SQUARE ROOT OF 3

{| border="1" style="float: right; border-collapse: collapse;"
| colspan="2" align="center" | List of numbers - Irrational numbers
√2 - φ - $sqrt\{3\}$ - √5 - e - π
|-
|Binary
| 1.1011101101100111101...
|-
| Decimal
| 1.7320508075688772935...
|-
| Hexadecimal
| 1.BB67AE8584CAA73B...
|-
| Continued fraction
|
|}
The 'square root of 3' is the positive real number that, when multiplied by itself, gives the number 3. It denoted by
:$sqrt\{3\}.$
Its numerical value is approximately 1.73205 .
The square root of 3 is an irrational number. It is also known as 'Theodorus' constant', named after Theodorus of Cyrene.

Contents

Geometry

See also

References

External links

Geometry

If an equilateral triangle (equilateral polygon with three sides) with sides of length 1 is cut into two equal halves, by bisecting an internal angle across to make a right angle with one side, the right angle triangle's hypotenuse is length one and the sides are of length 1/2 and $sqrt\{3\}/2.$ From this the trigonometric function tangent of 60 degrees equals $sqrt\{3\}.$
It is the distance between opposite flat sides of a regular hexagon with sides of length 1.
It is the length of the diagonal of a unit cube.
The shape Vesica piscis has a major axis: minor axis ratio equal to the square root of three, this can be shown by constructing two equilateral triangles within it.

See also

★ Square root of 2

★ Square root of 5

References

★ M. F. Jones, "22900D approximations to the square roots of the primes less than 100", ''Math. Comp'' '22' (1968): 234 - 235.

★ H. S. Uhler, "Approximations exceeding 1300 decimals for $sqrt\{3\}$, , and distribution of digits in them" ''Proc. Nat. Acad. Sci. U. S. A.'' '37' (1951): 443 - 447.

★ Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' Revised Edition. London: Penguin Group. (1997): 23

External links

★ Proof that square root of 3 is irrational

★ Theodorus' Constant at MathWorld