Archimedean spiral | Archimedes' spiral | bifoliate | bifolium | second butterfly curve | cardioid | Cartesian ovals | Cayley sextic | cycloid of Ceva | circle | circle parallel curve | circular arc | cochleoid | cranioid | folium of Descartes | conchoid of de Sluze | Dürer folium | kampyle of Eudoxus | Fermat spiral | Freeth nephroid | ... (total: 42)

arithmetic spiral

cardioide

Cartesian curve | ovals of Descartes

cycloidum anomalarum

cochlioid | oui-ja board curve | snail curve

Archimedean spiral | x(t) = a t^(1/n) cos(t) y(t) = a t^(1/n) sin(t) Archimedes' spiral | x(t) = a t cos(t) y(t) = a t sin(t) bifoliate | x(t) = (8 a sin^2(t) cos^2(t))/(cos(4 t) + 3) y(t) = (8 a sin^3(t) cos(t))/(cos(4 t) + 3) bifolium | x(t) = 4 a sin^2(t) cos^2(t) y(t) = 4 a sin^3(t) cos(t) second butterfly curve | x(t) = sin(t) (sin^5(t/12) + e^cos(t) - 2 cos(4 t)) y(t) = cos(t) (sin^5(t/12) + e^cos(t) - 2 cos(4 t)) cardioid | x(t) = a (1 - cos(t)) cos(t) y(t) = a sin(t) (1 - cos(t)) Cayley sextic | x(t) = a cos^3(t/3) cos(t) y(t) = a sin(t) cos^3(t/3) cycloid of Ceva | x(t) = a cos(t) (2 cos(2 t) + 1) y(t) = a sin(t) (2 cos(2 t) + 1) circle | x(t) = a cos(t) y(t) = a sin(t) circle parallel curve | x(t) = (a + k) cos(t) y(t) = (a + k) sin(t) circular arc | x(t) = a cos(t) y(t) = a sin(t) cochleoid | x(t) = a sinc(t) cos(t) y(t) = a sinc(t) sin(t) cranioid | x(t) = cos(t) (a sin(t) + b sqrt(1 - p cos^2(t)) + c sqrt(1 - q cos^2(t))) y(t) = sin(t) (a sin(t) + b sqrt(1 - p cos^2(t)) + c sqrt(1 - q cos^2(t))) folium of Descartes | x(t) = (3 a t)/(t^3 + 1) y(t) = (3 a t^2)/(t^3 + 1) conchoid of de Sluze | x(t) = cos(t) (a cos(t) + sec(t)) y(t) = sin(t) (a cos(t) + sec(t)) Dürer folium | x(t) = a sin(t/2) cos(t) y(t) = a sin(t/2) sin(t) kampyle of Eudoxus | x(t) = a sec(t) y(t) = a tan(t) sec(t) Fermat spiral | x(t) = a sqrt(t) cos(t) y(t) = a sqrt(t) sin(t) Freeth nephroid | x(t) = a (2 sin(t/2) + 1) cos(t) y(t) = a (2 sin(t/2) + 1) sin(t) Galilean spiral | x(t) = cos(t) (b t^2 - a) y(t) = sin(t) (b t^2 - a) Garfield curve | x(t) = a t cos^2(t) y(t) = a t sin(t) cos(t) fourth heart curve | x(t) = a cos(t) ((sin(t) sqrt(abs(cos(t))))/(sin(t) + 7/5) - 2 sin(t) + 2) y(t) = a sin(t) ((sin(t) sqrt(abs(cos(t))))/(sin(t) + 7/5) - 2 sin(t) + 2) hippopede curve | x(t) = 2 cos(t) sqrt(a - b sin^2(t)) y(t) = 2 sin(t) sqrt(a - b sin^2(t)) hyperbolic spiral | x(t) = (a cos(t))/t y(t) = (a sin(t))/t lima bean curve | x(t) = a sin(t) (sin^3(t) + cos^3(t)) y(t) = a cos(t) (sin^3(t) + cos^3(t)) limaçon | x(t) = cos(t) (a cos(t) + b) y(t) = sin(t) (a cos(t) + b) limaçon trisectrix | x(t) = a cos(t) (2 cos(t) + 1) y(t) = a sin(t) (2 cos(t) + 1) lituus | x(t) = (a cos(t))/sqrt(t) y(t) = (a sin(t))/sqrt(t) Maclaurin trisectrix | x(t) = (a (t^2 - 3))/(t^2 + 1) y(t) = (a t (t^2 - 3))/(t^2 + 1) Maltese cross curve | x(t) = (2 a cos(t))/sqrt(sin(4 t)) y(t) = (2 a sin(t))/sqrt(sin(4 t)) neoid | x(t) = cos(t) (a t + b) y(t) = sin(t) (a t + b) conchoid of Nicomedes | x(t) = cos(t) (a sec(t) + b) y(t) = sin(t) (a sec(t) + b) Poinsot csch spiral | x(t) = a cos(t) csch(n t) y(t) = a sin(t) csch(n t) Poinsot sech spiral | x(t) = a cos(t) sech(n t) y(t) = a sin(t) sech(n t) rose curve | x(t) = a cos(t) sin(n t) y(t) = a sin(t) sin(n t) scarabaeus curve | x(t) = cos(t) (b cos(2 t) - a cos(t)) y(t) = sin(t) (b cos(2 t) - a cos(t)) semicircle | x(t) = a cos(t) y(t) = a sin(t) superformula | x(t) = cos(t) (abs(cos((t m)/4)/a)^β + abs(sin((t m)/4)/b)^γ)^(-1/α) y(t) = sin(t) (abs(cos((t m)/4)/a)^β + abs(sin((t m)/4)/b)^γ)^(-1/α) swastika curve | x(t) = cos(t) sqrt(-csc(4 t)) abs(sin(2 t)) y(t) = sin(t) sqrt(-csc(4 t)) abs(sin(2 t)) trifolium | x(t) = a (-cos(t)) cos(3 t) y(t) = a sin(t) (-cos(3 t)) Tschirnhausen cubic | x(t) = a (1 - 3 t^2) y(t) = a t (3 - t^2)

