Mathematical Experiment 1

教師：全任重	e-mail: jcchuan@math.nthu.edu.tw
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網頁：http://poncelet.math.nthu.edu.tw/disk3/exp01/	上課地點：綜合三館三樓數學圖書館內
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The Astroidal Ellipsoid is given by the parametric equations

Construct the VRML model of this surface.

Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 304.

Construct the graph of

f(u,v) = u²v⁴,

-1 < u < 1, -1 < v < 1.

Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 308.

Construct the graph of

f(u,v) = u²v⁴,

as (u,v) ranges over the disk

u² + v² < 2.

Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 309.

Construct Pl𡡷ker's Conoid

as (x,y) ranges over the unit disk

x² + y² < 1.

Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 337.

Construct the Ennerper's Surface given by

Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 451.

Construct the Scherk's Fifth Surface given by

[arcsinh(u),arcsinh(v),arcsin(uv)]
-1 < u < 1, -1 < v < 1

Reference: A. Gray, Modern Differential Geometry of Curves and Surfaces, p. 451.

Construct the surface obtained by rotating about the x-axis of the curve

0 < t < 2p.

Construct the surface given by the equation

r = sin(2f)
0 < f <p/2

in spherical coordinates.