Amateur Ornithology - Part One: Problem-Solving Crows and Other Animals
Ah yes, we've all faced the problem... We need to use the minimal amount of gift wrapping paper (that's left over) to cover the maximum amount of gift box. (And as weird as it all
seemed, the more we tried different but similar gift boxes, the more (or less) the paper usage worked out.) Sometimes it really does seem that more is less and less is
more.
I first learned this lesson when laying out rectangular gardens with chicken wire... I'd have a 150' roll of chicken wire. Now, if I made the garden 25' by 50', I'd use all the chicken wire and have a garden consisting of 1,250 sq. ft. But, if I used that exact same 150 foot roll of chicken wire, and made the garden 10' by 65', I'd get a garden of only 650 sq. ft. With a little time I figured out that the most efficient way to make a rectangular garden was to make it 37.5' on each side; that way, I'd use all the chicken wire, and get the largest rectangular (square) garden with a total of 1,406.25 sq. ft. However, if I attached the fence to the side of a garage, I'd max my square footage at 2,812.5 using the dimensions of 37.5' by 75'... And if all that wasn't bad enough, if I broke the rules, and made the garden a perfect circle, I'd get a garden of almost 1,800 sq.ft.
What on earth is going on here, and why is CapeCodAlan trying to bore us to death with yet more math???
Here's the deal... What we're talking about are called "maxima" and "minima" in the field of calculus. In "people speak" we're asking, "How can we fit the most into a given area or volume using the least containment material?" Each and every one of us bear witness to the problem every day without even knowing it... What are the ideal dimensions for that soda can such that it still holds 12 oz., but uses the least amount of metal? What's the largest shelf size given a fixed amount of wood?
And what's the most efficient way to pack french fries and other stuff into a crow's mouth?
No, this isn't a joke. That last question was for real, and the answer has startling implications about the intellect of crows and other creatures.
Tune in for an explanation in Part Two of this series...
I'll be waiting for you right by those feeders,
CapeCodAlan
I first learned this lesson when laying out rectangular gardens with chicken wire... I'd have a 150' roll of chicken wire. Now, if I made the garden 25' by 50', I'd use all the chicken wire and have a garden consisting of 1,250 sq. ft. But, if I used that exact same 150 foot roll of chicken wire, and made the garden 10' by 65', I'd get a garden of only 650 sq. ft. With a little time I figured out that the most efficient way to make a rectangular garden was to make it 37.5' on each side; that way, I'd use all the chicken wire, and get the largest rectangular (square) garden with a total of 1,406.25 sq. ft. However, if I attached the fence to the side of a garage, I'd max my square footage at 2,812.5 using the dimensions of 37.5' by 75'... And if all that wasn't bad enough, if I broke the rules, and made the garden a perfect circle, I'd get a garden of almost 1,800 sq.ft.
Here's the deal... What we're talking about are called "maxima" and "minima" in the field of calculus. In "people speak" we're asking, "How can we fit the most into a given area or volume using the least containment material?" Each and every one of us bear witness to the problem every day without even knowing it... What are the ideal dimensions for that soda can such that it still holds 12 oz., but uses the least amount of metal? What's the largest shelf size given a fixed amount of wood?
Tune in for an explanation in Part Two of this series...
I'll be waiting for you right by those feeders,
CapeCodAlan
Comments
Oh, Boy! I can see that this is going to turn into something wonderful but weird!
I can't wait!
Posted by: Joanne | August 9, 2007 9:29 PM