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/

Visual Index

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:

Famous Curves Index: http://www-history.mcs.st-and.ac.uk/history/Curves/Curves.html
Cabri Geometry, http://www.cabri.net/index-e.html
J. Dennis Lawrence, A Catalog of Special Plane Curves
The Purple Bear's Web, http://purplebearsweb.co.uk/Fly/Knots/Why_collections_of_small_thing/why_collections_of_small_thing.html

pdf file submitted to ATCM


Compare with
@