Chapter 13.9, Problem 2AE

To determine

To make model to find the shortest connection between the vertices of triangle.Also find the measures of the angles where the soap film meets.

Answer to Problem 2AE

The angle between any two tangent planes to the intersecting surfaces, at any point along the line of intersection of three surfaces, is ${120}^0$

Explanation of Solution

Concept used:

Three smooth surfaces of a soap film intersect along a centroid. Soap films minimises the surface area thus leading to shortest connection.

Explanation: 

To make model

Requirements:

• A sheet of clear plastic
• 6split pin paper fasteners
• A drinking straw cut into three 3-cm long pieces

Bend the plastic sheet without creasing it. Cut three small slits (to represent four vertices of square) through both the layers of the sheet. Insert paper fasteners through all six slits. Slip two fasteners through each of three. The halves of the plastic sheet should be parallel, and the straws perpendicular to them.

Dip the model in a soap solution and carefully lift it out. A system of vertical soap films between two sheets of plastic and joining the straws will be seen (as shown in below pictures)

  

After taking out the model from soap solution we will obtain 3-D figure as shown above. The point at which planes meet is called centroid.

By placing the protector on top of the model where soap films meet, measure the angles.

The angle between any two tangent planes to the intersecting surfaces, at any point along the line of intersection of three surfaces, is ${120}^0$