The Fascinating Story of the Square Root of 2

📐The ratio between the long and short edges of A4 paper is equal to the square root of 2.

🧮The square root of 2 is an irrational number and cannot be expressed as a fraction of two integers.

😱The discovery and proof of the irrationality of the square root of 2 caused controversy and led to the persecution of mathematicians.

🔢The Pythagoreans believed in the harmony of natural numbers and thought that all of nature could be expressed as ratios of integers.

📚The square root of 2 is just one of many irrational numbers, including pi, that do not fit into the Pythagorean belief system.

What is the square root of 2 used for?

—The square root of 2 is used to define the ratio between the long and short edges of A4 paper, which is the standard paper size in most of the world.

Why is the square root of 2 an irrational number?

—The square root of 2 cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal.

Who were the Pythagoreans?

—The Pythagoreans were a cult-like group of mathematicians and philosophers who believed in the harmony of natural numbers and the idea that everything in nature could be expressed as ratios of integers.

Why did the Pythagoreans dislike irrational numbers?

—The Pythagoreans believed that all of nature could be expressed as ratios of integers, and irrational numbers like the square root of 2 went against their belief system.

Are there other irrational numbers besides the square root of 2?

—Yes, there are many other irrational numbers, including pi and the square root of other non-perfect square numbers.

00:00The square root of 2 is the number that, when multiplied by itself, equals 2.

00:10The ratio between the long and short edges of A4 paper is equal to the square root of 2.

00:36The square root of 2 is an irrational number and cannot be expressed as a fraction.

01:17The discovery and proof of the irrationality of the square root of 2 caused controversy and led to the persecution of mathematicians.

03:18The Pythagoreans believed in the harmony of natural numbers and thought that all of nature could be expressed as ratios of integers.

04:51The square root of 2 is just one of many irrational numbers, including pi, that do not fit into the Pythagorean belief system.

06:10The square root of 2 is proven to be irrational using a mathematical proof called contradiction.

06:35The Pythagoreans disliked the idea of irrational numbers and persecuted mathematicians who proved their existence, such as Hippasus.