## Devlin's Angle |

*MAA Online* readers should have no difficulty
seeing the insider joke here. Estimating a stock
valuation of around $2 billion, the company's geeky
founders (both former computer science graduate
students at Stanford) took the digits from the
decimal expansion of *e,* the base for natural
logarithms.

Mathematical constants are nothing new to Google.
Its very name is a derivation of the word
*googol,* a term invented in 1938 by
nine-year-old Milton Sirotta to denote a 1 followed
by 100 zeros. Milton was the nephew of the American
mathematician Edward Kasner, who introduced the
concept as a throwaway example of an extremely
large number in his book *Mathematics and the
Imagination.* A googol is greater than the
number of particles in the known universe, which is
estimated to be between 10^72 and 10^87. Even
bigger than a googol, according to Kasner, is a
*googolplex,* a 1 followed by a googol
zeros.

Before the rapidly growing Google moved to larger
premises in its Silicon Valley home earlier this
year, its old headquarters was called the
Googleplex, and the mathematical constants
*e,* pi, and *i* were used to number
buildings. When the company was planning its new
quarters, the new location was temporarily called
the *i*-plex, before being renamed the new
Googleplex when they moved in.

This summer Google turned to the number *e*
once again for assistance, this time to attract
potential employees. Large billboard suddenly
appeared in Silicon Valley and Cambridge,
Massachussetts, bearing nothing other than the
legend:

"(first 10 digit prime in consecutive digits of e).com"[Click here to see a photo of the billboard alongside Silicon Valley's Highway 101. And click here to listen to an NPR report on the ad's appearance.]

Although doubtless meaningless to most passersby,
this ad was red rag to a bull for the math-minded
techie types that it was aimed at. A
straightforward computer search quickly reveals the
first 10 digit prime number in the decimal
expansion of *e* to be 7427466391, so I am not
spoiling the fun by giving the answer here. If you
then visit the website www.7427466391.com, as the
billboard ad instructed, you will be presented with
a more difficult puzzle. Solve that and you will be
taken to a web page that asks you for your CV.

All in all, it makes you wonder why the Bay Area search engine company did not call itself e-Play. No, wait, that name is awfully reminiscent of another successful Silicon Valley startup.

While on the topic of *e* and other
mathematical constants, I can't resist repeating
the claim that I've made to generations of math
students that I've taught over the years that my
absolute favorite mathematical equation of all time
is the one discovered by the great Swiss
mathematician Leonhard Euler in 1748, that connects
the five most significant and most ubiquitous
constants in mathematics:

To me, this equation is the mathematical analogue of Leonardo Da Vinci's Mona Lisa painting or Michaelangelo's statue of David. It shows that at the supreme level of abstraction where mathematical ideas may be found, seemingly different concepts sometimes turn out to have surprisingly intimate connections. Consider:e^(i.pi) + 1 = 0

The number 1, that most concrete of numbers, is the
beginning of counting, the basis of all commerce,
engineering, science, and music. The number 0 began
life as a mere place holder in computation, a
marker for something that is absent, but eventually
gained acceptance as a symbol for the ultimate
abstraction: nothingness. As 1 is to counting and 0
to arithmetic, pi is to geometry, the measure of
that most perfectly symmetrical of shapes, the
circle - though like an eager young debutante, pi
has a habit of showing up in the most unexpected of
places. As for *e,* to lift her veil you need
to plunge into the depths of calculus - humankind's
most successful attempt to grapple with the
infinite. And *i,* that most mysterious square
root of -1, surely nothing in mathematics could
seem further removed from the familiar world around
us.

Five different numbers, with different origins, built on very different mental conceptions, invented to address very different issues. And yet all come together in one glorious, intricate equation, each playing with perfect pitch to blend and bind together to form a single whole that is far greater than any of the parts. A perfect mathematical composition.

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence. It brings together mental abstractions having their origins in very different aspects of our lives, reminding us once again that things that connect and bind together are ultimately more important, more valuable, and more beautiful than things that separate.

Devlin's Angle is updated at the beginning of each month.