The Science Book

(Elle) #1

A CENTURY OF PROGRESS 123


Fourier focused on the idea of
waves, and finding a way to
represent them mathematically.
He saw that every wavelike
movement, which is what a
temperature gradient is, can be
approximated mathematically by
adding together simpler waves,
whatever the shape of the wave to
be represented. The simpler waves
that are to be added together are
sines and cosines, derived from
trigonometry, and can be written
out mathematically as a series.


These individual waves each move
uniformly from a peak to a trough.
Adding more and more of these
simple waves together produces
increasing complexity that can
approximate any other type of
wave. These infinite series are
now called Fourier series.
Fourier published his idea in
1807, but it attracted criticism, and
it was not until 1822 that his work
was finally accepted. Continuing
his study of heat, in 1824, Fourier
examined the difference between
the heat that Earth gains from the
Sun and the heat it loses to space.
He realized that the reason Earth is
pleasantly warm, considering how
far it is from the Sun, is because
gases in its atmosphere trap heat
and stop it from being radiated
back into space—the phenomenon
now called the greenhouse effect.
Today, Fourier analysis is
applied not only to heat transfer
but also to a host of problems
at the cutting edge of science,
ranging from acoustics, electrical
engineering, and optics to
quantum mechanics. ■

Mathematics compares the
most diverse phenomena and
discovers the secret analogies
that unite them.
Joseph Fourier

A Fourier series can approximate
a wave of any shape—even a square
one (shown here in pink). Adding more
sine waves to the series gives a closer
and closer approximation of the square
wave. The first four approximations in
the series (shown here in black) each
incorporate an extra sine wave.

See also: Isaac Newton 62–69 ■ Joseph Black 76–77 ■ Antoine Lavoisier 84 ■ Charles Keeling 294–95


Joseph Fourier The son of a tailor, Joseph Fourier
was born in Auxerre, France.
Orphaned at 10, he was taken
into a local convent before going
on to a military school, where he
excelled at mathematics. France
was in the throes of revolution,
and during the Terror of 1794, he
was briefly imprisoned after
falling out with fellow
revolutionaries.
After the Revolution, Fourier
accompanied Napoleon on an
expedition to Egypt in 1798.
He was made governor of Egypt
and put in charge of the study of
ancient Egyptian relics. Returning

to France in 1801, Fourier was
made governor of Isère in the
Alps. In between administrative
duties overseeing road building
and drainage planning, he
published a groundbreaking
study of ancient Egypt and
started his studies of heat. He
died in 1831 after tripping and
falling down a flight of stairs.

Key works

1807 On the Propagation of
Heat in Solid Bodies
1822 The Analytic Theory
of Heat
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