eleganza is basically a beauty pageant for historic cars. Based on similar contests for horse-drawn carriages, called Concours d'Élégance, the Italian name references the fact that the most famous competition in the genre for cars has taken place in Italy since 1929.
The Japanese version was launched in 2016, with the amusingly-named "Artistic Cars at the World Heritage, since 2016" exhibit at Nijô-jô, Kyôto. I say amusing, because they were using the "since 2016" tag in 2016, and... it hasn't used that name since! Nonetheless, the sight of these immaculately preserved cars in the lovely palace gardens was impressive.
Among the cars built between the 1950s and 1990s, there was an exhibit with rare Zagato specials. Particularly obscure is the Autech Zagato Stelvio, shown above and below. Of the three names, Zagato is the best known: they are an Italian coachbuilder, who make unique bodywork. Autech is a Japanese tuner, working most closely with Nissan. And the Stelvio is a late-80s mix of all that: a modified Nissan Leopard with very unique design choices, such as the wing mirrors in the fenders.
The Concorso d'Eleganza Kyoto is set to resume this year, having been put off due to the pandemic and the restrictions surrounding it since 2020. The principle hasn't changed: they're going to show some remarkable historic cars in a historic Japanese setting - at Nara this time.
@chitaka45 just published some gorgeous photos of Shinsen-en in the snow (I love their photos in general BTW, Kyoto's shrines and temples in all their glory!). I found this place by chance while walking to Nijô-jô in 2016 - different season, different colours.
Part garden, part temple, part shrine, Shinsen-en dates back to the start of the Heian period, when it was an Imperial property. One of its most distinctive features is the Dragon Boat, which apparently serves for Moon viewing events. Several Japanese seasonal traditions, like Moon viewing and cherry blossom viewing, are said to originate in Heian-period Kyôto.
Something you don't see every year down South: ice! And not just a little, some proper icicles on this fountain on Place de la Trinité in Toulouse.
Plus a bit of snow sticking to the ground in the parks, as seen from the Natural History Museum.
Up the Monumental Stairs at Auch
Some 75 km West of Toulouse, the city of Auch is far away enough for red brick to be far less prevalent in buildings. It developed along the Gers river, with the higher-ups living... well, higher up.
The Monumental Stairs were built in the 1850s when, following a rebellion against Napoleon III's coup installing the Second French Empire, the prefect decided to give the townsfolk something to do (per the city council, "créer des chantiers afin de donner de l'ouvrage à ceux qui en manquent"), rather than just repress. The results were a water and gas distribution network, and the Monumental Stairs, creating a comfortable link between the upper town and the riverside 35 metres below. Later, a statue of d'Artagnan, a musketeer made famous by Alexandre Dumas novels, was added.
Behind d'Artagnan here, rises the Tour d'Armagnac, a 14th-century prison. Unfortunately, it is privately owned and cannot be visited, unlike the neighbouring cathedral, built between 1489 and 1680.
While the back of the cathedral, visible in the top photo, is clearly gothic, which fits the start of construction, the front facade is in a later, classical style. This would fit the timeline, as cathedral building usually started with the crypt and the altar, working outwards, and finishing with the massive entrance and towers. Walking away, further West, we encounter one more figure of the town: Intendant Mégret d'Étigny, who administrated the Auch-Pau area under King Louis XV, and is credited with infrastructure improvements in the region at the time.
Gimont
During my only winter down South, way back when I'd do road trips (solo of course), I set out from Toulouse for a day to visit Auch, with a break in the countryside each way, partly to admire the snow on the Pyrenees. This first picture was taken on the outbound leg, and I forget where it was.
On the return leg, I stopped at Gimont, possibly drawn in by the distinctive church. There is also a Cahuzac Chapel next to the town, which gets a laugh because it has the same name as a former budget minister who was convicted for tax evasion. The shameless git even tried to run for Parliament again once his ineligibility sentence was served. Same name, but no relation, I should stress.
Like a lot of places in this corner of France, there are a lot of brick buildings in Gimont, and some peculiar traditional structures, like the Halle covered market. Inexplicably, a road runs through it.
The town also boasted a world-class motocross track, which hosted rounds of the 250cc World Championship in 1985 and 1990. But in 2019, so not long after my visit, the land owner wanted their turf back, and the Gimont Moto Club has since been looking for another location to open a new circuit. Here's how it rode:
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!
ICE 3 (Gen.1)
After visiting Karlsruhe Palace, I had a bit of time while waiting for a (packed) regional train South to wander around the station. There was quite a lot going on, as on top of the local traffic from S-Bahns to REs, busy intercity lines to Freiburg and Basel, Stuttgart and Munich, Mannheim and Frankfurt meet here. A chance to see my favourite German high-speed train: the Baureihe 403 ICE 3.
