id: 06475320
dt: j
an: 2016e.00656
au: Zhou, Li
ti: Do dogs play with rulers and compasses?
so: Forum Geom. 15, 159-164 (2015).
py: 2015
pu: Florida Atlantic University, Department of Mathematical Sciences, Boca
Raton, FL
la: EN
cc: G40 G80 I40 N60
ut: optimization; ruler and compass construction; rate of speeds
ci:
li: http://forumgeom.fau.edu/FG2015volume15/FG201514index.html
ab: Consider the following problem: a dog runs at the speed of 1 and swims at
the speed of $s<1$. A dog is at a point $A$ of a shoreline and tries to
get to a ball which is in the water at point $B$. He wants to get there
as soon as possible. What path should the dog take? This is a very
classical problem of optimization that can be found, with different
contexts, in virtually every elementary calculus book. In fact, this is
related to Snellâ€™s law of refraction. The author gives a ruler and
compass construction of this and some other close related settings.
This is a nice paper to be read by advanced high school students.
rv: Antonio M. Oller (Zaragoza)