Vuvuzelas and Surfaces of Revolution

Before the World Cup disappears forever (to me, four years = forever) , I must point out that the vuvuzela

reminds me a lot of the surface of revolution known as the Horn of Gabriel,

which is obtained by rotating the function y = \frac{1}{x} around the x-axis.  The curious thing about this surface is that it has finite volume but infinite surface area.

Thus, if this object existed in the real world, you could fill it up with a finite amount of paint, but you couldn’t cover the surface with a finite amount of paint.  If that means anything.

Player Evaluation

The New York Knicks have agreed with Amare Stoudemire on a 5-year, $100 million contract, which will likely be their only major acquisition during this much-hyped NBA free agent bonanza.  I like Stoudemire, but he strikes me as a player who, like many others, looks much better playing with Steve Nash than he’ll look with whomever the Knicks sign to play point guard.

Stoudemire can’t really create his own shot, so someone has to get Stoudemire the ball, and Nash gets scorers the ball as well as any point guard in the league.  Is Stoudemire going to look like a $20 mil / year player with Sergio Rodriguez setting him up?  As a longtime Knick-hater, I’m looking forward to 5 years of “No”.

It would be interesting and useful to quantify a player’s efficiency conditioned on whether a certain teammate is playing with him or not.  My hunch is that, for example, Stoudemire would look a lot less efficient playing without Nash than playing with him.  There is a basic evaluation of player-pairs here http://basketball-statistics.com/nbaplayerpairs.php, but these numbers don’t tell us how Stoudemire performs when Nash isn’t on the floor.

An effective analysis along these lines might have saved the Knicks some money.  In theory, anyway.

Visual Representation of Data

A friend claimed that this video about Mariano Rivera contained the best info-graphic ever made, and it’s hard to argue.

The whole thing is fascinating, but at about the 1:40 mark the 1300 hundred or so pitches Rivera threw in 2009 are tracked from the mound and plotted in the strike zone.  Not only is it a supremely cool visualization of statistical analysis, but it absolutely helps explain why Rivera is so successful (and, indeed, one of the greatest pitchers in baseball history).

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.

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