What is a circle in geometry?
A circle is a shape consisting of all points in a plane that lie at a given distance from a given point called the centre. That fixed distance from the centre to any point on the circle is the radius.
Questions about Circle
Short answers, pulled from the story.
What is the difference between the radius and the diameter of a circle?
The radius is a line segment joining the centre of a circle to any single point on it, while the diameter passes from one point through the centre to another. The diameter is twice the length of the radius and is the longest chord of the circle.
What does the word circle come from?
The word circle derives from the Greek kirkos and kuklos, a metathesis of the Homeric Greek krikos, meaning hoop or ring. The origins of the words circus and circuit are closely related.
Who proved the area of a circle?
Archimedes proved the area of a circle in his work Measurement of a Circle. He showed the enclosed area equals that of a triangle whose base is the circle's circumference and whose height is its radius, which comes to pi times the radius squared.
Why is squaring the circle impossible?
Squaring the circle is impossible because pi is a transcendental number, proven by Ferdinand von Lindemann in 1880 CE. In 1882, the impossibility followed from the Lindemann-Weierstrass theorem, since pi is not the root of any polynomial with rational coefficients.
What is the relationship between a circle's circumference and pi?
The ratio of a circle's circumference to its diameter is pi, an irrational constant approximately equal to 3.141592654. The Egyptian Rhind papyrus, dated to 1700 BCE, gave an early method for a circle's area corresponding to about 3.16049 as a value of pi.