geom3d - Maple Programming Help

Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Plane Functions : geom3d/IsEquilateral

geom3d

 IsEquilateral
 test if a given triangle is equilateral

 Calling Sequence IsEquilateral(ABC, cond )

Parameters

 ABC - triangle cond - (optional) name

Description

 • This routine tests if the given triangle ABC is equilateral. It returns true if ABC is equilateral; false if it is not; and FAIL if it is unable to reach a conclusion.
 • In FAIL is returned, and the optional argument is given, then the condition that makes ABC equilateral is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $&\mathrm{or}\left(\mathrm{expr_1}=0,\mathrm{expr_2}=0,...,\mathrm{expr_n}\right)$ where expr, expri_i are Maple expressions.
 • The command with(geom3d,IsEquilateral) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{triangle}\left(\mathrm{ABC},\left[\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,2,0,0\right),\mathrm{point}\left(C,1,2,0\right)\right]\right)$
 ${\mathrm{ABC}}$ (1)
 > $\mathrm{IsEquilateral}\left(\mathrm{ABC}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{point}\left(C,1,a,0\right):$
 > $\mathrm{IsEquilateral}\left(\mathrm{ABC},'\mathrm{cond}'\right)$
 IsEquilateral:   "hint: one of the following conditions must be satisfied: {-a^2+3 = 0}"
 ${\mathrm{FAIL}}$ (3)
 > $\mathrm{cond}$
 ${-}{{a}}^{{2}}{+}{3}{=}{0}$ (4)
 > $\mathrm{assume}\left(\mathrm{cond}\right)$
 > $\mathrm{IsEquilateral}\left(\mathrm{ABC}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{assume}\left(\mathrm{op}\left(1,\mathrm{cond}\right)\ne \mathrm{op}\left(2,\mathrm{cond}\right)\right)$
 > $\mathrm{IsEquilateral}\left(\mathrm{ABC}\right)$
 ${\mathrm{false}}$ (6)