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Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre. —
where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width. = where A is the area of a circle. More generally, =
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
In particular, the sum of the angles of a spherical triangle is strictly greater than the sum of the angles of a triangle defined on the Euclidean plane, which is always exactly π radians. Sides are also expressed in radians. A side (regarded as a great circle arc) is measured by the angle that it subtends at the centre.
This definition makes sense because this direct sum is unique up to a unique isomorphism. 3. Exclusive or: if E and F are two Boolean variables or predicates, may denote the exclusive or. Notations E XOR F and are also commonly used; see ⊻. 1.
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a) 2 + (y − b) 2 = r 2 where a and b are the coordinates of the center (a, b) and r is the radius. In Cartesian geometry, equations are used to describe geometric figures.
The distance formula is homogeneous in each variable, with d(λu, μv) = d(u, v) if λ and μ are non-zero scalars, so it does define a distance on the points of projective space. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is non-orientable. It erases the distinction ...