Geometry and Trigonometry
If an equilateral triangle 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 √3/2. From this the trigonometric function tangent of 60 degrees equals √3, and the sine of 60° and the cosine of 30° both equal half of √3.
The square root of 3 also appears in algebraic expressions for various other trigonometric constants, including the sines of 3°, 12°, 15°, 21°, 24°, 33°, 39°, 48°, 51°, 57°, 66°, 69°, 75°, 78°, 84°, and 87°.
It is the distance between parallel sides of a regular hexagon with sides of length 1. On the complex plane, this distance is expressed as i√3 mentioned below.
It is the length of the space 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.
Read more about this topic: Square Root Of 3
Famous quotes containing the word geometry:
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)