circular arc | x^2 + y^2 = a^2 and -p/2<=tan^(-1)(x, y)<=p/2 semicircle | x^2 + y^2 = a^2 and y>=0

bifoliate | x^4 + y^4 = 2 a x y^2 bifolium | (x^2 + y^2)^2 = 4 a x y^2 cardioid | (a x + x^2 + y^2)^2 = a^2 (x^2 + y^2) Cartesian ovals | (-(m^2 - n^2) (a^2 + x^2 + y^2) + 2 a x (m^2 + n^2) + k^2)^2 - 4 k^2 n^2 ((a + x)^2 + y^2) = 0 Cayley sextic | -a^3 x^3 - 3 a^2 (5 x^2 + 9 y^2) (x^2 + y^2) - 48 a x (x^2 + y^2)^2 + 64 (x^2 + y^2)^3 = 0 cycloid of Ceva | a^2 (y^2 - 3 x^2)^2 = (x^2 + y^2)^3 circle | x^2 + y^2 = a^2 circle parallel curve | x^2 + y^2 = (a + k)^2 folium of Descartes | x^3 + y^3 = 3 a x y conchoid of de Sluze | (x - 1) (x^2 + y^2) = a x^2 Dürer folium | a^4 y^2 + 4 (x^2 + y^2)^3 = 4 a^2 (x^2 + y^2)^2 kampyle of Eudoxus | x^4 = a^2 (x^2 + y^2) Fermat spiral | tan((x^2 + y^2)/a^2) = y/x Freeth nephroid | a^4 (y^2 - 3 x^2) + 8 a^3 x (x^2 + y^2) - 6 a^2 (x^2 + y^2)^2 + (x^2 + y^2)^3 = 0 fourth heart curve | ((2401 x^12)/a^12 - (19208 x^10)/a^10 + (19208 y x^10)/a^11 + (11956 y^2 x^10)/a^12 + (38416 x^8)/a^8 - (76832 y x^8)/a^9 - (18816 y^2 x^8)/a^10 + (76440 y^3 x^8)/a^11 + (24390 y^4 x^8)/a^12 - (9800 y^2 x^7)/a^9 + (3500 y^3 x^7)/a^10 + (37632 y^2 x^6)/a^8 - (152096 y^3 x^6)/a^9 + (53016 y^4 x^6)/a^10 + (118680 y^5 x^6)/a^11 + (26020 y^6 x^6)/a^12 - (5600 y^3 x^5)/a^8 - (20400 y^4 x^5)/a^9 + (10500 y^5 x^5)/a^10 + (8591 y^4 x^4)/a^8 - (93696 y^5 x^4)/a^9 + (94864 y^6 x^4)/a^10 + (89480 y^7 x^4)/a^11 + (15265 y^8 x^4)/a^12 - (7200 y^5 x^3)/a^8 - (11400 y^6 x^3)/a^9 + (10500 y^7 x^3)/a^10 - (625 y^6 x^2)/a^8 - (18432 y^7 x^2)/a^9 + (51456 y^8 x^2)/a^10 + (32640 y^9 x^2)/a^11 + (4656 y^10 x^2)/a^12 - (1600 