The problem of the CAP with three forms

One of the first problems posed in my classes is that call “The CAP with three forms“.

It serves as introduction to the descriptive geometry and forces to make a spatial analysis of great interest for the training of students.

The problem is to determine a plug used to fill three holes that we have made in a wooden box.

The CAP will only Plug one of the holes every time, but it has to meet one condition more: If we push it, you will have to exit at the other side of the box.

The box has three holes with the shapes and sizes that are seen in Figure:

• A circumference diameter “to”
• A square side “to”
• A isosceles triangle base “to” and altitude “to”

Our CAP if a cylinder of height “to” and diameter “to” It could cover the circumference, as well as the square getting standing, but it would not enter into the triangular shape.

If our plug out a cone of height “to” and diameter “to” at the base would enter the triangular shape, placing it by the apex it taparía the circular hole, but it would not cover of square shape.

Could you design a plug which resolved our problem?

Later we will put a link to the solution.