CIRCLE GROUP MEMBERS Xavier Claire Clarice

CIRCLE A circle is one of the important shapes in Geometry. A circle is a shape with all points the same distance from its center, which a point inside the circle. All points on the circle are equidistant (same distance) from the center point. The side around the circle is the Circumference. The line going through the center of the circle is the diameter. The line that goes half way through the circle is Radius.

History The etymology of the word circle is from the Greek, kirkos "a circle," from the base ker- which means to turn or bend. The origin of the word "circus" is closely related as well.circus The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle 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, astronomy, and calculus.wheelgearsastronomy

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.sciencegeometryastrology and astronomymedieval scholars 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 256/81 ( ) as an approximate value of π. [1]Rhind papyrus [1] 300 BC – Book 3 of Euclid's Elements deals with the properties of circles.Euclid's Elements In Plato's Seventh Letter there is a detailed definition and explanation of the circle. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation.Seventh Letter 1880 – Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle.Lindemannsquaring the circle

History Of Pi Long time ago, the beginning of π was discovered by the early civilization of agriculture. The need of shelter helped develop a better skill of engineering with mathematics. Engineering skills is concerning the relations between the circle and the square. During 400 B.C. in Greece, the first record of math that was dealing with π was called the “Squaring of Circle”, it is the insoluble problem of constructing a square having exactly the same area as a given circle.

Surface Area of the Circle and Volume of the Cylinder Diameter The line passing through the center of the circle. The Diameter is equal to twice the radius. Diameter = 2radius Radius The radius is a line segment that begin from the center and touches any point around any parts of the circle. Radius is twice the diameter. R=2/diameter Circumference The circumference of a circle is the actual length around the circle. 3.14/ Pi is the number needed to compute the circumference of the circle. Circumference = 23.14r

Area The space inside of each shape A = (3.14r)2 Height The distance from the base of the surface and its upper part. Reference d= Diameter r= Radius pi= 3.14 Formula: V= (3.14)(R)(R)(H) A cylinder basically has 2 shapes a rectangle and a circle. Separating each shape will make solving problems easier rather than looking at it 2 dimensional

Surface Area of the Sphere A sphere is a shape that is bounded by a surface whose every point is the same distance Half of the sphere is called the Hemisphere. Archimedes discovered that a cylinder that circumscribes a sphere, as shown in the following diagram, has a curved surface area equal to the surface area, S, of the sphere. for example: Find the surface area with a diameter of 28 cm using π = 3.14 S=4πr.r S=4(3.14)(14)(14) S=2464 cm 2

Finding Arc lengths Arcs are measured in two ways: as the measure of the central angle, or as the length of the arc itself. Central Angle The angle in a circle whose vertex is the center of the circle is called the Central Angle. s = arc length r = radius of the circle θ = measure of the central angle in radian How to find it: EXAMPLE : We'll use a circle with radius 10 cm and central angle 60°. First : you have to find out what decimal of the circle is represented by the central angle 60° 60/360 = Second: Then we have to find the circumference of the circle C=2πr C=2π.10 Third: Then multiply it by 1/6 (the fraction of the central angle), then you'll get the length of the arc. A=1/ A= A= cm

Finding the Sector Area How to find it : EXAMPLE: a circle with radius of 20 cm and Central angle of 40 ° First : you have to find out what decimal of the circle is represented by the central angle 40° 40/360 = Second: Then we need to find the area of the circle using 20 cm as the radius. A=π.r.r A= A=1256 cm Third: Lastly, you multiply the decimal of the central angle and the area of the circle to get the over all sector area. A= cm 2 A= cm 2