patrick honner

Math teacher in Brooklyn, New York

Fluctuating Batting Averages

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?”

By patrick honner, ago

Geometry of BBQ

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.

By patrick honner, ago

Creative Seating Charts

Suppose an organization is hosting a banquet with tables numbered 1 through 12, and they are looking for a fun, math-y way to get guests to their assigned table.  So, when the guests arrive and find their name-card in the lobby, they must solve a simple math problem to determine their seating assignment.

It’s easy to figure out simple math problems whose answers are the numbers 1 through 12–the tough part is to do it in some uniform way, as with a theme.  For example, a past theme for this event was to use mathematical expressions that only involved the number 4:   thus, ( 4  /  4 ) would be table 1, or ( 4 ^ 4  – 4 / 4 )  /  ( 4 + 4 – 4 / 4 ) would be table x.

My suggestion was to have a string of two of the four letters A,B,C, or D on each card in some order.  A guest’s table number would then be that string’s position in the alphabetical order of all such strings (AB would be table 1, for example).

If you can think of something more interesting, the banquet isn’t until September.  But it’s really 60 tables, not 12.

By patrick honner, ago

Real World Problems

I’ve been shopping for a new cell phone (doesn’t yours have an antenna?) and it reminded me about cell phone plans and linear algebra.

Cell phone plans used to be the prototypical real world problem for high school math classes.

Plan A costs $10 a month plus 25 cents a minute, while Plan B costs $30 a month plus 12 cents a minute.  Which plan should Sue Consumer choose?

Figure out the equations of some lines, find the intersection, make some conclusions.  Math in action!

Fast forward to the present, and it’s embarrassing how confused I am by all the options:  a serious multivariable analysis is necessary to figure out which plan is the right one for me.  This was once an exemplar of simple, relevant application, but now it has become ugly with the real real world details.

By patrick honner, ago
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