Unfortunately, during his life Roberval did not achieve much
notoriety because his work took place at the same time as Fermat and Pascal.
Roberval also worked on curves. Among his most famous are: the Cycloid, the
Limacon of Pascal, the Cissoid of Diocles, and the Folium of Descartes. Cycloid:
The cycloid is the locus of a point at distance h from the center of a circle
radius a that rolls along a straight line. If h * a it is a curtate cycloid
while if h * a it is a prolate cycloid. This curve has a = h. Limacon of Pascal:
This curve was discovered by Etienne Pascal, the father of Blaise Pascal.
However, it was named by Roberval in 1650 when he used it as an example of his
methods of drawing tangents.
The name Limacon comes from the Latin word limax
which means a snail. While Roberval is often given credit for this curve, many
of the members of the Mersenne group contributed to its development. When b = 2a
then the limacon becomes a * a while if b = a then it becomes a trisectrix.
Cissoid of Diocles: (no information) Folium of Descartes: This curve was first
thought of in 1638, but Roberval believed that the leaf shape was repeated in
each quadrant when it is only in quadrant I. This curve has an asymptote x + y +
a = 0. This curve passes through the origin at t = 0 and comes close to the
origin as t goes to infinity. As is clearly evident through this information,
both Michael Stifel and Gilles Personne de Roberval made great contributions to
the world of mathematics. Life today would just not be the same if these two men
had not done their important work.
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