(800) 434-2582
Call Now!Franchise Info

Get Math Help

Math Reading Science Test Prep

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Boy Surface

    Example plot

    Example plot

    Equations

    x(u, v) = (a (sqrt(2) cos(2 u) cos^2(v) + cos(u) sin(2 v)))/(2 - sqrt(2) sin(3 u) sin(2 v)) y(u, v) = (a (sqrt(2) sin(2 u) cos^2(v) + cos(u) sin(2 v)))/(2 - sqrt(2) sin(3 u) sin(2 v)) z(u, v) = (3 a cos^2(v))/(2 - sqrt(2) sin(3 u) sin(2 v))

    81 a^2 x^2 z^2 - 162 a^2 x y z^2 + 54 sqrt(2) a^2 x z^3 + 81 a^2 y^2 z^2 - 54 sqrt(2) a^2 y z^3 + 18 a^2 z^4 - 486 a x^3 y z + 1458 a x^2 y^2 z - 324 sqrt(2) a x^2 y z^2 - 216 a x^2 z^3 - 1458 a x y^3 z + 486 sqrt(2) a x y^2 z^2 + 216 a x y z^3 - 144 sqrt(2) a x z^4 + 486 a y^4 z - 162 sqrt(2) a y^3 z^2 - 216 a y^2 z^3 + 108 sqrt(2) a y z^4 - 48 a z^5 + 729 x^6 - 2916 x^5 y + 486 sqrt(2) x^5 z + 5103 x^4 y^2 - 972 sqrt(2) x^4 y z - 162 x^4 z^2 - 5832 x^3 y^3 + 972 sqrt(2) x^3 y^2 z + 1296 x^3 y z^2 - 216 sqrt(2) x^3 z^3 + 5103 x^2 y^4 - 972 sqrt(2) x^2 y^3 z - 2106 x^2 y^2 z^2 + 432 sqrt(2) x^2 y z^3 + 72 x^2 z^4 - 2916 x y^5 + 486 sqrt(2) x y^4 z + 1944 x y^3 z^2 - 540 sqrt(2) x y^2 z^3 - 144 x y z^4 + 96 sqrt(2) x z^5 + 729 y^6 - 648 y^4 z^2 + 108 sqrt(2) y^3 z^3 + 108 y^2 z^4 - 48 sqrt(2) y z^5 + 32 z^6 = 0

    Surface properties

    6

    Metric properties

    g_(uu) = (a^2 ((3 sqrt(2) cos(3 u) sin(2 v) (sqrt(2) sin(2 u) cos^2(v) + cos(u) sin(2 v)) + (2 - sqrt(2) sin(3 u) sin(2 v)) (2 sqrt(2) cos(2 u) cos^2(v) - sin(u) sin(2 v)))^2 + (3 sqrt(2) cos(3 u) sin(2 v) (sqrt(2) cos(2 u) cos^2(v) + cos(u) sin(2 v)) + (sqrt(2) sin(3 u) sin(2 v) - 2) (sin(u) sin(2 v) + 2 sqrt(2) sin(2 u) cos^2(v)))^2 + 648 cos^2(3 u) sin^2(v) cos^6(v)))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4 g_(uv) = (2 a^2 (27 sqrt(2) cos(3 u) sin(v) cos^4(v) (sqrt(2) sin(3 u - v) + sqrt(2) sin(3 u + v) - 4 sin(v)) + 2 (6 (cos(u) + cos(5 u)) sin(v) cos^3(v) - 4 sin(2 u) cos^2(v) (sqrt(2) - sin(3 u) sin(2 v)) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 cos(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v))) + 2 (4 sqrt(2) cos(2 u) cos^2(v) - 4 (sin(u) + sin(5 u)) sin(v) cos^3(v) + 6 sin(2 u) cos(3 u) sin(2 v) cos^2(v) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 sin(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4 g_(vu) = (2 a^2 (27 sqrt(2) cos(3 u) sin(v) cos^4(v) (sqrt(2) sin(3 u - v) + sqrt(2) sin(3 u + v) - 4 sin(v)) + 2 (6 (cos(u) + cos(5 u)) sin(v) cos^3(v) - 4 sin(2 u) cos^2(v) (sqrt(2) - sin(3 u) sin(2 v)) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 cos(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v))) + 2 (4 sqrt(2) cos(2 u) cos^2(v) - 4 (sin(u) + sin(5 u)) sin(v) cos^3(v) + 6 sin(2 u) cos(3 u) sin(2 v) cos^2(v) + sin(2 v) (sin(u) (sqrt(2) sin(3 u) sin(2 v) - 2) + 3 sqrt(2) cos(u) cos(3 u) sin(2 v))) (cos(u) cos(2 v) + 1/2 sin(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4 g_(vv) = (a^2 (9 cos^2(v) (sqrt(2) sin(3 u - v) + sqrt(2) sin(3 u + v) - 4 sin(v))^2 + 4 (2 cos(u) cos(2 v) + cos(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))^2 + 4 (2 cos(u) cos(2 v) + sin(2 u) cos(v) (sin(3 u - v) + sin(3 u + v) - 2 sqrt(2) sin(v)))^2))/(sqrt(2) sin(3 u) sin(2 v) - 2)^4

