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.

Explain the concept of proof by contradiction as demonstrated by Hippasus.

Discuss how irrational numbers can be represented on the number line despite not being expressible as ratios.