# Add Maths Project Spm 2009

Circles In Our Daily Life

Name : Chuah Khoy Yan Class : 5 Daisi School : SMK Bandar Utama Damansara (4)

PROJECT WORK FOR ADDITIONAL MATHEMATICS 2009 - CIRCLES IN OUR DAILY LIFE

CHUAH KHOY YAN

CONTENT

Title 1. 2. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Introduction Task Specification Part 1(a) Part 1(b) Part 2(a) Part 2(b) Part 2(c) Part 3(a) Part 3(b) Part 3(c) Part 3(d) Part 3(e) Conclusion Acknowledgement Page .. 1 - 2 .. 3 - 4 5 6 .. 7 - 8 .. 9 - 12 . 13 - 14 15 16 .. 17 - 19 20 .. 21 - 22 23 24

PROJECT WORK FOR ADDITIONAL MATHEMATICS 2009 - CIRCLES IN OUR DAILY LIFE

CHUAH KHOY YAN

Introduction

Circles are geometric figures whose points all lie the same distance from a given point, the circle's center. They are not polygons, because they are not made up of segments. Points that lie in the same line, like those in a segment, are never equidistant (an equal distance) from a single point. 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 centre. The common distance of the points of a circle from its center is called its radius. Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure (known as the perimeter) or to the whole figure including its interior. However, in strict technical usage, "circle" refers to the perimeter while the interior of the circle is called a disk. The circumference of a circle is the perimeter of the circle (especially when referring to its length). A circle is a special ellipse in which the two foci are coincident. Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone.

FURTHER TERMINOLOGY

The diameter of a circle is the length of a line segment whose endpoints lie on the circle and which passes through the centre of the circle. This is the largest distance between any two points on the circle. The diameter of a circle is twice its radius. The term "radius" can also refer to a line segment from the centre a circle to its perimeter, and similarly the term "diameter" can refer to a line segment between two points on the perimeter which passes through the centre. In this sense, the midpoint of a diameter is the centre and so it is composed of two radii.

PROJECT WORK FOR ADDITIONAL MATHEMATICS 2009 - CIRCLES IN OUR DAILY LIFE

CHUAH KHOY YAN

A chord of a circle is a line segment whose two endpoints lie on the circle. The diameter, passing through the circle's centre, is the largest chord in a circle. A tangent to a circle is a straight line that touches the circle at a single point. A secant is an extended chord: a straight line cutting the circle at two points. An arc of a circle is any connected part of the circle's circumference. A sector is a region bounded by two radii and an arc lying between the radii, and a segment is a region bounded by a chord and an arc lying between the chord's endpoints.

HISTORY

The circle has been known since before the beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus. Early science, particularly geometry and Astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles. Some highlights in the history of the circle are:

1700 BC - The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256 as an approximate value of π. 81 300 BC - Book 3 of Euclid's Elements deals with the properties of circles....

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