Entering service in 2000, over 10 years after the first InterCity Expresses, the ICE 3 was a revolution in European high-speed rail. These were the first 300 km/h-capable trains that weren't of a "power car & carriages" layout, using distributed traction (motors all along the unit) like Shinkansen trains. And a sleek shape to boot! They were designed by Alexander Neumeister, who also penned the 500 Series Shinkansen. Hmm, maybe that's why.
The ICE 3 would be the first example of Siemens's Velaro series, which would be an export hit: the Netherlands, Spain, China and Russia purchased this model. The type received a redesign in the late 2000s that I could only describe as "more beefy": the Velaro D was taken up by Germany, Turkey and Eurostar.
I failed to mention this in the original post, but Meiji-jingû is also a high point of sumo culture. Newly promoted yokozuna, the highest rank in the sport, perform their first ring entry dance there, before their first tournament at that level. This would be their first appearance with the "horizontal rope" (that's what yokozuna means), in the shimenawa style, around their waist.
That's just happened, with the 74th yokozuna making his debut.
The New Year shrine visit: Meiji-jingû
A common New Year ritual in Japan is to go to a shrine, possibly a large one, a visit known as 初詣, hatsumôde. NHK reported that Meiji-jingû in particular was very busy. Of course, I would avoid that, so here we are with a more tranquil time, closer to the Autumn festival.
Meiji-jingû was, as its name suggests, founded to enshrine the spirit of Emperor Meiji after his death. The first Emperor of the post-Edo period presided over sweeping societal reforms, such as the abolishment of classes like the samurai, as Japan re-opened to the rest of the world and sought to catch up. The Imperial attachment is symbolised by the Chrysanthemum crests on the torii.
One of the things that can be wished for at Meiji-jingû is a happy marriage and family life, particularly at this dedicated spot with two camphor trees planted in 1920, linked with sacred rope - these are called "married trees", 夫婦楠 Meoto Kusu.
Karlsruhe Palace
Thought I'd pop up to Karlsruhe today; it's not very far and I'd never been. It was... well, OK for a light outing. There's a lot of construction work going on in town, and it wasn't very animated being late January. Still, the weather was good enough for a pleasant walk around the centrepiece, the Palace, which houses the history museum of the State of Baden.
Karlsruhe is a relatively young town, by European history standards, as it was founded in 1715 as a new seat of power for the Margrave of Baden. A symmetric living building with a rear wing mounted by a tower was surrounded by vast gardens, and streets radiated out from the palace - a rather original urban arrangement, I don't remember seeing it in other places. Following French invasion in the late 18th century, Emperor Napoleon granted Baden the status of Grand Duchy: the ruler gained access to more riches and symbols such as a crown, a throne...
The Grand Duchy was briefly overthrown in a revolution in 1849, and abolished entirely following the fall of the German Empire in 1918. The region of Baden, stretching from Mannheim and Karlsruhe in the North, along the East side of the Rhine down to Freiburg and Konstanz, became a Republic within the Weimar Republic, and merged with neighbouring Württemberg, the area around Stuttgart, into the Land of Baden-Württemberg we have today in 1952. Baden was the smaller of the two former Grand Duchies, and was more reticent to the merger, as this poster in the museum shows.
"This is what the merger will be like!"
Ultimately, the merger wasn't as bad a deal as feared: when a Baden-only referendum was held in 1970, a return to a split was emphatically rejected. Still, it is not rare to see the yellow and red flag of Baden in the South-West corner of Germany - I've seen it outside a drinks hut near Oberkirch (bottom left picture) and on several castle ruins. It naturally flies atop the Karlsruhe Palace tower.
This monument needs no introduction. I just want to show the names of French scientists and engineers that adorn the base of the Tour Eiffel's first floor - just visible at the bottom of the above picture. Similarly to the German names on Strasbourg's Palais Universitaire, if you've studied science at length at any point, you'll know some of these: Cauchy, Navier, Lavoisier, Ampère...
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?
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.
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!
Ichibata Dentetsu
The only train to Izumo Taisha is operated by private company Ichibata Dentetsu, or Bataden. Twas not always thus, as the JNR had a short 7 km branch line from Izumo-shi to Taisha until 1990. It was served by direct expresses from Nagoya and Kanazawa (11-hour day express Taisha) and night expresses from Ôsaka (Daisen).
But Bataden is no upstart, they've been around for a long time. They've been connecting Matsue Shinjiko-Onsen, Dentetsu Izumo-shi (neighbour to JR Izumo-shi) to Izumo Taisha-mae since the 1920s. On of their trains of the time was the DeHaNi 50, left in its refurbished DeHa 50 form. On the right is the 7000 Series, the company's newest model... and their first new train since the DeHaNi 50!
