[This cache is part of a geoart to create I♥SH, in the Pu river - if you want to help - please see my bio]
Background: Liu Hui and the Haidao Suanjing
Liu Hui (c. 220–280 CE) was a mathematician of China’s Three Kingdoms period, famous for his Haidao Suanjing (Sea Island Mathematical Manual). This text introduced geometric surveying techniques to measure inaccessible heights and distances—like towers across rivers—using aligned sightlines and poles of known height (chong cha method).
The Puzzle: Measuring the Jade Pagoda
Scenario:
You stand on the north bank of the Silver River, facing the Jade Pagoda on the opposite shore. Using Liu Hui’s method, determine the pagoda’s height.
Tools:
-
Two vertical poles (biao), each 1.8 zhang tall
-
A flat, level ground to plant the poles.
Setup:
-
Place Pole A on the riverbank
-
Place Pole B 324 zhang directly behind Pole A (along the line to the pagoda).
-
Sight the pagoda’s tip:
-
From 6 bu behind Pole A, the tip aligns with the pole’s top.
-
From 24 bu behind Pole B, the tip aligns again.
Calculations (Use Liu Hui’s Formula or derive from first principles) :
-
Height of Pagoda (in bu)= Lo
-
Distance to Pagoda from pole B (in bu)= La
The Cache can be found at N 31° 14.La' , E 121° 29.Lon'
You can validate your puzzle solution with
certitude.