page_title: Mathematical constant
section_title: Simple representatives of sets of numbers
hierarchical_section_title: Mathematical constant / Mathematical curiosities and unspecified constants / Simple representatives of sets of numbers
caption_attribution_description: A black and white rendition of my own photograph of the Yale Babylonian Collection's Tablet YBC 7289 (c. 1800–1600 BCE), showing a Babylonian approximation to the square root of 2 (1 24 51 10 w: sexagesimal) in the context of Pythagoras' Theorem for an isosceles triangle. The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888...(30 x square root of 2). All use should attribute both me (mentioning http://www.math.ubc.ca/~cass/Euclid/ybc/ybc.html) and the Yale Babylonian Collection as the original holder of the tablet. Author: Bill Casselman (mailto:cass@math.ubc.ca)
context_page_description: A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol, or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus.
  What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste, just as some mathematical constants are notable more for historical reasons—than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places.
  All named mathematical constants are definable numbers, and usually are also computable numbers.
context_section_description: Some constants, such as the square root of 2, Liouville's constant and Champernowne constant:
  are not important mathematical invariants but retain interest being simple representatives of special sets of numbers, the irrational numbers, the transcendental numbers and the normal numbers (in base 10) respectively. The discovery of the irrational numbers is usually attributed to the Pythagorean Hippasus of Metapontum who proved, most likely geometrically, the irrationality of the square root of 2. As for Liouville's constant, named after French mathematician Joseph Liouville, it was the first number to be proven transcendental.
caption: This Babylonian clay tablet gives an approximation of the square root of 2 in four sexagesimal figures: 1; 24, 51, 10, which is accurate to about six decimal figures.[14]
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