Appreciation

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

On Flyswatters

Designing a flyswatter is an interesting exercise in optimization.

You want it have enough holes so that it can quickly achieve swatting speed, but you don’t want it to have so many holes as to substantially decrease the chance of actually making contact with the pest.

I wonder if there is an industry standard for a flyswatter’s empty-space-to-surface-area ratio.

By patrick honner, ago

Paul’s Perfect Prognostication

Paul the octopus must be enjoying his 15 minutes of fame for correctly predicting the outcomes of eight World Cup matches in a row.  In fact, a stamp in his honor is currently available at the Shanghai World Expo.  This must be a welcome relief from the death threats that followed his [ultimately accurate] prediction of Spain over Germany.

Assuming that the outcome of every match was equally likely (what if you don’t?), then Paul had a 1/256 chance ( that is, (1/2)^8 ) of nailing all eight predictions.  That’s roughly a .4% chance, on the order of getting dealt a straight in a five-card poker hand, or rolling a six three times in a row on a fair die.  Or, if you prefer, exactly equal to the likelihood of flipping a coin and getting Tails (Arms?) eight times in a row.

Apparently octopi have short lifespans, so it doesn’t look like Paul will be around in 2014 to put his record on the line.  At least he’ll go out on top.

By patrick honner, ago

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.

By patrick honner, ago

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.

By patrick honner, ago
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