The Spighi Model
of this material will join the National
Bank - A MATH Archive in thanking the Istituto
e Museo di Storia della Scienza, in Florence, Italy, for permitting
us to enjoy this model of the brachistochrone dating to the last half
of the 18th century. On November 29, 1602, Galileo, a resident of
Florence, demonstrated the observable effects that a body takes less
time to fall along an arc of a circumference, than to fall along the
"line" of the corresponding chord. The mathematical proof that
the faster path was the arc of a cycloid was provided later (1697) by
The model had to be larger than one might expect (~ 2.6 yards wide) in
order to vividly demonstrate the difference in times of the two
simultaneously falling balls. Interestingly, this
shares a room in the Museo
with another model of Galileo's investigations into timing a falling
body rolling down an inclined plane. Clearly, the experimental
genius of Galileo was invaluable to Newton's derivation of the
inverse-squares law, i.e., the attractive force varies inversely with
the square of the distance.
e Museo di Storia della Scienza is one of the world's greatest
collections related to science.
For more information please see Institute
and Museum of the History of Science - 18th Century Experimental
Physics Model built by Francesco Spighi.