Pythagorean

This created a contradiction within the Pythagorean school of thought.

This was an extension of a Pythagorean tradition, but went beyond it.

The Pythagorean school saw a strong connection between mathematics and beauty.

He is perhaps best known for his compendium on Pythagorean philosophy.

However, some Pythagorean intervals are also used in other tuning systems.

Pythagorean scales are ground zero for more than 2,000 years of European music that came after them.

The third level might be a Pythagorean level of mathematics.

Pythagorean mystics gave great importance to the odd and the even.

The Pythagorean result is recovered in the limit of small triangles.

A Pythagorean prime is a prime number of the form 4n + 1.

For the musical (rather than instrumental) scale, see Pythagorean tuning.

Then m, a, and b form a Pythagorean triple.

Further details about this table can be found in Size of Pythagorean intervals.

He actually makes the Pythagorean theorem fun and interesting.

There is evidence that women were active members of the Pythagorean school, not only as students, but also as scholars and teachers.

Many textbooks credit the Pythagorean school with several important discoveries, including:

Pythagorean scale refers to the relative lengths of strings within an instrument.

This was a Pythagorean version of the scale.

The Pythagorean identities give the two alternative forms for the latter of these:

A Pythagorean saying advises not to eat food that has fallen on the floor, because "it belongs to the heroes".

In Pythagorean music theory, the Epogdoon ratio is 9 to 8.

The Pythagorean school of mathematics originally insisted that only natural and rational numbers exist.

Pythagorean thought was dominated by mathematics, and it was profoundly mystical.

In music theory, a semiditone (or Pythagorean minor third) is the interval 32:27.

In Pythagorean tuning, the minor sixth is the ratio 128:81, or 792.18 cents.

Discoveries like this led the Pythagoreans to the conclusion that "all is number."

That the teachings of the Pythagoreans play a certain role in the novel, it is only obvious.

The Pythagoreans believed that a release from the "wheel of birth" was possible.

The Pythagoreans were notable as a sect for including women in their ranks.

Campaigning in Italy, he found time to study with the Pythagoreans.

As a mystical symbol, it was very important to the secret worship of the Pythagoreans.

Influenced by the Pythagoreans, he supported the doctrine of reincarnation.

The Pythagoreans developed a theory of ratio and proportion as applied to numbers.

The first number, according to the Pythagoreans, and the first male number.

Aristotle had written a separate work on the Pythagoreans, which unfortunately has not survived.

In their study of mathematical concepts, the Pythagoreans sorted numbers into categories.

Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties.

Length and breadth, when they merge, make the solid, which the Pythagoreans thought of as mind emerging into reality.

He started a group of mathematicians, called the Pythagoreans, who worshiped numbers and lived like monks.

As Aristotle was later to write, "the Pythagoreans construct the whole universe out of numbers".

The Pythagoreans acquired considerable influence with the supreme council of one thousand by which the city was ruled.

Like the Pythagoreans' perfect numbers, magic squares have passed from superstition into recreation.

The Pythagoreans were quite a political power in the city and were involved in a number of disturbances.

Pythagoras (and his entire philosophical school, the Pythagoreans) believed in the literal reality of numbers.

Shortly afterwards, however, an insurrection took place, by which the Pythagoreans were driven out and a democracy established.

Since he worked very closely with his group, the Pythagoreans, it is sometimes hard to tell his works from those of his followers.

Religion was important to the Pythagoreans.

The Pythagoreans have a further reason.

In his practice, Cleinias was a true Pythagorean.

Some of these later works, such as Aristotle's commentary on the Pythagoreans, are themselves only known from a few surviving fragments.