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Pythagoras’s Constant: The Square Root of 2

√2 is a fundamental mathematical constant also known as Pythagoras’s constant. It represents the length of the diagonal of a square with side length 1:

√2 ≈ 1.41421…

This special number was first studied in depth by the ancient Greek mathematician Pythagoras and his followers.

Why Is √2 Important?

√2 is an irrational number, meaning its decimal representation never ends or repeats. Despite its seemingly simple definition, √2 has profound implications in various fields including geometry, trigonometry, and physics. This constant appears in many important mathematical theorems and formulas, such as the Pythagorean theorem.

Where Else Does √2 Appear?

Beyond the Pythagorean theorem, √2 shows up throughout mathematics and everyday life. It is central to trigonometry as the value of sin(45°) + cos(45°) and appears in the diagonal calculations of any square or rectangular structure. Engineers and architects rely on it constantly when working with right angles. It also plays a role in the standard paper size system (A series), where each sheet has a width to height ratio of 1:√2, allowing the paper to be folded in half while maintaining the same proportions.