## Thursday, January 7, 2010

### Are you Leaning, or Diagonal?

We touched on the horizontal and vertical dimensions of life yesterday. Today I'd like to discuss the diagonal. (You can see I don't have enough fancy font attributes for all these math terms.)

A diagonal is a straight line connecting two non-adjacent vertices of a polyhedron. Or as a layman might say, a slanting line across the middle to opposite corners.

When you are used to vertical and horizontal, diagonal is a bit different. It seems weaker, or less stable, or something. Shall I give you some examples?

Fabrics can be cut and sewed in a diagonal way across the warp and weft threads. This technique is called "on the bias."

That's not the same as having diagonal stripes on your shirt which is pretty rare, I think. No wonder this man's looking confused!

Then there are cutting pliers called diagonal cutters, or dikes. And finally, I found a place that recommends diagonal bookcases. You don't need bookends, because the books are already tipped over.

One thing a diagonal does is ADD STRENGTH to a square or rectangular structure. We teach this in some activities where we ask kids to build things with straws and string.

Here's a tandem bicycle that I built 30 years ago which successfully employed many small diagonal tubes in an effort to improve rigidity. Notice that the diagonals connect sides of the main frame rather than the exact corners. This is due to the complexity of joining the tubes in the corners.

This building by Frank Gehry is leaning, NOT a diagonal!