    Vector properties

    left double bracketing bar x(u, v) right double bracketing bar = (a sqrt(2 sqrt(2) sin(v) cos^3(v) (sin(u) + sin(3 u) + cos(u) + cos(3 u)) + 2 cos^2(u) sin^2(2 v) + 11 cos^4(v)))/(2 - sqrt(2) sin(3 u) sin(2 v))

    N^^(u, v) = -(3 cos^2(v) (60 sin(u) + 32 sin(5 u) + 4 sin(7 u) - 6 sin(u - 4 v) + sqrt(2) sin(4 u - 4 v) - 8 sin(5 u - 4 v) - 2 sin(7 u - 4 v) - sqrt(2) sin(8 u - 4 v) - 8 sin(u - 2 v) + 40 sqrt(2) sin(2 u - 2 v) + 2 sqrt(2) sin(4 u - 2 v) + 8 sin(5 u - 2 v) - 2 sqrt(2) sin(8 u - 2 v) - 40 sqrt(2) sin(2 (u + v)) - sqrt(2) sin(4 (u + v)) - 8 sin(u + 2 v) - 2 sqrt(2) sin(4 u + 2 v) + 8 sin(5 u + 2 v) + 2 sqrt(2) sin(8 u + 2 v) - 6 sin(u + 4 v) - 8 sin(5 u + 4 v) - 2 sin(7 u + 4 v) + sqrt(2) sin(8 u + 4 v)))/(abs(cos(v)) sqrt(576 (4 cos(2 v) sin(2 u) sin(3 u) (sqrt(2) sin(3 u) sin(2 v) - 2) cos^3(v) + 4 sqrt(2) sin(2 u) sin(v) (sin^2(3 u) sin^2(2 v) + 2) cos^2(v) + (-16 (2 cos(u) + cos(3 u)) sin^2(u) sin^2(2 v) + 6 cos(u) cos(3 u) cos(2 v) (sin(3 u) sin(2 v) - sqrt(2)) sin(2 v) + sin(u) (8 sin^2(v) + sin(3 u) (sin(3 u) sin(2 v) - sqrt(2)) sin(4 v))) cos(v) + sin(v) sin^2(2 v) (2 sin(u) sin(3 u) (sin(3 u) sin(2 v) - 2 sqrt(2)) + cos(u) (3 sin(6 u) sin(2 v) - 6 sqrt(2) cos(3 u))))^2 + 9 cos^2(v) (-60 sin(u) - 32 sin(5 u) - 4 sin(7 u) + 6 sin(u - 4 v) - sqrt(2) sin(4 u - 4 v) + 8 sin(5 u - 4 v) + 2 sin(7 u - 4 v) + sqrt(2) sin(8 u - 4 v) + 8 sin(u - 2 v) - 40 sqrt(2) sin(2 u - 2 v) - 2 sqrt(2) sin(4 u - 2 v) - 8 sin(5 u - 2 v) + 2 sqrt(2) sin(8 u - 2 v) + 40 sqrt(2) sin(2 (u + v)) + sqrt(2) sin(4 (u + v)) + 8 sin(u + 2 v) + 2 sqrt(2) sin(4 u + 2 v) - 8 sin(5 u + 2 v) - 2 sqrt(2) sin(8 u + 2 