Sum of Two Cubes Activity Sheet

Ken Keeler has a PhD in applied math from Harvard.
When he was finishing up, there were very
few jobs, so he applied to both academic and TV writing jobs. After a
year at Bell Labs, he decided to try TV writing. In a gotfuturama.com (CGEF)
interview, when he was asked about his many years at school, Ken Keeler
joked that a
*Futurama* reference to 1729 was worth six years of grad
school:

Keeler refers to the episode *Xmas Story*
[2ACV04] written by David X. Cohen
in which Bender the robot receives a card from the machine that
built him wishing "Son #1729" a Merry Christmas.
**Answer the following questions on a separate sheet of paper.**

**Question 1** Use an effective
web search to find out what Ken Keeler means when he says that
1729 is "a historically significant integer to mathematicians everywhere."
Your answer should include information about the mathematicians
Ramanujan and Hardy and a calculation statement about the
number 1729.

**Question 2**
Verify that the related computation statement holds, but do not
prove that it is the smallest
such number. Show work. Next discuss a general proof method or
technique one could use to
show that 1729 is the *smallest* such number
but do not prove the statement.

Ken Keeler says that, "We didn't have the agenda of putting a
mathematical reference in there, other than that we needed a number for plot
reasons. We could have picked one at random, but there was no reason not
to make it an interesting one, and that's how many of these references found
their way in."
The number 1729 also appears in many episodes of
*Futurama*
on the hull of the space ship called the Nimbus
and as the reference number of the universe populated by "bobble head"
characters in the episode *The Farnsworth Parabox*
[4ACV15].
The sum of two cubes comes up again in the episode
*The Lesser of Two Evils*
[2ACV06].
Read the following and look for David X. Cohen's calculation hint.

**Question 3**
Express each of Bender and Flexo's identification numbers as the
sum of two cubes. Use a successful web search to help you, and then
use a computer algebra system or calculator to verify that each number is
indeed expressible as the sum of the cubes of the numbers you found.

**Question 4**
In David X. Cohen's calculation hint (see his comments above)
what did he
mean when he said that "it's a little tricky"? Specifically,
what kind of numbers do mathematicians usually look for when they
express numbers as the sum of two cubes,
and which serial number was "a little tricky" in this sense?

**Question 5**
Search the web to find
recent results about the sum of two cubes
(within the last five years)
and summarize what you found.

In an interview with frontwheeldrive.com,
David X. Cohen said that they try to put in as
much science as possible with the hope of making die-hard fans out of
those that appreciate it.
Thanks to the cleverness and
mathematical backgrounds of the writers,
*Futurama* can be especially fun to watch. And David X. Cohen was
correct in my case. Researching math in *Futurama* for an article I was
asked to write did indeed make a die-hard fan out of me.

Also see
Klein's Beer: *Futurama*
Comedy and Writers in the Classroom, PRIMUS, Volume XVII, Number 1,
March 2007, pp. 52-66.

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