Japan “Sangaku” Research Institute

Category: Sangaku

Hachiman Wake Shrine (1890), Sako, Akaiwa City, Okayama Prefecture (02)

Problem There are two sections with different heights, and the areas of the upper and lower sections are 155 $m^2$ and 175 $m^2$ respectively. The height difference between the upper and lower sections is 1.5 $m$. The soil obtained by digging up 3 $m$ in an area of 20 $m^2$ is brought from the outside…

June 5, 2023
Hachiman Wake Shrine (1890), Sako, Akaiwa City, Okayama Prefecture (01)

Hachiman Wake Shrine is located 4.6 km northwest of Kumayama Station on the JR Sanyo Main Line. Problem There are three sections (of different heights), upper, middle and lower, in the rice field. The areas of the upper, middle and lower sections are 210, 150 and 240$m^2$ respectively. The height differences between the upper and…

May 26, 2023
Tanokuma Hachiman Shrine (1891), Tanokuma, Tsuyama City, Okayama Prefecture (3)

Problem There are three circles in a right triangle $ABC$ as shown in the figure. When the product of the diameter of the middle circle and the length of $BD$ is 2.88, and the sum of the length of $AD$ and the diameter of the small circle is 3.6 inches, what is the diameter of…

May 19, 2023
Tanokuma Hachiman Shrine (1891), Tanokuma, Tsuyama City, Okayama Prefecture (2)

Problem There are three circles in a right triangle $ABC$ as shown in the figure. When the product of the diameter of the large circle and the length of $DA$ is 4.8 and the difference between the diameter of the middle circle and the side $AB$ is 1.4 inches, what is the diameter of the…

May 16, 2023
Tanokuma Hachiman Shrine (1891), Tanokuma, Tsuyama City, Okayama Prefecture (1)

Tanokuma Hachiman Shrine is located 4.2km southeast of Takano Station on the JR Inbi Line and 4.2km north of Nishi Katsumata Station on the JR Kishin Line. Problem There are three circles in a right triangle $ABC$ as shown in the figure. When the product of the square of the side $CA$ and the square…

May 10, 2023
Matobeyama Shrine (1900), Kamogata-cho, Asakuchi City, Okayama Prefecture (2)

Problem As shown, there is a triangle among three equal circles that are tangent to each other. The vertex of the triangle is in the center of the upper circle, the left edge of the triangle base is in the center of the lower left circle, and the right edge is on the circumference of…

May 2, 2023
Matobeyama Shrine (1900), Kamogata-cho, Asakuchi City, Okayama Prefecture (1)

Matobeyama Shrine is located 4 km north of Kamogata Station on the JR Sanyo Main Line. Problem As shown in the figure, when a square with a side of 17 inches has a circle with a diameter of 8 inches in the center, which is surrounded by 8 equal circles, what is the diameter of…

April 22, 2023
Tamamori Shrine (1912), Katsuyama, Maniwa City, Okayama Prefecture (3)

Problem Assuming that the area enclosed by the large and small circles in the figure is 237 square inches and the difference between the radii of the large and small circles is 3 inches, what are the diameters of the large and small circles? Note that $π=3.16$ is used in this problem. $$ $$ $$…

April 20, 2023
Tamamori Shrine (1912), Katsuyama, Maniwa City, Okayama Prefecture (2)

Problem Assuming that the area enclosed by the large and small circles in the figure is 237 square inches and the difference between the radii of the large and small circles is 5 inches, what are the diameters of the large and small circles? Note that $π=3.16$ is used in this problem. $$ $$ $$…

April 9, 2023
Tamamori Shrine (1912), Katsuyama, Maniwa City, Okayama Prefecture (1)

Tamamori Shrine is located 0.4km north of Chugoku Katsuyama Station on the JR Kishin Line. Problem When the area enclosed by the large and small circles in the figure is 395 square inches, and the difference between the radii of the large and small circles is 5 inches, what are the diameters of the large…

April 3, 2023