with the other Pythagoreans, had no personal possessions, and were vegetarians.
Those in the “outer circle” of the society were known as akousmatics.They lived in
their own houses and only came to the society gatherings during the day. Even
women were allowed to join, some of them becoming famous philosophers. Although
Pythagoras is thought to have written many works, the secrecy of his school and its
communalism has made it difficult to distinguish between the works of Pythagoras
and those of his followers. (For more information about Pythagoras and the
Pythagoreans, see above and “History of Mathematics.”)How did Jainisminfluence mathematics in India?
Jainism was a religion and philosophy founded around the 5th century BCEfollowing
the decline of the Vedic religion on the Indian subcontinent. Along with Buddhism, it
became one of the area’s main religions.Over the next several centuries, Jainism also became a major influence in Indian sci-
ence and mathematics. It was steeped in cosmological ideas in which time was thought of
as eternal and without form. The world was also considered to be infinite and to have
always existed. In fact, their cosmology included time periods with numbers larger than
our modern guesses about the universe’s age. Even their astronomical measurements
came close to some of our modern values. For example, the synodic lunar month was
thought to be 29 16/31 days (29.516129032 days); the correct value is 29.5305888.Jainism also produced a plethora of mathematical ideas, some of which were sur-
prisingly advanced for their time. For example, they understood such concepts as the
theory of numbers, arithmetic operations, sequences and progressions, the theory of
sets, square roots, knowledge of the fundamental laws of indices, geometry, an approx-
384 imation of pi (they believed πequaled the square root of 10, or 3.162278, which is
What is sangaku?
S
angaku—literally, “mathematical tablet” and often seen as “san gaku”—is
the name for a form of traditional Japanese temple geometry. From 1639
until 1854, Japan was isolated from the West. Because of this, Japan developed a
kind of native mathematics that was used by samurai, merchants, and farmers.
They would solve geometry problems, marking their work on delicately
inscribed, colored wooden tablets that hung under the roofs of shrines and tem-
ples. In general, sangaku problems dealt with Euclidean geometry, but they were
much different from Western geometric studies. Although the majority of the
sangaku are simple to solve by Western standards, others require the use of cal-
culus and other complex methods.