#sangaku

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.

"Mountains" (山岳, Sangaku), a 1989 colour silkscreen print, by Katsuda Yukio (勝田幸男, born 1941), a contemporary Japanese artist from Kyōto (京都), Japan's former imperial capital.

[Jaded in Japan]

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“A man would know the end he goes to, but he cannot know it if he does not turn, and return to his beginning, and hold that beginning in his being. If he would not be a stick whirled and whelmed in the stream, he must be the stream itself, all of it, from its spring to its sinking in the sea.”

On his blog MathWithBadDrawings, Ben Orlin reposted a couple of geometrical sangaku-like puzzles by math teacher Catriona Shearer. These are eleven of her personal favorites. If you dare, definitely give them a try!

Transit Across a Purple Sun. What’s the total shaded area?

Shearer’s Emerald. Four squares. What’s the shaded area?

The Pyramid with Two Tombs. Two squares inside an equilateral triangle. What’s the angle?

Setting Sun, Rising Moon. What fraction of the rectangle is shaded?

Hex Hex Six. Both hexagons are regular. How long is the pink line?

Four, Three, Two. What’s the area of this triangle?

The Trinity Quartet. All four triangles are equilateral. What fraction of the rectangle do they cover?

The Falling Domino. This design is made of three 2×1 rectangles. What fraction of it is shaded?

Slices in a Sector. The three colored sections here have the same area. What’s the total area of the square?

Disorientation. The right-angled triangle covers ¼ of the square. What fraction does the isosceles triangle cover?

A wooden votive plaque inscribed with mathematical problems and solutions presented to Sugawara Jinja Shrine (菅原神社) in 1854 by Hōjiroya Shōemon (喰代屋庄右衛門), disciple of Kōmoridō Hall (蝙蝠堂 “Bat Hall”), in present-day Iga, Mie Prefecture

Do you remember Nagakura is a math teacher in Hakuouki SSL ? 

Well you can make a reference about this in Hakuouki :D

During Edo period there are sangaku which are Japanese geometrical problems or theorems on wooden tablets.