barycenter
barycenter([point1,coeff1],...) draws the barycenter of point1 with weight coeff1...
barycenter([Pnt,Real],[Pnt,Real],[Pnt,Real])
center
Gives the coordinates of the center of circle A.
center(A) division_point
Returns the point M such that (z-a)=k*(z-b) and z=affix of M (MA=k*MB).
division_point(Pnt or Cplx(a),Pnt or Cplx(b),Cplx(k))
element
Shows a point chosen on a curve or a real chosen in an interval
element((Curve or Real_interval),[Val])
inter
With 2 arguments gives the intersection of 2 curves or surfaces as a vector. If a third argument is given, the intersection returned is the one closest to that argument.
inter(Curve,Curve,[Pnt])
isobarycenter
isobarycenter(A,B,C,...) draws the isobarycenter of the n points A,B,C,...
midpoint
midpoint(A,B) draws the midpoint of the segment AB midpoint((Pnt or Cplx),(Pnt or Cplx))
orthocenter
Shows the orthocenter of a triangle or of the triangle made with 3 points.
orthocenter((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx))
point
A:=point(za) (resp A:=point([a,b,c])) draws a point of affix za (resp of coordinates (a,b,c)) with the legend A
point(Cplx(za)||Vect)
point2d
Defines at random, the coordinates (between -5 and +5) of the 2-d points given as argument.
point2d(SeqVar(A,B,C...))
trace
Turns on tracing of the specified point.
Line
DrawSlp
Draws a line with slope m, going through the point (a, b).
DrawSlp(Real(a),Real(b),Real(m))
LineTan
Draws the tangent to y=f(x) at x=a.
LineTan(Expr(f(x)),[Var],Expr(a))
altitude
Draws a line through A that crosses segment BC at right angles.
altitude(A,B,C) bisector
Draws the bisector of the angle (AB,AC) given by 3 points A,B,C.
bisector((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Pnt(C) or Cplx))
exbisector
Draws the exterior bisector of the angle (AB,AC) given by 3 points A,B,C.
exbisector((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Pnt(C) or Cplx))
half_line
half_line(A,B) draws the half-line AB with A as origin half_line((Pnt or Cplx),(Pnt or Cplx))
line
line(A,B) or line(a*x+b*y+c=0) or
line(a*x+b*y+c*z+d=0,aa*x+bb*y+cc*z+dd=0) draws the line AB in the plane or in the 3D space. line(A,slope=m) draws the line going through A with slope m or of equation the argument in the plane or in 3D space.
line(Pnt||Cplx||Eq,[Pnt||slope||Var])
median_line
median_line(A,B,C) draws the median-line through A of the triangle ABC
median_line((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx))
parallel
parallel(A,D) (resp parallel(A,P) or parallel(A,D,DD)) draws the line (resp plane) through A parallel to the line D (resp parallel to the plane P or to the lines D,DD) and, parallel(d,D) draws the plane through d parallel to the line D.
parallel(Pnt or Line,Line or Plan,[Line])
perpen_bisector
perpen_bisector(A,B) draws the bisection (line or plane) of the segment AB.
perpen_bisector((Pnt or Cplx),(Pnt or Cplx))
perpendicular
perpendicular(A,line(B,C)) or perpendicular(A,B,C) draws the orthogonal line of line BC through A and
perpendicular(d,plane(B,C,D)) draws the orthogonal plane of plane(B,C,D) through the line d.
perpendicular((Pnt or Line),(Line or Plan))
segment
segment(A,B) draws the segment AB segment((Pnt or Cplx),(Pnt or Cplx),[Var],[Var])
tangent
tangent(C,A) draws the tangents (line or plane) to C through A.
tangent(Curve(C),Pnt(A))
Polygon
equilateral_triangle
equilateral_triangle(A,B) (resp equilateral_triangle(A,B,P)) draws the direct equilateral triangle ABC of side AB (resp in the half-plane ABP).
equilateral_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),[Pnt(P)],[Var(C)])
hexagon
Returns and draws the hexagon of side AB (ABCDEF is direct) (in the plane ABP.)