y^7 x)/a^8 - (800 y^8 x)/a^9 + (3500 y^9 x)/a^10 + (9216 y^10)/a^10 + (4608 y^11)/a^11 + (576 y^12)/a^12) ((2401 x^12)/a^12 - (19208 x^10)/a^10 + (19208 y x^10)/a^11 + (11956 y^2 x^10)/a^12 + (38416 x^8)/a^8 - (76832 y x^8)/a^9 - (18816 y^2 x^8)/a^10 + (76440 y^3 x^8)/a^11 + (24390 y^4 x^8)/a^12 + (9800 y^2 x^7)/a^9 - (3500 y^3 x^7)/a^10 + (37632 y^2 x^6)/a^8 - (152096 y^3 x^6)/a^9 + (53016 y^4 x^6)/a^10 + (118680 y^5 x^6)/a^11 + (26020 y^6 x^6)/a^12 + (5600 y^3 x^5)/a^8 + (20400 y^4 x^5)/a^9 - (10500 y^5 x^5)/a^10 + (8591 y^4 x^4)/a^8 - (93696 y^5 x^4)/a^9 + (94864 y^6 x^4)/a^10 + (89480 y^7 x^4)/a^11 + (15265 y^8 x^4)/a^12 + (7200 y^5 x^3)/a^8 + (11400 y^6 x^3)/a^9 - (10500 y^7 x^3)/a^10 - (625 y^6 x^2)/a^8 - (18432 y^7 x^2)/a^9 + (51456 y^8 x^2)/a^10 + (32640 y^9 x^2)/a^11 + (4656 y^10 x^2)/a^12 + (1600 y^7 x)/a^8 + (800 y^8 x)/a^9 - (3500 y^9 x)/a^10 + (9216 y^10)/a^10 + (4608 y^11)/a^11 + (576 y^12)/a^12) = 0 hippopede curve | 4 b^2 y^2 + (x^2 + y^2)^2 = 4 a b (x^2 + y^2) hyperbolic spiral | y/x = tan(a/sqrt(x^2 + y^2)) lima bean curve | (x^2 + y^2)^2 = a (x^3 + y^3) limaçon | a^2 x^2 - 2 a x^3 - 2 a x y^2 - b^2 x^2 - b^2 y^2 + x^4 + 2 x^2 y^2 + y^4 = 0 limaçon trisectrix | a^2 (3 x^2 - y^2) + (x^2 + y^2)^2 = 4 a x (x^2 + y^2) Maclaurin trisectrix | 3 a x^2 - a y^2 + x^3 + x y^2 = 0 Maltese cross curve | x y (x^2 - y^2) = a^2 (x^2 + y^2) conchoid of Nicomedes | b^2 x^2 = (x - a)^2 (x^2 + y^2) scarabaeus curve | (x^2 + y^2) (a x + x^2 + y^2)^2 = b^2 (x^2 - y^2)^2 swastika curve | x^4 + x y - y^4 = 0 trifolium | a (x^3 - 3 x y^2) + (x^2 + y^2)^2 = 0 Tschirnhausen cubic | (a - x) (8 a + x)^2 = 27 a y^2

