bean curve | butterfly catastrophe curve | circle | circle parallel curve | circular arc | cranioid | deltoid | cissoid of Diocles | ellipse | kampyle of Eudoxus | first heart curve | second heart curve | third heart curve | fifth heart curve | sixth heart curve | Laplace limit curve | line | nephroid | parabola parallel curve | pear-shaped curve | piriform curve | semicircle | serpentine curve | superellipse (total: 24)

eyeball curve

Steiner curve | Steiner hypocycloid | tricuspoid

flat visor curve | kidney curve

peg-top curve

half-circle

hyperellipse | hypoellipse | Lamé curve | Lamé oval

butterfly catastrophe curve | x(t) = 8 a t^3 + 24 t^5 y(t) = -6 a t^2 - 15 t^4 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) 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))) deltoid | x(t) = a ((2 cos(t))/3 + 1/3 cos(2 t)) y(t) = a ((2 sin(t))/3 - 1/3 sin(2 t)) cissoid of Diocles | x(t) = 2 a sin^2(t) y(t) = 2 a sin^2(t) tan(t) ellipse | x(t) = a cos(t) y(t) = b sin(t) kampyle of Eudoxus | x(t) = a sec(t) y(t) = a tan(t) sec(t) second heart curve | x(t) = a sin(t) cos(t) log(abs(t)) y(t) = a (t^2)^(3/20) sqrt(cos(t)) fifth heart curve | x(t) = 16 sin^3(t) y(t) = 13 cos(t) - 5 cos(2 t) - 2 cos(3 t) - cos(4 t) line | x(t) = b t y(t) = a (-t) - c/b nephroid | x(t) = a (3 cos(t) - cos(3 t)) y(t) = a (3 sin(t) - sin(3 t)) parabola parallel curve | x(t) = 2 a t + (k t)/sqrt(t^2 + 1) y(t) = a t^2 - k/sqrt(t^2 + 1) piriform curve | x(t) = a (sin(t) + 1) y(t) = b (sin(t) + 1) cos(t) semicircle | x(t) = a cos(t) y(t) = a sin(t) serpentine curve | x(t) = a cot(t) y(t) = b sin(t) cos(t)

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

bean curve | x^4 + x^2 y^2 + y^4 = a x (x^2 + y^2) butterfly catastrophe curve | 13824 a^5 x^2 + 4096 a^4 y^3 - 86400 a^3 x^2 y - 24576 a^2 y^4 + 144000 a x^2 y^2 + 84375 x^4 + 36864 y^5 = 0 circle | x^2 + y^2 = a^2 circle parallel curve | x^2 + y^2 = (a + k)^2 deltoid | -6 y^2 (a^2 + 4 a x + x^2) + (a - x)^3 (a + 3 x) - 3 y^4 = 0 cissoid of Diocles | y^2 = x^3/(2 a - x) ellipse | x^2/a^2 + y^2/b^2 = 1 kampyle of Eudoxus | x^4 = a^2 (x^2 + y^2) first heart curve | (-a^2 + x^2 + y^2)^3 = a x^2 y^3 third heart curve | (y/a - (2 (x^2/a^2 + abs(x/a) - 6))/(3 (x^2/a^2 + abs(x/a) + 2)))^2 + x^2/a^2 = 36 fifth heart curve | x^8 + 240 x^6 y + 8116 x^6 + 256 x^4 y^3 + 70464 x^4 y^2 + 597312 x^4 y + 15918304 x^4 + 67584 x^2 y^4 + 1818624 x^2 y^3 + 6081792 x^2 y^2 - 471039744 x^2 y - 3937380544 x^2 + 16384 y^6 + 589824 y^5 + 2899968 y^4 - 71958528 y^3 - 246497280 y^2 + 4261478400 y - 10061824000 = 0 sixth heart curve | (y/b - (x^2/a^2)^(1/3))^2 + x^2/a^2 = 1 Laplace limit curve | (x^2 + y^2) exp(sqrt(2) sqrt(sqrt((x^2 - 2 x + y^2 + 1) (x^2 + 2 x + y^2 + 1)) - x^2 + y^2 + 1)) = sqrt((x^2 - 2 x + y^2 + 1) (x^2 + 2 x + y^2 + 1)) + sqrt(2) sqrt(sqrt((x^2 - 2 x + y^2 + 1) (x^2 + 2 x + y^2 + 1)) - x^2 + y^2 + 1) + 1 line | a x + b y + c = 0 nephroid | (-4 a^2 + x^2 + y^2)^3 = 108 a^4 y^2 parabola parallel curve | 16 a^4 k^2 - 16 a^4 y^2 - 32 a^3 k^2 y + 8 a^3 x^2 y + 32 a^3 y^3 + 8 a^2 k^4 + 20 a^2 k^2 x^2 + 8 a^2 k^2 y^2 - a^2 x^4 - 32 a^2 x^2 y^2 - 16 a^2 y^4 - 8 a k^4 y - 2 a k^2 x^2 y + 8 a k^2 y^3 + 10 a x^4 y + 8 a x^2 y^3 + k^6 - 3 k^4 x^2 - k^4 y^2 + 3 k^2 x^4 + 2 k^2 x^2 y^2 - x^6 - x^4 y^2 = 0 pear-shaped curve | x^8 + 4 x^7 + 4 x^6 y^2 + 6 x^6 + 12 x^5 y^2 + 6 x^5 + 6 x^4 y^4 + 14 x^4 y^2 + 5 x^4 + 12 x^3 y^4 + 4 x^3 y^2 + 2 x^3 + 4 x^2 y^6 + 10 x^2 y^4 + 2 x^2 y^2 + x^2 + 4 x y^6 - 2 x y^4 + 2 x y^2 + y^8 + 2 y^6 - 3 y^4 + y^2 = a^2 piriform curve | a^4 (-y^2) = b^2 x^3 (x - 2 a) serpentine curve | y (a^2 + x^2) = a b x superellipse | abs(x/a)^r + abs(y/b)^r = 1

