where
i
is the
imaginary unit
. Note that Euler's
polyhedral formula
is sometimes also called the Euler formula, as is the
Euler
curvature formula
. The equivalent expression
an equation connecting the fundamental numbers
i
,
pi
,
e
, 1, and 0 (
zero
),
the fundamental operations
,
,
and exponentiation, the most important relation
, and nothing else. Gauss is reported to have commented that
if this formula was not immediately obvious, the reader would never be a first-class
mathematician (Derbyshire 2004, p. 202).
The Euler formula can be demonstrated using a series expansion
,
,
and exponentiation, the most important relation
, and nothing else. Gauss is reported to have commented that
if this formula was not immediately obvious, the reader would never be a first-class
mathematician (Derbyshire 2004, p. 202).
The Euler formula can be demonstrated using a series expansion