281:
202:
322:
92:
63:
229:
141:
121:
253:
315:
351:
308:
146:
341:
346:
288:
17:
68:
39:
292:
214:
126:
208:
97:
238:
231:(the integral of curvature with respect to arc length along the curve) is equal to the
335:
33:
25:
232:
280:
29:
36:
intimately related to the curvature of the original curve. Let
197:{\displaystyle T={\frac {\dot {\gamma }}{|{\dot {\gamma }}|}}}
65:
be a closed curve with nowhere-vanishing tangent vector
296:
241:
217:
149:
129:
100:
71:
42:
247:
223:
196:
135:
115:
86:
57:
143:is the closed curve on the unit sphere given by
316:
264:Solomon, B. "Tantrices of Spherical Curves."
8:
323:
309:
240:
216:
186:
175:
174:
169:
158:
156:
148:
128:
99:
73:
72:
70:
41:
7:
277:
275:
295:. You can help Knowledge (XXG) by
14:
279:
87:{\displaystyle {\dot {\gamma }}}
187:
170:
110:
104:
94:. Then the tangent indicatrix
52:
46:
1:
266:American Mathematical Monthly
352:Differential geometry stubs
368:
274:
58:{\displaystyle \gamma (t)}
224:{\displaystyle \gamma }
136:{\displaystyle \gamma }
291:-related article is a
249:
225:
198:
137:
117:
88:
59:
342:Differential geometry
289:differential geometry
250:
226:
199:
138:
118:
89:
60:
18:differential geometry
239:
215:
147:
127:
116:{\displaystyle T(t)}
98:
69:
40:
347:Spherical geometry
245:
221:
194:
133:
113:
84:
55:
22:tangent indicatrix
304:
303:
268:103, 30–39, 1996.
248:{\displaystyle T}
192:
183:
166:
81:
359:
325:
318:
311:
283:
276:
254:
252:
251:
246:
230:
228:
227:
222:
203:
201:
200:
195:
193:
191:
190:
185:
184:
176:
173:
167:
159:
157:
142:
140:
139:
134:
122:
120:
119:
114:
93:
91:
90:
85:
83:
82:
74:
64:
62:
61:
56:
367:
366:
362:
361:
360:
358:
357:
356:
332:
331:
330:
329:
272:
261:
237:
236:
213:
212:
209:total curvature
168:
145:
144:
125:
124:
96:
95:
67:
66:
38:
37:
12:
11:
5:
365:
363:
355:
354:
349:
344:
334:
333:
328:
327:
320:
313:
305:
302:
301:
284:
270:
269:
260:
257:
244:
220:
189:
182:
179:
172:
165:
162:
155:
152:
132:
112:
109:
106:
103:
80:
77:
54:
51:
48:
45:
13:
10:
9:
6:
4:
3:
2:
364:
353:
350:
348:
345:
343:
340:
339:
337:
326:
321:
319:
314:
312:
307:
306:
300:
298:
294:
290:
285:
282:
278:
273:
267:
263:
262:
258:
256:
242:
234:
218:
210:
205:
180:
177:
163:
160:
153:
150:
130:
107:
101:
78:
75:
49:
43:
35:
31:
27:
23:
19:
297:expanding it
286:
271:
265:
206:
24:of a closed
21:
15:
34:unit sphere
26:space curve
336:Categories
259:References
233:arc length
219:γ
181:˙
178:γ
164:˙
161:γ
131:γ
79:˙
76:γ
44:γ
32:on the
20:, the
287:This
30:curve
28:is a
293:stub
207:The
235:of
211:of
123:of
16:In
338::
255:.
204:.
324:e
317:t
310:v
299:.
243:T
188:|
171:|
154:=
151:T
111:)
108:t
105:(
102:T
53:)
50:t
47:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