In the 90-year interim, Ichibata has relied on second-hand trains (yes, that's a thing in Japan), mostly from Tokyo-based Keiô. A rather nice retreat for these vehicles, from the crowded suburban lines around the capital, to scenic moseys around Lake Shinji... There are some special liveries and trains, such as Shimane-no-ki below, with some nice wooden decking inside, and single-seat semi-compartments! "Wait, is this First class?", I remember thinking to myself.
Izumo Taisha's rabbits
@shoku-and-awe made a great post on the rabbit statues at Izumo Taisha and why they're there, so I'll only add that they are all over the shrine's grounds, and as far as East as the Ancient Izumo History Museum.
In the gardens, the rabbits are depicted doing all kinds of things: reading a book, taking pictures, birdwatching... Yes, all that!
And of course, there are a lot of rabbits facing the shrine buildings and praying.
The plaque behind these two recognises Senge Takamasa and Kunimaro, father and son, current and presumed future chief priest of Izumo Taisha. Tracing their origins back to the rulers of the Izumo province way back in the Nara period (Takamasa is the 84th head of the clan), the aristocratic-priestly Senge family has very much stayed in high society to this day, from being involved in politics and governor of Tokyo around 1900 (the shrine had been taken out of their control following the Meiji revolution and the abolition of the nobility), to Kunimaro marrying an Imperial princess (who no longer holds the title as per the rules) in 2014.
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.
Statement on my Instagram regarding Meta's moderation policy updates
Meta's updated policy on hate speech can best be described as... "weird", I guess.
The highlighted sentence, which is factually inept, is what is causing the uproar. Political and religious discourse on homosexuality, or any other group of people for that matter, does not use, and has never used, unsubstantiated allegations of mental illness or the word "weird" in a light or "non-serious" way. They are always used with the ulterior motive to discredit and stigmatise, and make exclusion of said group, a core element of the law & order doctrine they aspire to. But this is now explicitly permitted on Facebook and Instagram.
The law in most European countries currently does not allow this double standard on hate speech. While this does offer protection to all citizens in the applicable countries, the fact that Meta is in open disagreement with these protections, regardless of the reason, is something to think about.
I will be evaluating my presence on this platform [Instagram] in the coming days and weeks. Meanwhile, a normal blogging schedule will be maintained on the companion Tumblr. Cheers.
Meoto Iwa - the married rocks of Futami
We noted the presence of "married camphor trees" at Meiji-jingû last time, so I guess we can talk about other sacred things linked by rope.
One of the most famous of these is the couple of "married rocks" on the coast of Mie, on the premises of Okitama-jinja at Futami, near Ise. The Meoto Iwa represent the founding couple of Japan according to Shinto, Izanagi and Izanami.
The shimenawa ropes are more heavy-duty than what we saw on the camphor trees: 5 strands, 40 kg each. Still, as they are exposed to the seawater spray from crashing waves, they need to be changed several times a year, which involves quite a few people as you'd expect, as shown on the poster below. Ceremonies occur in May, September and December.
The ropes certainly look heavy on the smaller rock in particular, they look like they could slip off, but instead they cling on rather gracefully.
Dotted around the shrine are statues of the messengers of the gods: frogs.
While Futami's Meoto Iwa is the most important example of "paired rocks" in Japan, owing to how far the tradition dates back and its proximity to Ise Grand Shrine, there are quite a few others across the country. Below is another Meoto Iwa in Mihonoseki, Shimane.
The New Year shrine visit: Meiji-jingû
A common New Year ritual in Japan is to go to a shrine, possibly a large one, a visit known as 初詣, hatsumôde. NHK reported that Meiji-jingû in particular was very busy. Of course, I would avoid that, so here we are with a more tranquil time, closer to the Autumn festival.
Meiji-jingû was, as its name suggests, founded to enshrine the spirit of Emperor Meiji after his death. The first Emperor of the post-Edo period presided over sweeping societal reforms, such as the abolishment of classes like the samurai, as Japan re-opened to the rest of the world and sought to catch up. The Imperial attachment is symbolised by the Chrysanthemum crests on the torii.
One of the things that can be wished for at Meiji-jingû is a happy marriage and family life, particularly at this dedicated spot with two camphor trees planted in 1920, linked with sacred rope - these are called "married trees", 夫婦楠 Meoto Kusu.
Sangaku Sunday Bonus - what about the other problems?
