Square root of 3: Difference between revisions
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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. |
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. |
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==Cultural References== |
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Poem inspired by it. |
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I’m sure that I will always be |
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A lonely number like root three |
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The three is all that’s good and right, |
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Why must my three keep out of sight |
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Beneath the vicious square root sign, |
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I wish instead I were a nine |
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For nine could thwart this evil trick, |
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with just some quick arithmetic |
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I know I’ll never see the sun, as 1.7321 |
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Such is my reality, a sad irrationality |
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When hark! What is this I see, |
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Another square root of a three |
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As quietly co-waltzing by, |
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Together now we multiply |
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To form a number we prefer, |
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Rejoicing as an integer |
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We break free from our mortal bonds |
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With the wave of magic wands |
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Our square root signs become unglued |
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Your love for me has been renewed |
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==See also== |
==See also== |
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*[[Square root of 2]] |
*[[Square root of 2]] |
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*[[Square root of 5]] |
*[[Square root of 5]] |
Revision as of 23:24, 4 June 2008
List of numbers - Irrational numbers √2 - φ - - √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 is denoted by
The first sixty significant digits of its decimal expansion are:
- 1.73205 08075 68877 29352 74463 41505 87236 69428 05253 81038 06280 5580... (sequence A002194 in the OEIS)
The rounded value of 1.732 is correct to within 0.01% of the actual value.
The square root of 3 is an irrational number. It is also known as Theodorus' constant, named after Theodorus of Cyrene.
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 From this the trigonometric function tangent of 60 degrees equals
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
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 , , 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