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Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle.. In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle.
The diameter is the maximum distance between any pair of convex hull vertices found as the two points of contact of the parallel lines in this sweep. The time for this method is dominated by the time for constructing the convex hull: O ( n log n ) {\displaystyle O(n\log n)} for a finite set of n {\displaystyle n} points, or time O ( n ...
In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
Eratosthenes also calculated the Sun's diameter. According to Macrobius, Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth. [17] The actual figure is approximately 109 times. [26] During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ecliptic of the Earth. He ...
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
Jung's theorem provides more general inequalities relating the diameter to the radius. [5] The isodiametric inequality or Bieberbach inequality , a relative of the isoperimetric inequality , states that, for a given diameter, the planar shape with the largest area is a disk, and the three-dimensional shape with the largest volume is a sphere.
In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter ) ( D {\displaystyle D} ) is twice the equivalent radius.
The number 2 π (approximately 6.28) is the ratio of a circle's circumference to its radius, and the number of radians in one turn. The meaning of the symbol was not originally fixed to the ratio of the circumference and the diameter.