v) + 6 sin(u + 4 v) + 8 sin(5 u + 4 v) + 2 sin(7 u + 4 v) - sqrt(2) sin(8 u + 4 v))^2 + cos^2(v) (-18 sqrt(2) cos(u) + 14 sqrt(2) cos(3 u) - 2 sqrt(2) cos(5 u) + 4 sqrt(2) cos(7 u) + 2 sqrt(2) cos(9 u) + sqrt(2) cos(u - 4 v) - 6 cos(2 u - 4 v) + sqrt(2) cos(3 u - 4 v) - 6 cos(4 u - 4 v) + sqrt(2) cos(5 u - 4 v) - 2 cos(6 u - 4 v) - 2 sqrt(2) cos(7 u - 4 v) - sqrt(2) cos(9 u - 4 v) + 24 sqrt(2) cos(u - 2 v) - 4 cos(2 u - 2 v) + 8 sqrt(2) cos(3 u - 2 v) + 20 cos(4 u - 2 v) + 4 cos(6 u - 2 v) + 4 cos(2 (u + v)) + 6 cos(4 (u + v)) + 24 sqrt(2) cos(u + 2 v) + 8 sqrt(2) cos(3 u + 2 v) - 20 cos(4 u + 2 v) - 4 cos(6 u + 2 v) + sqrt(2) cos(u + 4 v) + 6 cos(2 u + 4 v) + sqrt(2) cos(3 u + 4 v) + sqrt(2) cos(5 u + 4 v) + 2 cos(6 u + 4 v) - 2 sqrt(2) cos(7 u + 4 v) - sqrt(2) cos(9 u + 4 v) - 18 sqrt(2) sin(u) + 70 sqrt(2) sin(3 u) + 2 sqrt(2) sin(5 u) + 4 sqrt(2) sin(7 u) + 2 sqrt(2) sin(9 u) + sqrt(2) sin(u - 4 v) + 6 sin(2 u - 4 v) - 11 sqrt(2) sin(3 u - 4 v) - 6 sin(4 u - 4 v) - sqrt(2) sin(5 u - 4 v) - 6 sin(6 u - 4 v) - 2 sqrt(2) sin(7 u - 4 v) - sqrt(2) sin(9 u - 4 v) + 24 sqrt(2) sin(u - 2 v) + 4 sin(2 u - 2 v) + 24 sqrt(2) sin(3 u - 2 v) + 20 sin(4 u - 2 v) - 4 sin(6 u - 2 v) - 120 sin(2 v) - 12 sin(4 v) - 4 sin(2 (u + v)) + 6 sin(4 (u + v)) + 24 sqrt(2) sin(u + 2 v) + 24 sqrt(2) sin(3 u + 2 v) - 20 sin(4 u + 2 v) + 4 sin(6 u + 2 v) + sqrt(2) sin(u + 4 v) - 6 sin(2 u + 4 v) - 11 sqrt(2) sin(3 u + 4 v) - sqrt(2) sin(5 u + 4 v) + 6 sin(6 u + 4 v) - 2 sqrt(2) sin(7 u + 4 v) - sqrt(2) sin(9 u + 4 v))^2))

    Properties

    algebraic surfaces | nonorientable surfaces | sextic surfaces

    Back to List | POWERED BY THE WOLFRAM LANGUAGE