Plant Care and Trigonometry

My Mom recently explained to me how to tell if an aloe plant needs to be watered:  if there isn’t enough water in the surrounding soil, the roots will draw water down from the stalks.   As water is drawn down, the stalks will start to sag, kind of like a hot-dog balloon losing air.

This got me thinking that there may be a formula that relates the angle an aloe stalk makes with the normal to the ground and its percent water capacity–perhaps involving cosine?  The basic idea is that as percent water capacity decreases, the angle with the normal increases.

Movie Pricing

I wonder if there are any theaters that take movie length into account when pricing admission.  Last night, I saw “The Girl with the Dragon Tattoo”, which came in around 2.5 hours.  Compare that with “Toy Story 3”, which (according to secondary sources) runs approximately 1.6 hours.  Basically,  for every two showings of TGwtDT, a theater could instead put on three showings of TS3.

I’m sure there are demand issues involved here, but simple logic to me suggests that more showings means more people in the seats, which yields more revenue through admissions and concessions (I’m assuming the margninal cost of showing a movie is negligible).  Inversely, a longer movie means fewer viewings and consequently less revenue.

So maybe longer movies should be more expensive?  Or shorter movies should be cheaper?  As an aside, If quality were a determining factor in price, then I paid too much last night.

Birthdays

My friend recently met a girl who shares a birthday with him.  He is not the romantic type, but he was definitely moved by this remarkable coincidence.

Assuming all birthdays are evenly distributed (are they?), and ignoring freaks born on February 29th, the probability that a person you meet will have the same birthday as you is 1/365, which is approximately .27%.

This is about twice as likely as getting dealt a full house in a five-card poker hand, which hardly qualifies as “fated”.  If she had his initials, too, that would be another story.

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