## Rhyme Time

*September 27, 2010 at 9:26 pm* *
2 comments *

My friend Josh Zucker created a joke about math and poetry:

Why don’t 8 and 15 make good poets?

Because they only relatively rhyme.

Painful, I know. Hopefully the following poems will ease the hurt.

The first poem yields a system of equations in two variables. I can tell you that using algebra is not so easy, but I was able to find the solution in about four minutes with an Excel spreadsheet.

Take five times which plus half of what,

And make the square of what you’ve got.

Divide by one-and-thirty square,

To get just four — that’s right, it’s there.

Now two more points I must impress:

Both which and what are fractionless,

And what less which is not a lot:

Just two or three. So now, what’s what?

The following poem by Leo Moser poked fun at Paul Erdös’ tendency to publish important proofs in obscure journals.

A conjecture both deep and profound

Is whether a circle is round.

In a paper of Erdös,

Written in Kurdish,

A counterexample is found.

And one of my favorites from Shel Silverstein:

My dad gave me one dollar bill,

‘Cause I’m his smartest son.

And I swapped it for two shiny quarters,

‘Cause two is more than one!And then I took the quarters

and traded them to Lou

For three dimes — I guess he doesn’t know

That three is more than two!Just then, along came old blind Bates,

And just ’cause he can’t see,

He gave me four nickels for my three dimes,

And four is more than three!And I took the nickels to Hiram Coombs

Down at the seed-feed store.

And the fool gave me five pennies for them,

And five is more than four!And then I went and showed my dad,

And he got red in the cheek.

He closed his eyes and shook his head —

Too proud of me to speak!

Entry filed under: Uncategorized. Tags: Erdos, math, poem, poetry, rhyme, Shel Silverstein.

1.xander | September 27, 2010 at 11:46 pmFor simplicity, let x=which, and y=what. Then the first four lines of the poem give us the equation (5x+y/2)^2/31^2=4. I think that line 6 is a little bit ambiguous, as it could be interpreted to mean that both x and y are irrational (i.e. have no representation as fractions) or are integers (i.e. can be expressed without using fractions). However, the set of solutions dictates the latter interpretation. Finally, the last line indicates that either y-x=2 or y-x=3.

We can start by simplifying the first equation. Multiplying each side by 31^2, then taking the square root, we get

(5x+y/2)^2 = 3644

+/-(5x+y/2) = 62. (*)

At this point, we are more or less done with the first equation. We can now start substituting from the second set of equations.

If we assume that y-x=2, then we have y=2+x. Substituting this into (*), we have x = {122/11, -126/11}. Both of these are rational, and neither is an integer, so we conclude that y-x≠2. So we assume y-x=3. So y=3+x. Substituting this into (*), we have x = {11, -127/11}. Thus, assuming that x is an integer, we have x=11.

Finally, as y-x=3, we can substitute our value for x and solve for y, concluding that y=14. Therefore (x,y)=(11,14).

In conclusion:

With much work and a bit of thought,we conclude that fourteen is what.

From this we find (though it’s a bitch):

eleven’s the value of which.

xander

2.venneblock | September 28, 2010 at 5:42 amXander, I was really dumb and failed to take the square root to get (*). Instead, I was stuck with a quadratic equation, a linear equation, and a headache! That’s when I relied on Excel to save the day.

Your solution is mathematical and poetical… I love it!

But once you get (*), you can just use a little logic. The equation is 5x + y/2 = 62, and the fact that they differ by 2 or 3 all but tells you that they’re integers. So just use guess-and-check. If x = 10, then y = 24, and that’s too much of a difference. Try x = 12, then y = 4, and that’s too much, too, but in the opposite direction (that is, this time y is smaller). The sweet spot is in the middle, so x = 11 and y = 14 gives the solution, with |x – y| = 3.