Search Results for ""

If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.

A ruled surface M is said to be a binormal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vB^^(u), where B is the binormal vector.

A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

The Bowley skewness, also known as quartile skewness coefficient, is defied by ((Q_3-Q_2)-(Q_2-Q_1))/(Q_3-Q_1)=(Q_1-2Q_2+Q_3)/(Q_3-Q_1), where the Qs denote the interquartile ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

For a curve with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2, (1) the Gaussian curvature is K=(M_1-M_2)/((EG-F^2)^2), (2) where M_1 = |-1/2E_(vv)+F_(uv)-1/2G_(uu) 1/2E_u ...

A quartic curve with implicit equation (a^2)/(x^2)-(b^2)/(y^2)=1 (1) or a^2y^2-b^2x^2=x^2y^2 (2) and a,b>0. In parametric form, x = +/-acost (3) y = bcott. (4) The curvature ...

The 6-polyiamond illustrated above.

The evolute of the cardioid x = cost(1+cost) (1) y = sint(1+cost) (2) is the curve x_e = 2/3a+1/3acostheta(1-costheta) (3) y_e = 1/3asintheta(1-costheta), (4) which is a ...

The evolute of Cayley's sextic with parametrization x = 4acos^3(1/3theta)cost (1) y = 4acos^3(1/3theta)sint (2) is given by x_e = 1/4[2+3cos(2/3t)-cos(2t)] (3) y_e = ...