#2016-10

[merpmonde]

As the maths problems take a break, maybe we can have a brief pub quiz. So...

Q. What's that building on the 10-yen coin?

A. The Phoenix Hall at Byôdô-in, Uji.

Initially built as a villa by a member of the Minamoto clan just before the year 1000, the land was sold not long after to members of a rival clan, the Fujiwaras, who turned it into a Buddhist temple named Byôdô-in in 1052. The most striking feature of the temple is the Amida Hall, which with time gained the name Phoenix Hall due to its overall appearance: the two outer corridors are the wings, and a corridor extending behind is the tail.

At the same time, tea production was picking up in Uji, and by the 14th century, Uji tea had become well renowned. I need to go back there someday, my first visit was just an afternoon flick after completing the climb of Mt Inari in the morning. I thought of going back there in the summer of 2023, but couldn't quite make time for it.

[merpmonde]

Sangaku Saturday #4

In the previous info post, we went over the debate on the religious aspect of sangaku, and the fact that the absence of prayers on these tablets was more puzzling to some than the mathematics. As such, the tablets are not ema prayer tablets, but donations, which usually don't feature prayers on them. Case in point, some consecrated sake and French wine seen at Meiji-jingû in 2016.

Beyond wishing for good fortune and health, such donations serve two very worldly purposes: to contribute to the life and prestige of the shrine or temple (having a famous contributor makes the shrine famous by association), and to advertise the donor in return, as their name is on display. See this large torii at Fushimi Inari Taisha paid for by TV Asahi (テレビ朝日).

With that in mind, Meijizen's cynical comment from 1673 that sangaku aim "to celebrate the mathematical genius of their authors" may not far from the truth. The authors of sangaku are looking to gain notoriety through the publicity that the shrine or temple provides. But was the bemused Meijizen the target audience?

More on that in a couple of weeks. Below the cut is the solution to last week's problem.

The solution to the first problem (below the cut in this post) is the key. Name K, L and M the intersections of the three circles with the horizontal line. Then, by using that previous result,

Indeed, as in that problem, we can construct three right triangles, ABH, ACI and BCJ and apply Pythagoras's theorem in each.

Now, it suffices to note that KL = KM + LM, so

or, dividing by 2*squareroot(pqr), we get the desired result:

Inverting and squaring this yields the formula for r:

This gives us the means to construct this figure on paper using a compass and a marked ruler. Having chosen two radii p and q and constructed the two large circles (remember that AB=p+q) and a line tangent to both, placing M and C is done after calculating the lengths IK=CM=r and IC=KM=2*sqrt(pr).

[merpmonde]

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...

[desenho-do-alex]

[bbromanets]

Аналитический отчет

2016-10-02 Провел исследование для X5 Retail и ответил на запрос “Как сделать обучение в стиле Pokemon Go для капусты и колбасы?”

В гугле

[hellomagmoe]

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[hellomagmoe]

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[hellomagmoe]

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