代数曲线分类图

lilianjie

algebraic curve
( Z& ^2 d5 ~# u. `/ ~* H
. A3 ?9 _, H3 c: b# ^代数曲线是一维的代数簇。最典型的例子是射影平面  上由一个齐次多项式 f(X,Y) 定义的零点。
& B5 ^& o4 x" l3 N+ R1 [6 p2 V7 \2 o
+ S) P$ o  s8 S3 h( w& K8 v" c% i5 A9 D代数簇是多项式集合的公共零点解的集合
: L- s# ?5 T5 t3 x
6 t3 F( t0 n  a# \6 ]簇----variety
6 n( E% F8 q2 ?, r/ {1 P+ B
3 f0 @' n2 d& b2 c  t$ ~) C8 [光三次椭圆曲线就够难了，高次的。。。
( P. ^7 ^3 J- W* B
' g3 P9 h) ^' ^0 O1 t7 f! W2 quadratic curve circle, ellipse, hyperbola, parabola
4 d2 T, V" _9 }% n! E
7 W; B" Z1 t8 r' z, d; |6 R3 cubic curve cissoid of Diocles, conchoid of de Sluze, folium of Descartes, Maclaurin trisectrix, Maltese cross curve, Mordell curve, Ochoa curve, right strophoid, semicubical parabola, serpentine curve, Tschirnhausen cubic, witch of Agnesi

' w( ~" m2 e5 x5 h2 P4 quartic curve ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, bow, bullet nose, butterfly curve, capricornoid, cardioid, Cartesian ovals, Cassini ovals, conchoid of Nicomedes, cruciform, deltoid, devil's curve, Dürer's conchoid, eight curve, fish curve, folium, hippopede, Kampyle of Eudoxus, Klein quartic, knot curve, lemniscate, limaçon, links curve, pear-shaped curve, piriform, swastika curve, trefoil curve, trifolium
2 a' _+ N. ?9 o5 y
5 quintic curve Burnside curve, butterfly catastrophe curve, stirrup curve

6 **tic curve astroid, atriphtaloid, Cayley's **tic, cornoid, cycloid of Ceva, dumbbell curve, ellipse evolute, epicycloid, Freeth's nephroid, heart curve (first), limaçon evolute, nephroid, quadrifolium, scarabaeus, Talbot's curve

8 octic curve pear curve
8 n8 T" R/ Y: n! k% _
) p& x+ q' o! b$ W( p( X* {12 dodecic curve ranunculoid
& ?  A; _7 r1 S/ @" y( G
3 s' k9 K, O8 N. Y
* u8 O- q* }8 a二次曲线圆，椭圆，双曲线，抛物线
1 p8 V* ?* c2 F, P
0 s0 S( ^- ]* I3 {3 Diocles立方米曲线CISSOID，conchoid DE Sluze，大青叶，笛卡尔，麦克劳林trisectrix，马耳他十字曲线，莫德尔曲线，曲线奥乔亚，右strophoid，semicubical抛物线，蛇形曲线，Tschirnhausen立方米Agnesi巫
! ?! F' V5 `' r2 ?$ h8 M% j# J* ?
7 b. u2 V4 h/ A; Z5 K( b4四次曲线与符号的曲线，绿豆曲线，bicorn，二尖瓣曲线，bifoliate，bifolium，二重，丰富的曲线，低头，子弹鼻子，蝴蝶曲线，capricornoid，心，笛卡尔的椭圆形，卡西尼号的椭圆形，conchoid Nicomedes，十字形，三角肌，魔鬼的曲线，丢勒的conchoid，八个曲线，曲线鱼，大青叶，hippopede欧多克斯Kampyle，克莱因四次，结曲线，双纽线，limaçon，链接曲线，曲线梨形，梨，卍曲线，三叶曲线，车轴
# [" F0 q- h5 t# h) q
5五次曲线伯恩赛德曲线，蝴蝶灾难曲线，箍筋曲线
. N3 u0 i5 i5 e+ i
( |8 A8 L2 K1 G# \3 ~9 d% g" I6 **tic曲线astroid，atriphtaloid，凯莱的**tic，cornoid，摆线针轮CEVA，哑铃形曲线，椭圆形渐，外摆线，Freeth的nephroid，心脏曲线（第一），limaçon渐，nephroid，quadrifolium，scarabaeus，塔尔博特的曲线
" t+ M' n9 x4 B4 q: `
8 octic曲线梨曲线
$ @4 s5 R6 y! h( V/ v: J4 l
12 dodecic曲线ranunculoid
) {# r2 ~' {; P9 t+ E5 V

lilianjie

和代数几何代数曲线概念不同的曲线分类在拓扑和分析上不同：
. u+ j0 G4 ?1 C  ^% {
4 x  u" h) v! PTOPOLOTY:一维连续统
  z7 p5 x6 x: p* S2 ]+ s) a6 V分析上是一维空间到n维空间的连续映射------空间曲线，包括平面球面双曲马鞍曲线等等

孤寂冷逍遥

xxgzftj

xxgzftj

图呢？