Circles Maths
Circles in mathematics are a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius. Circles are important in geometry and trigonometry, and their properties are used in various mathematical calculations and real-world applications.
6 Key excerpts on "Circles Maths"
- Sandra Rush(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...All of the other properties listed are true. Circles The last of the plane (two-dimensional) figures we will look at is the circle, an important shape indeed. Just look around you, and you will see many circular objects. It is important in life, as well as on the GED ® test, that you know some facts about circles. A circle is defined as all the points at a fixed distance from a certain point. That certain point is called the center of the circle, which is usually designated by an O. The fixed distance from the center to the circle is called the radius of the circle. If we extend the radius across the center to the other side of the circle, we get the diameter, which is just twice the radius. The circle is usually named by its center, so this is circle O. Another important value when talking about circles is the Greek letter pi(π), which is the ratio of the circumference (perimeter) of the circle to its diameter. Pi has a value of or roughly 3.14. The GED ® test will indicate what form to use for an answer, but it usually is in terms of π. C ALCULATOR The calculator has a button labeled π, and you can treat π just as you would any constant. That is, to total 2 π + 3 π, you can press those buttons, with “enter” and the value 5 π appears. If you then use the toggle button, the calculator will give the decimal equivalent, but that usually isn’t required. The angle with the center of a circle at its vertex and two radii (plural of radius) as its sides is called a central angle. The sum of the central angles in a complete rotation (or circle) is 360°. Think of the hands of a clock. At 3:00, the angle between the hands on a clock is 90° (one-fourth of the way around the whole clock face). It is also 90° at 9:00. The portion of the circumference of a circle between two points is called an arc. Its measurement is the same as the measure of the central angle drawn to it (see the figure below). Be careful when figuring the angle between the hands of a clock...
eBook - ePub- Douglas K. Brumbaugh, Peggy L. Moch, MaryE Wilkinson(Authors)
- 2004(Publication Date)
- Routledge(Publisher)
...In fact, these items are right circular cylinders; they may be very short cylinders, but they are not figures in a plane and they have more dimensions than do circles. A circle is a point and every member of the set of points is the exact same distance from the center in the plane. The circular array of points is the circumference of the circle. The circle is the ring. The set of points inside the ring is not the circle; it is the interior of the circle. Similarly, the points outside the ring are not the circle; they make up the exterior of the circle. A circle has no substance, so the best way to model a circle is with a wire ring. Of course, the wire of the ring has thickness, but it represents a much better model of a circle than a solid plastic disk. There are several important terms associated with circles, some of which are shown in Fig. 4.18. The diameter is a segment that joins two points on the circle and passes through the center. A radius is half a diameter and goes from the center to any point on the circumference. A chord is a line segment that joins any two points on a circle. The diameter is the longest chord of a circle. A few additional terms are shown in Fig. 4.19. A sector of a circle is a pie-wedge region bounded by two radii and an arc. A segment is a region bounded by a chord and an arc. Fig. 4.19. Your Turn 16. Use the information in Fig. 4.18 and Fig. 4.19 to write your own informal definitions for the following terms: a) Center b) Chord c) Circle d) Circumference e) Diameter f) Radius g) Sector h) Segment Constructions Classic constructions, completed with nothing more than a compass and straightedge (not a ruler), are elegant and beautiful in form. However, the basic concepts of construction can be introduced using paper folding. For this, you need a straightedge, a pencil, and some paper. Waxed paper, tracing paper, or meat patty paper are best, because these are thin and show the creases of the construction well...
eBook - ePub- Kylie A. Peppler(Author)
- 2017(Publication Date)
- SAGE Publications, Inc(Publisher)
...Maria Droujkova Maria Droujkova Droujkova, Maria Ray Droujkov Ray Droujkov Droujkov, Ray Math Circles Math circles 469 472 Math Circles A math circle is a social occasion to enjoy mathematics as a creative tool, a topic of philosophical discourse, or a game. A math circle is also a group of people who meet to study mathematics for its own sake, because they are interested. Math circles come in different types defined (a) by the target audience (e.g., children, teachers, or families), (b) by the format of activities (e.g., problem solving, projects, or discussions), and (c) by their organization (e.g., one-time gatherings, short-term cooperatives, and ongoing groups). Some math circles are informal gatherings of friends at someone’s home or a park, while others are run by organizations with dedicated staff and systematic planning. Math circles can be as small as three or four students or as large as hundreds of participants. Other entities similar to math circles include maker groups, robotics groups, science clubs, and coding communities. This entry discusses the roles and purpose of math circles, their prevalence and the different types that exist, the resources that are available for math circles, and the origin of math circles. Roles and Purpose of Math Circles What roles do math circles fill in the communities that support them, and what do they give their participants? It is common for math circle leaders to describe their circles in contrast to math classes in school, because math circles provide mathematical experiences that are different in some way, fulfilling a need not otherwise addressed. Two such differences are breadth and depth. The website of The Math Circle in Boston says, “We are careful to choose topics which are unlikely to be in the school curriculum—we see our role as widening and deepening the river, rather than accelerating its flow between narrow banks” (The Math Circle, n.d.)...
