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The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
Heron's formula for the area of a triangle is the special case obtained by taking d = 0. The relationship between the general and extended form of Brahmagupta's formula is similar to how the law of cosines extends the Pythagorean theorem .
The solution to the quadrilateral isoperimetric problem is the square, and the solution to the triangle problem is the equilateral triangle. In general, the polygon with n sides having the largest area and a given perimeter is the regular polygon , which is closer to being a circle than is any irregular polygon with the same number of sides.
The textbooks are in color-print and are among the least expensive books in Indian book stores. [11] Textbooks created by private publishers are priced higher than those of NCERT. [ 11 ] According to a government policy decision in 2017, the NCERT will have the exclusive task of publishing central textbooks from 2018, and the role of CBSE will ...
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
It uses only the arc length formula, expression for the area of a plane region from Green's theorem, and the Cauchy–Schwarz inequality. For a given closed curve, the isoperimetric quotient is defined as the ratio of its area and that of the circle having the same perimeter. This is equal to
The solution to partial fraction was known to the Rigvedic People as states in the purush Sukta (RV 10.90.4): With three-fourths Puruṣa went up: one-fourth of him again was here. The Satapatha Brahmana (c. 7th century BCE) contains rules for ritual geometric constructions that are similar to the Sulba Sutras. [22]