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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 ...
This equation, known as the equation of the circle, ... we know that it is a part of a diameter of the circle. Since the diameter is twice the radius, ...
where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, ... Einstein's field equation of general relativity: ...
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler . It is a special case of Euler's formula e i x = cos x + i sin x {\displaystyle e^{ix}=\cos x+i\sin x} when evaluated for x = π {\displaystyle x=\pi } .
Circle with similar triangles: circumscribed side, inscribed side and complement, inscribed split side and complement. Let one side of an inscribed regular n-gon have length s n and touch the circle at points A and B. Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter.
The circumference of a circle is the distance around it, but if, as in many elementary treatments, distance is defined in terms of straight lines, this cannot be used as a definition. Under these circumstances, the circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides ...
A circle is drawn centered on the midpoint of the line segment OP, having diameter OP, where O is again the center of the circle C. The intersection points T 1 and T 2 of the circle C and the new circle are the tangent points for lines passing through P, by the following argument.