Thales and Pythagoras

Who was Thales of Miletus?

Thales of Miletus (circa 625-547 BCE) was a Greek philosopher and one of the Seven Sages of Antiquity.

What is Thales known for in the field of mathematics?

Thales is considered the first mathematician due to the geometric properties he formulated.

What method did Thales use to calculate the height of a pyramid?

Thales measured the length of the pyramid's shadow and compared it to the length of a vertical stick's shadow to calculate the height.

Which of Thales’ properties are still applied today?

Thales' properties include the equality of angles at the base of an isosceles triangle and the equality of angles opposite each other when two lines intersect.

What is Thales’ theorem?

Thales’ theorem states that the ratio of lengths in a triangle cut by a line parallel to one side is proportional.

What other mathematical property did Thales establish?

Thales also proved that a circle is bisected into two equal parts by any diameter.

Who was Pythagoras?

Pythagoras (circa 570-495 BCE) was a Greek philosopher and mathematician, known for his work on right-angled triangles.

What is the most famous theorem associated with Pythagoras?

Pythagoras’ theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (c² = a² + b²).

What did Pythagoras discover about numbers?

Pythagoras discovered the properties of even numbers, prime numbers, and perfect numbers.

What are prime numbers?

Prime numbers are numbers greater than 1 that cannot be divided evenly by any number other than 1 and themselves.

What are perfect numbers?

Perfect numbers are numbers equal to the sum of their divisors, such as 6 (1+2+3) and 28 (1+2+4+7+14).

What was the "Harmony of the Spheres" theory?

The "Harmony of the Spheres" was a theory developed by Pythagoras and his followers, suggesting that the Earth is at the center of an universe governed by harmonious numerical relations.

What fields did Pythagoras and his disciples contribute to?

Pythagoras and his disciples made contributions to mathematics, music, philosophy, and astronomy.

What did the Pythagoreans believe about the universe?

The Pythagoreans believed the universe operated according to numerical and harmonic principles.

How did Pythagoras contribute to the understanding of numbers?

Pythagoras developed an understanding of the relationships between different types of numbers, such as even, prime, and perfect numbers.

What is the significance of the number 6 in Pythagorean theory?

The number 6 is a perfect number because it is the sum of its divisors (1+2+3).

How did Thales and Pythagoras influence later mathematical thinking?

Thales and Pythagoras laid the groundwork for many of the mathematical concepts still used today in geometry, number theory, and astronomy.

What was Thales' approach to mathematical problems?

Thales used a systematic and logical approach to geometry and applied it to practical problems like measuring the height of pyramids.

How did Pythagoras’ work relate to music?

Pythagoras discovered mathematical ratios that correspond to musical harmony, showing the link between numbers and sound.