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A presentation on mathematics

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A presentation on mathematics

1. 1. 1. The word "circle" derives from the Greek, kirkos "a circle," from the base ker- which means to turn or bend.2. Natural circles would have beenobserved, such as the Moon, Sun.3. In mathematics, the study of the circlehas helped inspire the development ofgeometry, astronomy, and calculus.
2. 2. A SET OF POINTSWHICH AREEQUIDISTANT FROM AFIXED POINT IS CALLEDCIRCLE.
3. 3. An arc of a circle is any connected part of thecircles circumference.A sector is a region bounded by two radii and anarc lying between the radii.A segment is a region bounded by a chord and anarc lying between the chords endpoints.A line segment joining centre and any point on thecircle is called radius.
4. 4. Circle Area = πr 2Circumference=2πr r = radius
5. 5. The circumference is the distancearound the outside of a circle.A chord is a line segment whoseendpoints lie on the circle. A diameteris the longest chord in a circle. A tangent to a circle is a straight linethat touches the circle at a singlepoint. A secant is a line passing through thecircle.
6. 6. or Sagitta The sagitta is the vertical segment. •The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle. •Given the length y of a chord, and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle which will fit around the two lines: Another proof of this result which relies only on two chord properties given above is as follows. Given a chord of length y and with sagitta oflength x, since the sagitta intersects the midpoint of the chord, we know it is part of a diameter of the circle. Since the diameter is twice the radius, the “missing” part of the diameter is (2r − x) in length. Using thefact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y/2)2. Solving for r, we find the required result.
7. 7. PI π (sometimes written pi) is a mathematical constant that is the ratio of any circles circumference to its diameter. π is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants. For instance, the area of a circle is equal to π times the square of the radius of the circle
8. 8. π is an irrational number, which means that itsvalue cannot be expressed exactly as a fraction having integers in both the numerator and denominator (unlike 22/7). Consequently, its decimal representation never ends and never repeats. π is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers(powers, roots, sums, etc.) can render its value; proving this fact was a significantmathematical achievement of the 19th century
9. 9. THANK YOUWITH SMILE.
10. 10. Key facts•Circumference = thedistance around theedge of the circle.•Diameter = a lineacross the widest partof a circle that passesthrough the centre.•Radius = 1/2 thediameter.Maybe a drawing willhelp you to rememberthese facts: