# Fixed-points Sentence Examples

The diurnal rotation of the earth furnishes two

**fixed points**or poles, the axis joining which is fixed or nearly so in its direction in space.Thus the best approximation to the average depth of the ocean is little more than an expert guess; yet a fair approximation is probable for the features of sub-oceanic relief are so much more uniform than those of the land that a smaller number of

**fixed points**is required to determine them.But while we have yet to wait for that expansion of principal triangulation which will bring Asia into connexion with Europe by the direct process of earth measurement, a topobetween graphical connexion has been effected between Russian Russ/an and Indian surveys which sufficiently proves that the and deductive methods employed by both countries for the Indian determination of the co-ordinate values of

**fixed points**so surveys.The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two

**fixed points**is constant and is equal to the square of half the distance between these points.Its cartesian equation, when the line joining the two

**fixed points**is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is r 2 = 2a 2 cos 20.AdvertisementBut the book of Acts, our only continuous authority for the period, contains two synchronisms with secular history which can be dated with some pretence to exactness and constitute

**fixed points**by help of which a more or less complete chronology can be constructed for at least the latter half of the apostolic age.The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two

**fixed points**at infinity.Certain

**fixed points**were first determined upon the stem of the instrument.Similarly any other property might be used as a definition; an ellipse is the locus of a point such that the sum of its distances from two

**fixed points**(the foci) is constant, &c., &c.A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two

**fixed points**at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.AdvertisementThe definitions given above reflect the intimate association of these curves, but it frequently happens that a particular conic is defined by some special property (as the ellipse, which is the locus of a point such that the sum of its distances from two

**fixed points**is constant); such definitions and other special properties are treated in the articles Ellipse, Hyperbola and Parabola.The north and south poles, instead of being

**fixed points**on the earth's surface, wander round within a circle about 50 ft.Because of this, marram plantations seldom remain fixed unless fences are used to act as

**fixed points**of sand buildup.