80 likes | 91 Views
Discover five different walking strategies to navigate a minefield, with distances ranging from 0.5 miles to 2.82 miles. References provided for further reading.
E N D
What’s the French for“Ba Ba Boom”? Last known location: 77, Minefield Strip, Somewhere Dark,Between the Hellarwiand the Nagumba
Walking strategy #1 5 Ba Ba Boom! 1 2 Spiralling out Takes½ n (n+1) L Where (n-2)*L = 1760yd Distance is between 4 - 900 miles depending on L 4 3
Walking strategy #2 Ba Ba Boom! Circular Of diameter 1 mile Takes miles
Walking strategy #3 Ba Ba Boom! 2 1 Orthogonally With segments of length 2 Takes 22 2.82 miles 2
Walking strategy #4 Ba Ba Boom! 2/3 1/3 1 Equilaterally With segments of length 2/3 Takes 4/3 2.31 miles 1/3
Reference Solution • From the book Problem-Solving Strategies by Arthur Engel (Springer, 1998) • “The last is only slightly above the ideal 2.278 which is very difficult to find. It consists of a curve ABCDC`D`E where BC and D`C` are circular arcs, AB is a tangent of BC, ED` a tangent to D`C` and DC and DC` are tangents to both arcs. This is the shortest curve which does not completely lie inside a 1 mile wide strip.”
Walking strategy #5 E Ba Ba Boom! D Ingeniously Via tangent AB, chord BC, tangent CD, and mirrored by DC`, C`D`, D`E Takes 2.278 miles C B A
Optimum strategy Wait for dawn! Takes 0.5 miles