umbilic造句

• The equivalence classes of such cubics under uniform scaling form a three-dimensional real projective space and the subset of parabolic forms define a surface  called the umbilic bracelet by Christopher Zeeman.
• Umbilics can also be characterised by the pattern of the principal direction vector field around the umbilic which typically form one of three configurations : star, lemon, and lemonstar ( or monstar ).
• Whilst principal directions are not uniquely defined at an umbilic the limits of the principal directions when following a ridge on the surface can be found and these correspond to the root-lines of the cubic form.
• In 2010, it was announced that Jim Simons had commissioned an Umbilic Torus sculpture to be constructed outside the Math and Physics buildings at Stony Brook University, in proximity to the Simons Center for Geometry and Physics.
• All the proofs mentioned above are based on Hamburger's reduction of the Carath閛dory conjecture to the following conjecture : "'the index of every isolated umbilic point is never greater than one " '.
• In 2012, Ghomi and Howard showed, using a M鯾ius transformation, that the global conjecture for surfaces of smoothness C 2 can be reformulated in terms of the number of umbilic points on graphs subject to certain asymptotics of the gradient.
• In 2010, the Simons Foundation, a private institution committed to the advancement of science and mathematics, commissioned him to create the Umbilic Torus SC, a massive 8.5 meter-high cast bronze and granite sculpture weighing more than nine tons.