I can’t understand why they don’t shoot several extremely high res split-second timed videos from inside the cockpits of various kinds of planes making absolutely perfect landings during 100 percent visibility conditions both in the day time and at night in airports around the world. So that the next time it’s so foggy or raining or sleeting or snowbound or whatever when the pilot can’t see the end of his or her eyeballs and passengers are prepared to leap out to meet their lovers instead of their makers, the same can be projected either on the windscreen in front or on a pair of virtual reality goggles. If the plane’s speed, altitude and distance can be matched up in precision lockstep with the same parameters in the video, the pilot should be able to land the aircraft. In fact, it’ll be like a simulator experience with reality in the background.Like this is a great idea or what for which all airlines should give me free tix forever or am I waffling out the bottom of my head as usual?
THROUGHPUT
(The doublethink question was: “What’s the shortest bisecting arc of an equilateral triangle? By this time you’re thinking, ‘This guy’s gotta be kidding me -- it’s the angle bisector dude. No wait, it’s a chord parallel to the base because it’s shorter than an angle bisector. Yup, that’s it.’ Actually it isn’t.”)
According to Isoperimetric theorem, among all shapes with a given area, a circle has the shortest perimeter. Using this principle, it is found that, in an equilateral triangle, the shortest bisector is the 60 degrees arc of a circle, starting at one side and ending in another side of the equilateral triangle. This arc divides the equilateral triangle into two halves of equal area. -- Narayana Murty Karri, k_n_murty@yahoo.com
The correct answer is a 60 degree arc of a circle. Reflect the triangle about successive bases to make a regular hexagon. Now we need a figure that occupies half the hexagon’s area and has the shortest possible perimeter. That’s a circle: -- Jaya Krisnamoorthy. jkmoorth@hotmail.com
(The second one was about an illegible question with the following answers: (a) All of the below; (b) None of the below; (c) All of the above; (d) One of the above; (e) None of the above; (f) None of the above. Your problem was to figure out which one was correct.)
If A is true, then B to F are true. But if B is true, then C to F must be false. That is a contradiction. So eliminate A. If B is true, then D must be false. But to make B true, D has to be true. Another contradiction. So eliminate B. C says A and B are true. But we proved that A and B are false. So C is eliminated. Since A, B and C are eliminated, D cannot be true. Now if F is true, then A to E are false; but E is true in saying that A to D are false. So F cannot be true. So the only option true is E. -- Saifuddin S F Khomosi, Dubai
(The third problem was: “You and I drive from A to B in separate cars. We depart simultaneously, and you stay always ahead of me, dutifully driving the speed limit throughout the trip. Nonetheless I get caught by the cops for speeding. How?”)
One possibility is like this: I drive the car at a uniform speed below the speed limit. But, you, though, following me throughout the trip, drive the car at times slowly and at times faster exceeding the speed limit and thus get caught by the cops. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com
The dutiful driver goes at normal speed but the other one drives very slowly at the beginning and he lags behind at a stage. At this point he tries to catch up with the dutiful driver. In his attempt to do so he exceeds the permissible speed limits and gets caught. No arithmetic here; just simple logic. -- Sanath Kumar T S, sanathkumarts1958@gmail.com
BUT GOOGLE THIS NOW
1. You have a 3-inch cube that you want to cut into 27 1-inch cubes. This can be done by making six cuts. Can it be done with fewer cuts by rearranging the pieces between cuts?
2. It’s been observed that a slanted roof receives less rain per unit area than level ground does. Does this mean that rain falling at a slant will be less wetting than rain that falls vertically? Okay time for a hint: it doesn’t; by why not?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)