1) The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

2) Pythagorean triplets are sets of three integers that satisfy the Pythagorean theorem.

3) Pythagorean tuning is a system of musical tuning based on simple ratios of frequencies.

4) Pythagorean philosophy emphasized the importance of mathematics and harmony in the universe.

5) Pythagorean triples include the numbers 3, 4, and 5 which form a right triangle.

6) A Pythagorean cup is a type of drinking cup that prevents overconsumption by draining the liquid if filled past a certain level.

7) Pythagorean symbolism can be found in various ancient cultures and societies.

8) Pythagorean numerology assigns numerical values to letters and words for divinatory purposes.

9) Pythagorean intervals in music are based on the ratios of small whole numbers.

10) Pythagoreanism was a prominent school of thought in ancient Greece.