circle | r(θ) = a circle parallel curve | r(θ) = a + k circular arc | r(θ) = a cranioid | r(θ) = a sin(θ) + b sqrt(1 - p cos^2(θ)) + c sqrt(1 - q cos^2(θ)) cissoid of Diocles | r(θ) = 2 a sin(θ) tan(θ) ellipse | r(θ) = (a b)/sqrt((b^2 - a^2) cos^2(θ) + a^2) kampyle of Eudoxus | r(θ) = a sec^2(θ) line | r(θ) = -c/(a cos(θ) + b sin(θ)) nephroid | r(θ) = sqrt(2) a ((1 - cos(θ))^(1/3) + (cos(θ) + 1)^(1/3))^(3/2) semicircle | r(θ) = a serpentine curve | r(θ) = sqrt(a sec(θ) (b csc(θ) - a sec(θ)))

simple

circle | r = a circular arc | r = a

circular arc | 2 a sin(p/2)

circle | d = 2 a

circle | C = 2 π a

bean curve | A = (7 π a^2)/(12 sqrt(3)) 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)) deltoid | A = (2 π a^2)/9 cissoid of Diocles | A = 3 π a^2 ellipse | A = π a b third heart curve | A = 36 π a^2 fifth heart curve | A = 180 π nephroid | A = 12 π a^2 piriform curve | A = π a b semicircle | A = (π a^2)/2 superellipse | A = (sqrt(π) a b 4^(1 - 1/r) Γ(1 + 1/r))/Γ(1/2 + 1/r)

circle | s = 2 π a circle parallel curve | s = 2 π (a + k) circular arc | s = a p deltoid | s = (16 a)/3 ellipse | s = 4 a E(1 - b^2/a^2) nephroid | s = 24 a semicircle | s = π a

bean curve | d = 4 butterfly catastrophe curve | d = 5 circle | d = 2 circle parallel curve | d = 2 circular arc | d = 2 deltoid | d = 4 cissoid of Diocles | d = 3 ellipse | d = 2 kampyle of Eudoxus | d = 4 first heart curve | d = 6 third heart curve | d = 12 fifth heart curve | d = 8 sixth heart curve | d = 6 line | d = 1 nephroid | d = 6 parabola parallel curve | d = 6 pear-shaped curve | d = 8 piriform curve | d = 4 semicircle | d = 2 serpentine curve | d = 3

| eccentricity | focal parameter | semilatus rectum circle | e = 0 | | circle parallel curve | e = 0 | | ellipse | e = sqrt(1 - b^2/a^2) | p = b^2/sqrt(a^2 - b^2) | L = b^2/a | foci | directrix ellipse | {(-sqrt(a^2 - b^2), 0), (sqrt(a^2 - b^2), 0)} | piecewise | {x = -a^2/sqrt(a^2 - b^2) ∨ x = a^2/sqrt(a^2 - b^2)} | ba | (otherwise)

| evolute | involute circle | point at origin | circle involute circle parallel curve | point at origin | ellipse | ellipse evolute | ellipse involute nephroid | nephroid | nephroid parabola parallel curve | point at origin | 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