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Syntractrix
A syntractrix is a curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ... of the form :x+\sqrt= a \ln \frac. It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve. Dionysius Lardner, ''A system of algebraic geometry'' 1823, p. 261–26/ref> References {{geometry-stub Plane curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntractrix A=1
A syntractrix is a curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ... of the form :x+\sqrt= a \ln \frac. It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve. Dionysius Lardner, ''A system of algebraic geometry'' 1823, p. 261–26/ref> References {{geometry-stub Plane curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntractrix A=0
A syntractrix is a curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ... of the form :x+\sqrt= a \ln \frac. It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the point of tangency is moved along the curve. Dionysius Lardner, ''A system of algebraic geometry'' 1823, p. 261–26/ref> References {{geometry-stub Plane curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geometry), point. This is the definition that appeared more than 2000 years ago in Euclid's Elements, Euclid's ''Elements'': "The [curved] line is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width." This definition of a curve has been formalized in modern mathematics as: ''A curve is the image (mathematics), image of an interval (mathematics), interval to a topological space by a continuous function''. In some contexts, the function that defines the curve is called a ''parametrization'', and the curve is a parametric curve. In this artic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tractrix
In geometry, a tractrix (; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the ''tractor'') that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed. It is therefore a curve of pursuit. It was first introduced by Claude Perrault in 1670, and later studied by Isaac Newton (1676) and Christiaan Huygens (1693). Mathematical derivation Suppose the object is placed at (or in the example shown at right), and the puller at the origin (mathematics), origin, so is the length of the pulling thread (4 in the example at right). Then the puller starts to move along the axis in the positive direction. At every moment, the thread will be tangent to the curve described by the object, so that it becomes completely determined by the movement of the puller. Mathematically, if the coordinates of the object are , the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dionysius Lardner
Professor Dionysius Lardner FRS FRSE (3 April 179329 April 1859) was an Irish scientific writer who popularised science and technology, and edited the 133-volume '' Cabinet Cyclopædia''. Early life in Dublin He was born in Dublin on 3 April 1793 the son of William Lardner, a solicitor in Dublin, who wished his son to follow the same calling. After some years of uncongenial desk work, Lardner entered Trinity College, Dublin, in 1812, and obtained a B.A. in 1817 and an M.A. in 1819, winning many prizes. He married Cecilia Flood on 19 December 1815, but they separated in 1820 and were divorced in 1835. About the time of the separation, he began a relationship with a married woman, Anne Maria Darley Boursiquot, the wife of a Dublin wine merchant. It is believed that he fathered her son, Dion Boucicault, the actor and dramatist. Lardner provided him with financial support until 1840. Whilst in Dublin, Lardner began to write and lecture on scientific and mathematical matters, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
