The Economy Bender

If you want to build a column that has two elliptical cross sections at the top and bottom with different major and minor axis and that can roll, you can just take the ruled surface whose lines connect points with parallel tangents on the two ellipses.

Column

When placed horizontally on a sheet of paper, the column will touch the paper in these lines, and you can wrap the paper around the column, making evident that this is a developable (or flat) surface. You can try it out yourself with the template below.

Template
This simple trick has dramatic economic applications. Suppose you want to transform a boring, stagnating economy into a vibrant, growing economy:

Economies 01

To do so, you just need to join points with parallel tangents on the two economy graphs by straight lines. Here is Martha with a wooden prototype of the Economy Bender.

DSC 3596

You can now wrap some expensive looking material over it. To explain to your CEO how you will be able to transform your failing company into a successful one, just take a printout of last year’s dire company report, put it onto the lower part of the bender next to the stagnating economy curve, and slowly move it upward towards the growing economy curve. You can do this by keeping the report tight on the surface, neither tearing not stretching it. This should convince anybody that a smooth transition into a brave new world is always possible. Here is the template:

Economy
Anybody buying it?

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