eBook - ePubDyslexia, Dyscalculia and Mathematics
A practical guide
- Anne Henderson(Author)
- 2013(Publication Date)
- Routledge(Publisher)
...the: radius — r, diameter — D, circumference — C. Figure 9.16 Properties of a circle Circle facts ● The circumference is the perimeter of a circle. ● The diameter is twice the length of the radius. ● The radius is half the length of the diameter (divide D by 2). ● Pi π (pronounced pie) is important. ● Pi π has a value of 3.142. ● Press EXP on the calculator to use π. ● A 3D shape with circular top and bottom is a cylinder. To find the circumference of a circle: (answer is in units) π × D or π × 2r A rhyme to help: Fiddle de-dum, Fiddle de-dee The ring round the moon is π times D. Figure 9.17 How to find the circumference of a circle To find the area of a circle (answer is in units 2) π × radius × radius which is written πr 2 A rhyme to help: A round hole in my sock Has just been repaired. The area mended Is pi r squared. Figure 9.18 How to find the area (A) of a circle Polygons ● Copy, cut out, stick onto card and turn the angle pictures and facts given into a memory card. (number 23, see page 144). ● Multi-sided figures are generally called polygons. They have individual names depending on the number of sides, but many students find these difficult to remember. Figure 9.19 Polygons Section E: Co-ordinates The two straight lines at right angles to each other on a graph are called the axes. Coordinates are a pair of numbers, usually in brackets, which describe the precise location of a point on the axes. The one which is horizontal is called the x -axis (because x is a cross) and the vertical line is called the y -axis. The first number indicates the x -axis value (across the hall) and the second number indicates the y -axis value (up the stairs). For example: (3, 5) means 3 units across to the right and 5 units up. Figure 9.20 Graph to show the position of co-ordinate (3,5) Section F: Rotational symmetry This is the description given when a pattern is rotated around a point to identify the number of times the pattern is repeated...
- Rebecca Dayton(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...Chapter 9 Circles Your Goals for Chapter 9 1. You should be able to identify the parts of a circle. 2. You should be able to determine the measure of arcs and the angles created in a circle. 3. You should be able to solve problems using circumference, arc length, and areas of circles and sectors. 4. You should be able identify the center and radius of a circle and graph the circle on a coordinate plane from an equation in center-radius form. 5. You should be able to write an equation of a circle given the center and radius. Standards The following standards are assessed on Florida’s Geometry End-of-Course exam either directly or indirectly: MA.912.G.6.2: (Low) Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles. MA.912.G.6.4: (Moderate) Determine and use measures of arcs and related angles (central, inscribed, and intersections of chords, secants and tangents). MA.912.G.6.5: (High) Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. MA.912.G.6.6: (Moderate) Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle. MA.912.G.6.7: (Moderate) Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle. Lines and Segments A radius is a segment whose endpoints are the center and any point on the circle. A chord is a segment whose endpoints are on the circle. A diameter is a segment whose endpoints are on the circle and passes through the center. A diameter is the longest chord of the circle. A secant is a line that intersects the circle at two points. A tangent is a line that intersects the circle at exactly one point. Example: Identify each of the following in the given circle. A. chord B. secant C...
eBook - ePub- Thomas Heath(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...Names too stand, in a sense, in the same relation to definitions; for the name denotes a certain whole without distinction[of parts or properties], e.g. a circle, whereas the definition of a circle analyses it into its particular components.’On the interpretation of this passage as a whole I need only refer to Ross’s remarks.1On the contrast between things prior and better knownto usand things prior in the order of nature, and the necessity of basing definitions on the latter rather than the former, cf.TopicsVI. 4. 141a24 andpp. 85–6, above.The definition of a circle is not given by Aristotle in so many words, but if he had given one, it would hardly have been substantially different from Euclid’s: ‘a circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another; and the point is called the centre of the circle.’ Aristotle actually has the expression ‘the circular figure bounded by one line’;2he also speaks of ‘the plane equal (i.e. extending equally all ways) from the middle’, meaning a circle,3and he contrasts with the circle ‘any other figure which has not the lines from the middle equal, as, for example, an egg-shaped figure’.4Cf. Plato,Parmenides137E: ‘Round 〈i.e. circular〉 is, I take it, that the extremes of which are every way equally distant from the middle.’(c) Mathematics and PhysicsPhys. II. 2. 193b22–194a15‘Since we have determined in how many senses we speak of Nature, we must next consider wherein the mathematician differs from the physicist or the philosopher of Nature. For physical bodies contain planes, solids, lengths, and points, which are what the mathematician investigates...
