Five households share a deep well for their water supply. Each household owns a few ropes of a certain length, which varies only from household to household. The five households, A, B, C, D, and E, own 2, 3, 4, 5, and 6 ropes, respectively. Even when tying all their ropes together, none of the households alone are able to reach the water, but As two ropes together with one of B\s ropes just reach the water. Likewise, Bs three ropes with one of Cs ropes, Cs four ropes with one of Ds ropes, Ds five ropes with one of Es ropes, and Es six ropes with one of As ropes all just reach the water. How long are the ropes of the various households, and how deep is the well? Commentary: As stated, this problem leads to a system of 5 linear equations in 6 variables; with the given information, we are unable to determine the depth of the well. The Nine Chapters gives one particular solution, where the depth of the well is 7 zhang,'5 2 chi, 1 cun, or 721 cun (since 1 zhang = 10 chi and 1 chi = 10 cun). Using this particular value for the depth of the well, find the lengths of the various ropes.

Chapter 9 Section 3 SNOW DAY PRESENTATION 02/24/2016 Chapter 9 Section 3 Terminology: Space- is an undefined term (like point, line and plane) Dihedral angle- angle formed when 2 planes meet Parallel- if the line doesn’t intersect the plane Perpendicular- if the line if intersects and is perpendicular to EVERY point in plane Two planes are parallel if they do not intersect Two planes are perpendicular if dihedral angle measures 90 degrees Polyhedral- figures in space whose sides are polygonal regions Faces- polygonal regions or sides Edges- 2 faces intersect