Tangent Construction Made Hard
Jen-chung Chuan
NTHU, Taiwan
| e-mail: jcchuan@math.nthu.edu.tw |
webpage: http://poncelet.math.nthu.edu.tw/disk6/atcm-02/talk/ |
| Kappa curve |
r = cot t |
| Kampyle of Eudoxus |
r = sec 2 t |
| inverse of the quadrifolium |
r = sec 2t |
| double folium |
r = sin t sin 2t |
| Right Strophoid |
r = sec t cos 2t |
| Logocyclic |
r = - sec t cos 2t |
| trifolium |
r = cos 3t |
| quadrifolium |
r = cos 2t |
| Freeth's nephroid |
r = 1 + 2 sin(t/2) |
| conchoid of Nicomedes |
r = b + a sec t |
| Cayley's sextic |
r = cos 3 t/3 |
| trisectrix |
r = sec t - 4cos t |
| trisectrix of Maclaurin |
r = sec t/3 |
| trisectrix of Catalan |
r = sec3 t/3 |
| limacon of Pascal |
r = a cos t + b |
| cissoid of Diocles |
r = sin t tan t |
| conchoid of de Sluze |
r = k2 cos t / a + a sec t |
| ellipse | x = a cos t y = b sin t |
| hyperbola | x = a sec t y = b tan t |
| bullet nose | x = a cos t y = b cot t |
| cross curve | x = a sec t y = b csc t |
| Lissajous | x = cos 3t y = sin 4t |
| Chebyshev polynomial | x = cos t y = cos 3t |
| lemniscate of Gernono | x = cos t y = sin t cos t |
| witch of Agnesi | x = tan t y = cos 2 t |
| piriform | x = 1+sin t y = a cos t (1+sin t) |
| serpentine curve |
x 2y + a2y - bx = 0 |
| butterfly curve |
x6 + y6 = x2 |
| falling sand |
y2 (1 - x2) =1 |
| folium of Descartes |
x 3 + y 3 - 3xy = 0 |
| semi-parabolic |
y2 = x4 - x6 |
| semi-parabolic |
y2 = x2 (1- x2)2 |
References:
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