TED-ED: Making sense of irrational numbers - Ganesh Pai

Hippasus, a Pythagorean mathematician, discovered irrational numbers, challenging the belief that all numbers could be expressed as ratios of integers. His proof by contradiction showed that the square root of 2 could not be expressed as a ratio, contradicting Pythagorean beliefs. Despite myths of divine punishment, his discovery revolutionized mathematics. Irrational numbers like root 2 and pi can be precisely plotted on a number line, illustrating that decimals and ratios are just expressions of numbers. Hippasus's work highlights the importance of exploring the impossible in mathematics.

What was the main belief of the Pythagorean mathematicians that Hippasus challenged?

• All numbers can be expressed as ratios of integers.

• All numbers are irrational.

• Numbers are the building blocks of the universe.

• Numbers have no relation to the universe.

What shape did Hippasus use to demonstrate the existence of an irrational number?

• A square

• A triangle

• A circle

• A rectangle

In Hippasus's proof, what was the contradiction that proved root 2 is irrational?

• p was odd and q was even.

• p and q were both prime numbers.

• p and q were both odd.

• p and q had a common factor of 2.

How can irrational numbers like root 2 be represented on a number line?

• By using a protractor.

• By approximating them with rational numbers.

• By using a compass and straightedge.

• By forming a right triangle with sides of length 1.

What is the significance of the number pi in mathematics?

• It is the ratio of a circle's circumference to its diameter.

• It is the sum of a circle's radius and diameter.

• It is the area of a circle with a unit radius.

• It is the difference between a circle's circumference and diameter.