Through Math for America, I have been contributing to the New York Times Learning Network. Here is my latest contribution:
http://learning.blogs.nytimes.com/2010/07/29/test-yourself-july-29-2010/
This problem is based on New York Yankees pitcher Mariano Rivera as his remarkable record as a closer.
Blockbuster Video will always have a special place in my heart. When a store opened up a few blocks from my childhood home, it was a big deal. We were excited to walk over, browse the rows of VHS (and, for a short time, Beta) cassettes, and bring back a movie or two for three days / two nights.
Oh, how times have changed. Once valued at nearly $5 billion (in 1996 dollars), Blockbuster stock is currently trading at around 17 cents a share, which means that the company is currently valued at around $37 million.
So where is this $37 million in value? The company has dropped more than 100-fold in value, but $37 million stills seems like a lot of money. Does Blockbuster have any significant revenue? Do they have exclusive agreements with movie studios that have value? Is the Blockbuster brand worth something? Can they sell all their old VHS tapes to Panama?
Determining the value of a company is an interesting and complicated problem. Facebook provides another good example of the complexities involved. Recent reports suggest Facebook has a value between $10 and $20 billion, even though Facebook’s revenue is on the order of $1 billion. How does one determine that all the non-revenue-related stuff (brand identity, user base, etc) is worth $9 billion?
One thing is for sure: Netflix, currently valued at around $5 billion, is definitely 133 times more valuable than Blockbuster. At least.
Through Math for America, I have been contributing to the New York Times Learning Network. Here is my latest contribution:
http://learning.blogs.nytimes.com/2010/07/28/test-yourself-july-28-2010/
This problem is based on the amount of oil leaking into the Gulf of Mexico as a result of the British Petroleum accident.
When Miguel Cabrera came up to the plate in the fifth inning of last night’s Tigers-Rays game, he was 0-for-1 in the game and his up-to-the-minute batting average was announced as .349. I found this strange because, when the game started, Cabrera’s batting average was .350.
A player’s batting average is equal to (total hits) / (total at-bats). Thus the effect of one more at-bat without a hit dropped his average by .001, or 1/1000 (Note: rounding probably plays an important role here).
I wondered if this information uniquely determined both Cabrera’s hits and at-bats this season. Or maybe some combination of mathematics, baseball knowledge, and guessing could help me get those numbers. I did get the numbers–unfortunately, they were wrong.
An interesting question here is “What is the smallest possible number of hits such that one more hitless at-bat results in one’s rounded batting average dropping by .001?”
There seemed to be a lot of geometry involved in my grilling this weekend. The circular grill, the cylindrical chimney starter, the pyramid of coals. The charcoal briquettes themselves look like solids with mirrored parabolas as vertical cross-sections and squares as horizontal cross-sections.
As I cooked a few times over different coal arrangements, I wondered about the heat distribution on the grill over the perfect pyramid of charcoal. Obviously the hottest point is the center (nearest the peak of the pyramid), and the temperature drops as you move toward the edge along a radius. Does it drop linearly? Like a parabola? Like a log function?
My guess is it looks like the image below. I don’t have any evidence for this speculation, but this is a representation of a Gaussian distribution, and when in doubt, go with Gauss. Gauss seems to have a hand in everything. Maybe I’ll bring the meat thermometer next time and take some readings.
