geom3d - Maple Programming Help

Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Sphere Functions : geom3d/IsTangent

geom3d

 IsTangent
 test if a plane is tangent to a sphere

 Calling Sequence IsTangent(p, s)

Parameters

 p - plane s - sphere

Description

 • The routine returns true if the plane p is tangent to the sphere s; false if they are not; and FAIL if it is unable to reach a conclusion.
 • In case of FAIL, if the third optional argument is given, the condition that makes p tangent to s is assigned to this argument.
 • The command with(geom3d,IsTangent) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{sphere}\left(s,\left[\mathrm{point}\left(o,0,0,1\right),1\right]\right)$
 ${s}$ (1)

Find the condition that makes the plane $ax+by+cz+d=0$ tangent to the sphere s

 > $\mathrm{assume}\left(a\ne 0\right)$
 > $\mathrm{plane}\left(p,ax+by+cz+d=0,\left[x,y,z\right]\right)$
 ${p}$ (2)
 > $\mathrm{IsTangent}\left(p,s,'\mathrm{condition}'\right)$
 IsTangent:   "unable to determine if 1-abs(c+d)/(a^2+b^2+c^2)^(1/2) is zero"
 ${\mathrm{FAIL}}$ (3)

Hence, the condition is:

 > $\mathrm{condition}$
 ${1}{-}\frac{\left|{c}{+}{d}\right|}{\sqrt{{{\mathrm{a~}}}^{{2}}{+}{{b}}^{{2}}{+}{{c}}^{{2}}}}{=}{0}$ (4)