My goal last summer (or maybe it was the summer before that, but it didn't get done until the beginning of last summer) was to construct a fence for our house. A fence can add beauty to a house. It can give a mom increased comfort that her little ones won't inadvertently find themselves in the traffic passing by the front of the house. My back door neighbor at our previous house helped a friend tear down his tall privacy fence. He asked if I wanted to use that material. After cutting it down so it would go further installing the fence I power-washed it and it looked great. This time I even stained it. So I've built two fences in my life. For both I used my good ol' TI-89 to graph the equation and then I use 'Trace" to get the height value I needed. (Interestingly, building the fence was the last time I had used that TI-89 Titanium. Last summer I moved on to using and teaching with the TI-Nspire CAS.)
Both fences have been modeled after my favorite shapes, the hyperbolic cosine. Some may know it better as a catenary. Inverted, this amazing shape is great for providing a smooth ride to a vehicle with square wheels: link 1, link 2. You may also enjoy the poem my favorite mathematical physicist, James Clerk Maxwell, wrote about 'an inextensible heavy chain' in "A Problem in Dynamics" (see page 317-18 of his biography and try to read it with a Scottish accent.) I quote a portion of this on page 8 of a paper I wrote a while back.
So what is a project for this summer?
You may recall a recent post where I stated the goal was to park our little mini-van in the garage this winter. Much to my surprise, when I got back from a recent trip, our smaller vehicle was IN THE GARAGE. (Thanks sweet wife!) I don't know if this has ever happened in the five years we've lived here. This may be partially attributed to our lack of a garage door opener. Perhaps we will now consider making this expenditure. Although there probably was a day not too long ago when people actually got out of their car and hoisted the door manually, got back in the car, and drove in. Come to think of it, my grandfather doesn't have an automatic garage door opener, but his is on hinges and opens out.