This is what Theoni Pappas writes on page 129 of her Magic of Mathematics:
"[Zoologist Frank H. Heppner] established 4 simple rules based on avian behavior, and used triangles for birds. By varying the intensity of each rule, the flock of triangles would fly across the computer's monitor in familiar fashions."
So Pappas is writing about a computer simulation to determine exactly why birds fly the way that they do. She lists Heppner's four rules as follows:
(1) Birds are attracted to a focal point or roost.
(2) Birds are attracted to each other.
(3) Birds want to maintain a fixed velocity.
(4) Flight paths are altered by random occurrences such as gusts of wind.
As we can see, these rules are easy to program into a computer. What appears on the screen looks almost like an actual flock of birds -- um, flock of triangles....
Pappas ends the section on birds with, "It seems chaos theory is at it again!"
Well, there you have it -- mathematics does explain the ways of the birds and the bees. I still think it might be interesting to have a life science unit that connects nature to math, just as Pappas has demonstrated in this chapter.
This is what I wrote last year about today's test:
Today is approximately the end of the fifth hexter -- the midpoint of the third trimester -- so it's a good test day.
Today is the Chapter 14 Test. Here are the answers to my posted test:
1. DE = 32, EF = 16sqrt(3).
2. TU = 16, US = 8sqrt(3), SK = 8, TK = 8sqrt(2).
8. sqrt(3) (Some people may consider this question unfair, since the above question and both corresponding questions on the practice had rational answers, leading students to believe that they can just use a calculator to find the exact value rather than use 30-60-90 triangles.)
9-10. These are vectors that I can't reproduce easily here.
11. BC/AC (or a/b, if the students learned it that way).
12. AB and AD
13. ACD and CBD
14. This is a vector that I can't reproduce easily here.
15. (9, 6)
16. 115 feet, to the nearest foot.
17. (1, 4)
18. (3, -3)
19. (3, 2). (I hope students don't get confused here and solve these three backwards!)
20. This is a vector that I can't reproduce easily here.
Thus concludes Chapter 14. Stay tuned -- we're starting Chapter 15 tomorrow!