91:. Thus a curve intersecting any line in an infinite number of points, while not containing it, must be transcendental. This applies not just to
174:
99:
53:
116:
49:
76:
79:, give rise to criteria for showing curves actually are transcendental. For example, an algebraic curve
146:
131:
125:
69:
48:
is an algebraic curve (pedantically, the real points of such a curve); the usual parametrisation by
65:
37:
17:
136:
56:, but certainly the unit circle is defined by a polynomial equation. (The same remark applies to
170:
61:
193:
29:
57:
187:
45:
92:
121:
141:
95:
curves, therefore; but to large classes of curves showing oscillations.
111:
25:
87:
in a finite number of points, or possibly contains all of
36:, what matters is the point set (typically in the
44:, not a given parametrisation. For example, the
8:
75:The properties of algebraic curves, such as
167:The Universal Encyclopedia of Mathematics
158:
98:The term is originally attributed to
7:
14:
1:
169:, Pan Reference Books, 1976,
64:; and in fact to curves of
210:
177:, "Transcendental curves".
83:either meets a given line
147:Tricomplex cosexponential
54:transcendental functions
117:Trigonometric functions
50:trigonometric functions
70:automorphic functions
32:. Here for a curve,
22:transcendental curve
18:analytical geometry
137:Logarithmic spiral
132:Archimedes' spiral
62:elliptic functions
52:may involve those
201:
178:
163:
106:Further examples
77:BĂ©zout's theorem
209:
208:
204:
203:
202:
200:
199:
198:
184:
183:
182:
181:
164:
160:
155:
108:
58:elliptic curves
30:algebraic curve
28:that is not an
12:
11:
5:
207:
205:
197:
196:
186:
185:
180:
179:
157:
156:
154:
151:
150:
149:
144:
139:
134:
129:
119:
114:
107:
104:
13:
10:
9:
6:
4:
3:
2:
206:
195:
192:
191:
189:
176:
175:0-330-24396-9
172:
168:
162:
159:
152:
148:
145:
143:
140:
138:
135:
133:
130:
127:
123:
120:
118:
115:
113:
110:
109:
105:
103:
101:
96:
94:
90:
86:
82:
78:
73:
71:
67:
63:
59:
55:
51:
47:
43:
40:) underlying
39:
35:
31:
27:
23:
19:
166:
165:Newman, JA,
161:
97:
88:
84:
80:
74:
41:
33:
21:
15:
126:exponential
122:Logarithmic
68:> 1 and
46:unit circle
153:References
93:sinusoidal
128:functions
188:Category
142:Catenary
112:Cycloid
100:Leibniz
194:Curves
173:
66:genus
38:plane
26:curve
24:is a
171:ISBN
124:and
60:and
20:, a
72:.)
16:In
190::
102:.
89:L
85:L
81:C
42:C
34:C
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.