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The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to 2π radians, 360 degrees or 400 gradians.
In modern terms, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [57] The size of an angle is formalized as an angular measure. In Euclidean geometry, angles are used to study polygons and triangles, as well as forming an object of study in their own right. [43]
In mathematics, particularly in geometry, quadrature (also called squaring) is a historical process of drawing a square with the same area as a given plane figure or computing the numerical value of that area. A classical example is the quadrature of the circle (or squaring the circle).
The four quadrants of a Cartesian coordinate system. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.
Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. [23] Analytic geometry allows the study of curves unrelated to circles and lines.
The fifth vertex is the rightmost intersection of the horizontal line with the original circle. Steps 6–8 are equivalent to the following version, shown in the animation: 6a. Construct point F as the midpoint of O and W. 7a. Construct a vertical line through F. It intersects the original circle at two of the vertices of the pentagon.