We begin by recapitulating the definition of a circle and the terminology used for circles. Spheres and cylinders are the first approximation of the shape of planets and stars, of the trunks of trees, of an exploding fireball, and of a drop of water, and of manufactured objects such as wires, pipes, ball-bearings, balloons, pies and wheels. Circles are the first approximation to the orbits of planets and of their moons, to the movement of electrons in an atom, to the motion of a vehicle around a curve in the road, and to the shapes of cyclones and galaxies. The theoretical importance of circles is reflected in the amazing number and variety of situations in science where circles are used to model physical phenomena. Students traditionally learn a greater respect and appreciation of the methods of mathematics from their study of this imaginative geometric material. The logic becomes more involved − division into cases is often required, and results from different parts of previous geometry modules are often brought together within the one proof. They clearly need to be proven carefully, and the cleverness of the methods of proof developed in earlier modules is clearly displayed in this module. The theorems of circle geometry are not intuitively obvious to the student, in fact most people are quite surprised by the results when they first see them. Tangents are introduced in this module, and later tangents become the basis of differentiation in calculus. Lines and circles are the most elementary figures of geometry − a line is the locus of a point moving in a constant direction, and a circle is the locus of a point moving at a constant distance from some fixed point − and all our constructions are done by drawing lines with a straight edge and circles with compasses. The diameter is a special type of chord that goes through the center point of the circle.Most geometry so far has involved triangles and quadrilaterals, which are formed by intervals on lines, and we turn now to the geometry of circles. Sort of like a piece of pizza or pie.Ĭhord - A chord is a line segment that joins two points on the circle. Other Circle Geometry terms Sector - A sector is a section of the circle made by two different radii. Where c = circumference, d = diameter, and r = radius. It's close enough.īack to circumference There are a few handy formulas we will use: The decimals actually go on for a long time (forever), but we will round it off to 3.14. We won't go into the details right now, but let's just agree to use it and that it works for now. It stands for a number that we use with circles. We use the following formula to figure the circumference: So the diameter is two times the radius and the radius is one half of the diameter.Ĭircumference - The circumference is the distance around the circle. This gives you our first math equation for the circle: This is the same distance R we used to make the circle in our definition.ĭiameter - The diameter is a straight line that goes across the circle and through the center. Terms used in circle geometry Radius- The radius is the distance from the center point to the edge of the circle. Watch as we add in equal distanced points in the movie below: Now pick all the other points on the screen that are the exact same distance R away from point P. Let's pick a point on a flat surface, like this screen, for instance. Okay, so let's start out with the "given point". We can learn a lot about the real world and how it works by understanding circles.įirst, what is the official definition of a circle?Ī circle is a shape that is made up of all the points on a plane (a flat surface) that are the same distance from a given point. There are circles all around us in the real world. A circle is an important shape in geometry.
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