Gabriel's
Wedding
Cake
Julian
F.
Fleron
Julian Fleron (j_fleron@foma.wsc.mass.edu) has been
Assistant Professor of Mathematics at
Westfield State College
since completing his Ph.D.
in
several complex variables at
SUNY University at
Albany
in
1994. He has broad
mathematical passions that he strives to share with all of his
students, whether mathematics for
liberal arts students,
pre-service teachers, or mathematics majors.
Family hobbies
include popular music, cooking, and restoring the family's
Victorian house.
We obtain the solid which nowadays
is
commonly, although
perhaps
inappropri-
ately,
known
as Gabriel's
hom
by
revolving
the
hyperbola y =
1/x
about
the line
y = 0, as
shown
in
Fig.
1.
(See, e.g.,
[2],
[5].) This
name
comes from the archangel
Gabriel
who,
the
Bible tells us,
used
a
hom
to
announce
news
that was some-
times heartening (e.g. the birth
of
Christ in Luke 1)
and
sometimes fatalistic
(e.g. Armageddon in Revelation
8-11).
Figure 1. Gabriel's
Horn.
This object
and
some
of
its remarkable properties
were
first discovered in
1641
by
Evangelista Torricelli.
At
this time Torricelli was a little
known
mathematician
and
physicist
who
was the successor to Galileo at Florence.
He
would
later
go
on
to
invent
the
barometer
and
make
many
other
important contributions to mathematics
and
physics. Torricelli communicated his discovery
to
Bonaventura Cavalieri
and
showed
how
he
had
computed
its volume using Cavalieri's principle for indivisibles.
Remarkably, this volume
is
finite! This result propelled Torricelli into the mathemati-
cal spotlight, gave rise to
many
related paradoxes
[3],
and
sparked
an
extensive
philosophical controversy that included Thomas Hobbes,
John
Locke, Isaac Barrow
and
others [
4].
VOL. 30, NO. 1, JANUARY 1999
35