hypercyclen.

/ˈhʌɪpəsʌɪk(ə)l/

Etymology: In sense 1, < French hypercycle (E. N. Laguerre 1882, in Compt. Rend. 94 779): compare hyper- prefix, cycle n.¹ Sense 2 was coined independently in English.

Mathematics.

a. Any of a class of sextic curves to which the line at infinity is a double tangent. Now rare.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > other

quadratrix1656

section1665

family1705

semiparabola1728

tractrix1728

witcha1760

tractory1820

sinusoid1823

tractatrix1828

indicatrix1841

hodograph1847

tetrazomal1867

space curve1875

horograph1879

hypercycle1889

Peano curve1900

multiple arc1967

unknot1971

fractal1975

analemma1978

1889 in Cent. Dict. (at cited word) Hypercycle, a plane curve of the sixth order and fourth class having the line at infinity as a double tangent, which possesses the property that two pairs of tangents to it may be so taken that, whatever fifth tangent be considered, the two circles inscribed or escribed in the two triangles formed each with one of the pairs of fixed tangents and the variable tangent have their points of contact with the latter at a constant distance.

b. In Lobachevskian geometry, a curve consisting of all points at the same perpendicular distance from a particular straight line.

ΘΚΠ

the world > relative properties > number > geometry > curve > [noun] > locus

locus1675

evolute1704

place1704

trajectory1795

syntractory1820

focal surface1828

synharmonic1850

syntractrix1852

pedal1862

umbilical focal conic1862

stigmatic1863

synchronism1867

synchronous curve1867

Steinerian1873

tac-locus1873

strophoid1880

orthoptic locus1882

strophoidal1908

hypercycle1909

1909 Cent. Dict. Suppl. s.v. Hypercycle, n. 2. Same as equidistantial.

1942 H. S. M. Coxeter Non-Euclidean Geom. xi. 213 Some authors use the distinctive word cycle for the general circle in hyperbolic geometry, and distinguish the three kinds as a circle, a horocycle, and a hypercycle.

1981 Sci. Amer. Oct. 16/3 The lines are called equidistant curves or hypercycles.

2. In mathematical biology, a system of self-replicating molecules each of which reproduces itself only when catalysed as a result of the replication of another molecule in the system, the whole being considered as a possible intermediate stage in the development of spontaneously self-replicating molecules.

ΚΠ

1971 M. Eigen in Naturwissenschaften 58 504/1 The system represents a ‘cyclic hierarchy’ in which many cyclic (complementary) nucleotide collectives are linked together by an enzymic ‘hyper-cycle’.

1981 Bio Systems 13 235 The notion of hypercycles has been introduced..in order to characterize a functional entity which integrates information stored in individual self-replicating elements.

1986 Jrnl. Theoret. Biol. 118 9 From the study made so far we come to a conclusion that a catalytic hypercycle evolves into a more complex and organized one by a succession of alternate instability and stability.

This entry has not yet been fully updated (first published 1993; most recently modified version published online June 2018).

单词	hypercycle
释义	hypercyclen. /ˈhʌɪpəsʌɪk(ə)l/ Etymology: In sense 1, < French hypercycle (E. N. Laguerre 1882, in Compt. Rend. 94 779): compare hyper- prefix, cycle n.¹ Sense 2 was coined independently in English. Mathematics. 1. a. Any of a class of sextic curves to which the line at infinity is a double tangent. Now rare. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > other quadratrix1656 section1665 family1705 semiparabola1728 tractrix1728 witcha1760 tractory1820 sinusoid1823 tractatrix1828 indicatrix1841 hodograph1847 tetrazomal1867 space curve1875 horograph1879 hypercycle1889 Peano curve1900 multiple arc1967 unknot1971 fractal1975 analemma1978 1889 in Cent. Dict. (at cited word) Hypercycle, a plane curve of the sixth order and fourth class having the line at infinity as a double tangent, which possesses the property that two pairs of tangents to it may be so taken that, whatever fifth tangent be considered, the two circles inscribed or escribed in the two triangles formed each with one of the pairs of fixed tangents and the variable tangent have their points of contact with the latter at a constant distance. b. In Lobachevskian geometry, a curve consisting of all points at the same perpendicular distance from a particular straight line. ΘΚΠ the world > relative properties > number > geometry > curve > [noun] > locus locus1675 evolute1704 place1704 trajectory1795 syntractory1820 focal surface1828 synharmonic1850 syntractrix1852 pedal1862 umbilical focal conic1862 umbilical focal conic1862 stigmatic1863 synchronism1867 synchronous curve1867 Steinerian1873 tac-locus1873 strophoid1880 orthoptic locus1882 strophoidal1908 hypercycle1909 1909 Cent. Dict. Suppl. s.v. Hypercycle, n. 2. Same as equidistantial. 1942 H. S. M. Coxeter Non-Euclidean Geom. xi. 213 Some authors use the distinctive word cycle for the general circle in hyperbolic geometry, and distinguish the three kinds as a circle, a horocycle, and a hypercycle. 1981 Sci. Amer. Oct. 16/3 The lines are called equidistant curves or hypercycles. 2. In mathematical biology, a system of self-replicating molecules each of which reproduces itself only when catalysed as a result of the replication of another molecule in the system, the whole being considered as a possible intermediate stage in the development of spontaneously self-replicating molecules. ΚΠ 1971 M. Eigen in Naturwissenschaften 58 504/1 The system represents a ‘cyclic hierarchy’ in which many cyclic (complementary) nucleotide collectives are linked together by an enzymic ‘hyper-cycle’. 1981 Bio Systems 13 235 The notion of hypercycles has been introduced..in order to characterize a functional entity which integrates information stored in individual self-replicating elements. 1986 Jrnl. Theoret. Biol. 118 9 From the study made so far we come to a conclusion that a catalytic hypercycle evolves into a more complex and organized one by a succession of alternate instability and stability. This entry has not yet been fully updated (first published 1993; most recently modified version published online June 2018). > as lemmas hypercycle Categories » hypercycle n. Brit. /ˈhʌɪpəˌsʌɪkl/ , U.S. /ˈhaɪpərˌsaɪk(ə)l/ [ < French hypercycle] Geometry name given by Laguerre to a class of curves comprising the hypocycloid with four cusps, the parabola, the anticaustics of the parabola, etc. (1882 Comptes Rendus XCIV. 778, etc.). extracted from hyper-prefix < n.1889 as lemmas
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hypercyclen.

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