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Mathematician develops an app to reduce Jet Lag

April11

Danny_forger2In his Research Statement, Mathematician Danny Forger says that he devotes his research to “understand biological clocks”…using “techniques from many fields, including computer simulation, detailed mathematical modeling and mathematical analysis, to understand biological timekeeping.”

Perhaps this is why he has developed an app to reduce jet lag for travellers. “Overcoming jet lag is fundamentally a math problem, and we’ve calculated the optimal way of doing it.” says Danny.

The resultant smartphone app, Entrain, provides customised schedules for the first few days of a trip, instructing the user when to seek out the brightest light and when to draw the curtains. The recommendations may be distinctly antisocial, but Professor Forger says that sticking to the timetable can halve the length of time spent in a zombie-like state. For example, if you were taking a business trip from New York to London, which is five hours ahead, the app promises to shift your body clock within three days — less than the rule of thumb of one day for every hour your bodyclock is shifted.

To achieve this, on the day after arrival you are told to get light from 7.40am until about 9pm, and not after this. On the second day, you are required to rise at 6.20am and turn out the lights at 7.40pm. You may feel like going for an evening walk or meeting friends for a drink, but doing so would spoil the schedule.

On the third day, you should get up before sunrise, about 5am, and stay in the light until 7.20pm, at which point you should retreat to a dark, or at least dim, environment. “You don’t have to be asleep,” the scientists point out. The following day, in theory, you will be fully adjusted. Read the full article here.

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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