In the sangaku series, we've solved two of the four problems on this tablet, the middle two, which I believe were the easiest to work on in terms of geometric arguments - we hardly ever used more than Pythagoras's theorem, though the second one needed some more advanced algebra to finish off.
Here's a quick look at the problems at each end of the tablet, and the main ideas I had to solve them.
On the far left, we have two circles tangent to one another (with centres A and B), inside a larger circle (with centre O) so that their diameters add up to the diameter of the largest. The radii of these three circles, respectively p, q and p+q, are known. The unknown is the radius r of the circle with centre C, which must be tangent to all three original circles (it has a twin on the right-hand side with the same radius).
This is quite quick to solve. Remember that tangent circles mean that the distances between centres is equal to the sum of the radii, e.g. AC = p+r, BC = q+r... Al-Kashi's theorem, which is a general version of Pythagoras's theorem, links the lengths of three sides of a triangle with one of the triangle's angles, and the triangles CAO and CAB have an angle in common, which yields the equation for r by isolating this angle in each application of Al-Kashi's theorem. The result is:
The problem on the far right seems to start in a similar fashion: two circles with fixed radii are offset by a fixed distance. A third circle has its diameter equal to the remainder of the diameter of one of the large circles: this radius can be calculated with little difficulty. What we want to do next is construct circles which are tangent to the two large ones, and the one previously constructed.
The radius of the circle with centre C1 can be obtained as above, but this method does not seem to extend to the subsequent circles, as O, D and C1 are no longer aligned, and there no longer appears to be a common angle in the triangles we want to work with. So I went for a parametric approach, understanding the curves that contain points that are equidistant from two circles. The red curve (which looks like a circle but isn't one) is the set of points at equal distance from the two largest circles, and we seek to intersect this with the set of points that are at equal distance from one large circle and the smaller one, the green curve. The intersection is equidistant from all three circles, so it is the centre of the circle we want to construct. Rotate and repeat for subsequent circles.
The general formulas are horrible and not worth showing, but this is another problem where I have been able to read the results on the tablet. The large circles have radii 61 and 72, and the offset is 23. The radii of the smaller circles, starting with the one in the middle and working outwards are:
17, 15.55, 12.292, 8.832 and 6.038 (I see 八, but I'll give the authors the benefit of the doubt as the top of the character 六 may have been erased by time)
The results with our exact formulas are:
17, 15.58, 12.795, 9.076 and 6.444
Rather close! As with the "three circles in a triangle", I do not know how the authors originally solved this problem.
Port du Crouesty
We start the new year where we left off in the last, on Presqu'île de Rhuys, but one year later. Or should that be two? The previous post was from the stormy 2013-2014 New Year celebrations, whereas this covers the calmer 2014-2015 change with most of the same friends, and our walk around the tip of the peninsula and Port du Crouesty.
These aren't the best photos given the relatively low light, but also this was before my current camera. Still, point it towards the sunset and the result isn't too bad.
Your typical Breton winter weather...
11 years ago, our group of friends was celebrating New Year on the coast of South Brittany. It was a windy time, sometimes even stormy (the drive back a day or two later was possibly the most dangerous I've ever done), and it made for some impressive shots of waves breaking at Port aux Moines.
Some life in the rock pools of Hashigui-iwa! The crabs in the first picture were very small, but the one hiding in the second picture was more sizeable. I forget how big, but it was big enough to observe scuttling for shelter as I approached. Closest match on iNaturalist appears to be the Striped Shore Crab, which grows up to 5 cm.
The local birds of prey, likely kites, were also out, surveying the area.
Latest ambiance from Strasbourg, with love from our end-of-year mascot: Chris Moose!
Hashigui-iwa
Since the news took us back to Kushimoto, it's worth looking at another of the town's attractions, besides the southernmost point of Honshû and the nearby lighthouse. Up the coast is a remarkable rock formation known as Hashigui-iwa, which one could translate as "bridge column rocks", as if a viaduct used to settle on top of them.
These aren't standing stones in the archaeological sense of the term like Stonehenge (a popular spot for the winter solstice that also just happened), they weren't moved into a line and raised. Instead, they were originally an incrustation of magma in an otherwise less hard soil. The magma cooled off before becoming lava, and the ocean eroded the sediment around it. This would have created a wall of igneous rock, up to 15 m high and nearly a kilometre long. The wall was then smashed by a tsunami, leaving these tall rocks behind, and a beach of debris.
In the background of this photo, we see the bridge between the Shionomisaki peninsula and the island of Ôshima, where another lighthouse and monument to Japanese-Turkish friendship is located. There's a story behind that (the wreck of the Ertugrul), and I wish that was a segue, but I didn't visit Ôshima. On a hot day, energy isn't limitless so I had to choose...
