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The dot planimeter is physical device for estimating the area of shapes based on the same principle. It consists of a square grid of dots, printed on a transparent sheet; the area of a shape can be estimated as the product of the number of dots in the shape with the area of a grid square. [8]
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, [1] or its generalization to other kinds of mathematical spaces.As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist; conversely ...
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
Giving the area of a segment of a unit sphere in steradians is analogous to giving the length of an arc of a unit circle in radians. Just as the magnitude of a plane angle in radians at the vertex of a circular sector is the ratio of the length of its arc to its radius, the magnitude of a solid angle in steradians is the ratio of the area ...
Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .
There are continuous curves on which every arc (other than a single-point arc) has infinite length. An example of such a curve is the Koch curve. Another example of a curve with infinite length is the graph of the function defined by f(x) = x sin(1/x) for any open set with 0 as one of its delimiters and f(0) = 0.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.