Archimedean spiral | r(θ) = a θ^(1/n) Archimedes' spiral | r(θ) = a θ bifoliate | r(θ) = (8 a sin^2(θ) cos(θ))/(cos(4 θ) + 3) bifolium | r(θ) = 4 a sin^2(θ) cos(θ) cardioid | r(θ) = a (1 - cos(θ)) Cayley sextic | r(θ) = a cos^3(θ/3) cycloid of Ceva | r(θ) = a (2 cos(2 θ) + 1) circle | r(θ) = a circle parallel curve | r(θ) = a + k circular arc | r(θ) = a cochleoid | r(θ) = a sinc(θ) cranioid | r(θ) = a sin(θ) + b sqrt(1 - p cos^2(θ)) + c sqrt(1 - q cos^2(θ)) folium of Descartes | r(θ) = (3 a tan(θ) sec(θ))/(tan^3(θ) + 1) conchoid of de Sluze | r(θ) = a cos(θ) + sec(θ) Dürer folium | r(θ) = a sin(θ/2) kampyle of Eudoxus | r(θ) = a sec^2(θ) Fermat spiral | r(θ) = a sqrt(θ) Freeth nephroid | r(θ) = a (2 sin(θ/2) + 1) Galilean spiral | r(θ) = b θ^2 - a Garfield curve | r(θ) = a θ cos(θ) fourth heart curve | r(θ) = a ((sin(θ) sqrt(abs(cos(θ))))/(sin(θ) + 7/5) - 2 sin(θ) + 2) hippopede curve | r(θ) = 2 sqrt(a - b sin^2(θ)) hyperbolic spiral | r(θ) = a/θ lima bean curve | r(θ) = a (sin^3(θ) + cos^3(θ)) limaçon | r(θ) = a cos(θ) + b limaçon trisectrix | r(θ) = a (2 cos(θ) + 1) lituus | r(θ) = a/sqrt(θ) Maclaurin trisectrix | r(θ) = a (-2 cos(2 θ) - 1) sec(θ) Maltese cross curve | r(θ) = (2 a)/sqrt(sin(4 θ)) neoid | r(θ) = a θ + b conchoid of Nicomedes | r(θ) = a sec(θ) + b Poinsot csch spiral | r(θ) = a csch(θ n) Poinsot sech spiral | r(θ) = a sech(θ n) rose curve | r(θ) = a sin(θ n) scarabaeus curve | r(θ) = b cos(2 θ) - a cos(θ) semicircle | r(θ) = a superformula | r(θ) = (abs(cos((θ m)/4)/a)^β + abs(sin((θ m)/4)/b)^γ)^(-1/α) swastika curve | r(θ) = sqrt(-csc(4 θ)) abs(sin(2 θ)) trifolium | r(θ) = a (-cos(3 θ)) Tschirnhausen cubic | r(θ) = a sec^3(θ/3)

polar

circle | r = a circular arc | r = a

circular arc | 2 a sin(p/2)

