Circles

By:

Darshan Chaudhary, Roll No-11,Class IX F

History of the Circle

The circle has been known sincebefore the beginning of recordedhistory. Some highlightsin the history of the circle are:1. 1700 BC – The Rhind papyrus gives a method to find the area of a circular field.The result corresponds to 256/81 as an approximate value of π.1. 300 BC – Book 3 of Euclid's Elements deals with the properties of circles. 1. 1880 – Lindemann proves that π is transcendental, effectively settling themillennia-old problem of squaring the circle Circles drawn in the past

Introduction-What is a Circle and its Radius?

Circle: A circle is a simple shape of Euclidean Geometry consisting of those points in a plane which are the same distance from a given point called the center.

Radius: The common distance of the points of a circle from its center is called its radius.

Tycho crater, one of many examples of circles that arise in nature

Chord, Diameter and Circumference

Chord: A chord of a circle is a line segment whose two endpoints

lie on the circle. Diameter A diameter is a chord passing through the center and is the largest chord in a circle. The length of a diameter is twice

the length of the radius. Circumference The circumference of a circle is the perimeter of the circle

Pi (π) and the area of the circle

Pi or π is the ratio of a circle's circumference to its diameter. It is a constant that takes the same numeric value for all circles.

The area enclosed by a circle is π multiplied by the radius squared: Equivalently, denoting diameter by d,

that is, approximately 79% of the circumscribing square (whose side is of length d). The circle is the plane curve enclosing the maximum area for a given arc length.

Some Properties of a Circle

The circle is the shape with the largest area for a given length of perimeter.

A circle's circumference and radius are proportional.

The area enclosed and the square of its radius are proportional.

The circle centered at the origin with radius 1 is called the unit circle.

Inscribed Angle

An inscribed angle (examples are the blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed

angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the central angle is 180 degrees).

Circle And God

Early science, particularly geometry and astronomy/astrology, was connected to the divine for most medieval scholars. The compass in this 13th century manuscript is a symbol of God's act of Creation, as many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.

In ancient Rome, circles were worshiped as they were thought to be divine and holy.

Bibliography

I took the required information for reference from the following websites/books:

1. en.wikipedia.org

2. www.math2.org

3. The Mathematics of Circle

4. Circles in the Divine

5. Complete History of Circles