Problem If you lend someone a dollar and get it back $5$ years later with a total of $2.0113571875$ dollars in principal and interest, what is the annual interest rate? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…

Problem Find the length of one side of a cube that is $1881676371789154860897069 \ cubic \ inches$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution When $1881676371789154860897069$ is decomposed into prime factors, $$3^6×3607^3×3803^3=(3^2×3607×3803)^3.…

Problem What is the length of one side of a square inscribed in a triangle, of which the longest side is $21 \ inches$ and the perpendicular line from the vertex to the longest side is $8 \ inches$? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$…

Problem Find the diameter of a circle inscribed in a triangle, of which sides have lengths of $21, \ 17$ and $10 \ inches$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Let…

Problem What is the side length of a square with an area of ​​$85000 ft^2$ ? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution The prime factorization of $85000$ is:$$85000=2^3×5^4×17=2^2×5^4×(2×17),$$$$∴ \ \sqrt{85000}=2×5^2×\sqrt{2×17}≒291.547594742265.$$  …

Souzume Hachimangu Shrine is located 1.2 $km$ west-southwest of Kibitsu Station on the JR Kibitsu Line. Problem The contents are unknown as some parts are illegible.     Reference Yoshikazu Yamakawa, ed. (1997) Okayama ken no Sangaku (Sangaku in Okayama Prefecture), p.27; p.400.