circle | d = 2 a

circle | C = 2 π a

bifoliate | A = (π a^2)/(2 sqrt(2)) bifolium | A = (π a^2)/2 cardioid | A = (3 π a^2)/2 Cayley sextic | A = ((9 sqrt(3))/2 + 5 π) a cycloid of Ceva | A = 3 π a^2 circle | A = π a^2 circle parallel curve | A = π (a + k)^2 cranioid | A = 1/2 π (a^2 + 4 b c F_1(1/2 ;-1/2, -1/2;1;p, q) - b^2 (p - 2) - c^2 (q - 2)) folium of Descartes | A = (3 a^2)/2 Dürer folium | A = 1/2 (2 + π) a^2 Freeth nephroid | A = (8 + 3 π) a^2 fourth heart curve | A = a^2 (1/420 (-196 sqrt(5) 6^(3/4) tan^(-1)(root of 6 x^4 - 25 near x = -1.42872 + 1) + 2400 2F1(1, 1, 5/4, 24/49) + 2555 - 1176 log(6) + 98 sqrt(5) 6^(3/4) log(12 + 5 sqrt(6) - 2 sqrt(5) 6^(3/4)) - 98 sqrt(5) 6^(3/4) log(12 + 5 sqrt(6) + 2 sqrt(5) 6^(3/4)) + 196 sqrt(5) 6^(3/4) tan^(-1)(1 + sqrt(5)/6^(1/4))) - (5 π^(3/2) (25 2F1(3/4, 1, 1/2, 49/24) + 38 2F1(3/4, 1, 9/4, -25/24)))/(96 sqrt(2) Γ(5/4) Γ(9/4)) + (6 - (21 - 7 i)/(sqrt(5) 6^(1/4))) π) hippopede curve | A = 2 π (2 a - b) lima bean curve | A = (5 π a^2)/16 limaçon | A = 3/2 b sqrt(a^2 - b^2) + π (a^2/2 + b^2) - (a^2/2 + b^2) cos^(-1)(b/a) limaçon trisectrix | A = ((3 sqrt(3))/2 + 2 π) a^2 semicircle | A = (π a^2)/2 trifolium | A = (π a^2)/4

Cayley sextic | A^* = (15 π a^2)/2 Freeth nephroid | A^* = 6 π a^2 limaçon | A^* = 1/2 π (a^2 + 2 b^2) scarabaeus curve | A^* = 1/2 π (a^2 + b^2)

bifolium | s = 1/6 a (sqrt(4 sqrt(2) - 5) (4 sqrt(2) (K(1/7 (-57 - 40 sqrt(2))) + F(sin^(-1)(1/7 (9 - 4 sqrt(2)))|1/7 (-57 - 40 sqrt(2)))) + 5 E(1/7 (-57 - 40 sqrt(2))) + 5 E(sin^(-1)(1/7 (9 - 4 sqrt(2)))|1/7 (-57 - 40 sqrt(2)))) + 8/7 (8 + 5 sqrt(2))) cardioid | s = 8 a Cayley sextic | s = 6 π a cycloid of Ceva | s = a (-3 K(13/16) + 16 E(13/16) + 3 Π(1/4|13/16)) circle | s = 2 π a circle parallel curve | s = 2 π (a + k) circular arc | s = a p Dürer folium | s = 4 a E(-3) Freeth nephroid | s = (8 a (-3 K(2/3) + 3 E(2/3) + 4 Π(-1/3|2/3)))/sqrt(3) limaçon | s = 4 (a + b) E((4 a b)/(a + b)^2) limaçon trisectrix | s = 12 a E(8/9) rose curve | s = 2 sqrt(n^2 + 1) denom(n) E(n^2/(n^2 + 1)) (2 - (denom(n)^2 n) mod 2) semicircle | s = π a trifolium | s = 2 a E(-8)

bifoliate | d = 4 bifolium | d = 4 cardioid | d = 4 Cartesian ovals | d = 4 Cayley sextic | d = 6 cycloid of Ceva | d = 6 circle | d = 2 circle parallel curve | d = 2 circular arc | d = 2 folium of Descartes | d = 3 conchoid of de Sluze | d = 3 Dürer folium | d = 6 kampyle of Eudoxus | d = 4 Freeth nephroid | d = 6 fourth heart curve | d = 24 hippopede curve | d = 4 lima bean curve | d = 4 limaçon | d = 4 limaçon trisectrix | d = 4 Maclaurin trisectrix | d = 3 Maltese cross curve | d = 4 conchoid of Nicomedes | d = 4 scarabaeus curve | d = 6 semicircle | d = 2 swastika curve | d = 4 trifolium | d = 4 Tschirnhausen cubic | d = 3

| eccentricity circle | e = 0 circle parallel curve | e = 0

| evolute | involute cardioid | cardioid | cardioid circle | point at origin | circle involute circle parallel curve | point at origin | limaçon | limaçon evolute | semicircle | point at origin |

| mean line segment length circle | s^_ = (4 a)/π circle parallel curve | s^_ = (4 (a + k))/π semicircle | s^_ = (8 (π - 2) a)/π^2