hexagon(Pnt(A)||Cplx,Pnt(B)||Cplx,[Pnt(P)],[V ar(C)],[Var(D)],[Var(E)],[Var(F)])
isosceles_triangle
Draws the isosceles triangle ABC AB=AC and angle(AB,AC)=t (or in the plane ABP
angle(AB,AC)=angle(AB,AP) or angle(AB,AC)=t).
isosceles_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Angle(t) or Pnt(P) or
Lst(P,t)),[Var(C)] )
isopolygon
Draws a regular polygon having abs(n) vertices, given by 2 vertices (or 2 vertices and 1 point of the plane) if n>0 and by its center and 1 vertex (or its center, 1 vertex and 1 point of the plane) if n<0.
isopolygon(Pnt,Pnt,[Pnt],Intg(n))
parallelogram
Returns and draws the parallelogram ABCD such as vector(AB)+vector(AD)=vector(AC).
parallelogram(Pnt(A)||Cplx,Pnt(B)||Cplx,Pnt(C )||Cplx,[Var(D)] )
polygon
Returns and draws the polygon where its vertices are the element of l.
polygon(LstPnt||LstCplx)
quadrilateral
Returns and draws the quadrilateral ABCD.
quadrilateral(Pnt(A)||Cplx,Pnt(B)||Cplx,Pnt(C )||Cplx,Pnt(D)||Cplx)
rectangle
Returns and draws the rectangle ABCD, AD=k*AB if k>0 ABCD is direct else indirect (in the plane ABP AD=AP or AD=k*AB).
rectangle(Pnt(A)||Cplx,Pnt(B)||Cplx,Real(k)||
Pnt(P)||Lst(P,k),[Var(D)],[Var(C)])
rhombus
Returns and draws the rhombus ABCD such as the angle (AB,AD)=a (or in the plane ABP angle(AB,AD)=angle(AB,AP) or such that angle(AB,AD)=a).
rhombus(Pnt(A)||Cplx,Pnt(B)||Cplx,Angle(a)||P nt(P)||Lst(P,a)),[Var(C)],[Var(D)])
right_triangle
Draws the A_rectangular triangle ABC with AC=k*AB (or in the plane ABP AC=AP or AC=k*AB).
right_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Real(k) or Pnt(P) or
Lst(P,k)),[Var(C)])
square
Returns and draws the square of side AB (ABCD is direct) (in the plane ABP.
square((Pnt(A) or Cplx),(Pnt(B) or Cplx),[Pnt(P),Var(C),Var(D)])
triangle
triangle(A,B,C) draws the triangle ABC
triangle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx))
Curve
Function
Defines a function plot.
plotfunc(Expr)
circle
Define for 2-d a circle with a diameter (arg2=Point) or with center and radius (arg2=Complex, abs(arg2)=radius) [or the arc AB, A angle a, B angle b (arg1+arg2=angle 0)]
or by its equation and for 3-d with a diameter and a third point
circle((Pnt or Cplx),(Pnt(arg2) or
Cplx(arg2)),[Real(a)],[Real(b)],[Var(A)],[Var (B)])
circumcircle
circumcircle(A,B,C)=circumcircle of the triangle ABC.
circumcircle((Pnt or Cplx),(Pnt or Cplx),((Pnt or Cplx))
conic
Defines a conic by its equation with x,y as default variables and draws it.
conic(Expr,[LstVar])
ellipse
ellipse(F1,F2,M)=ellipse focus F1,F2 through M or such as MF1+MF2=2*a (geo2d) and ellipse(p(x,y)) draws the conic if deg(p)=2.
ellipse(Pnt(F1),Pnt(F2),(Pnt(M) or Real(a)) y ellipse(p(x,y))=conic si deg(p)=2.)
excircle
excircle(A,B,C) draws the A-excircle of the ABC triangle.
excircle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx))
hyperbola
hyperbola(F1,F2,M)=hyperbola focus F1,F2 through M or (|MF1-MF2|=2*a geo2d) and hyperbola(p(x,y)) draws the conic if deg(p)=2.
hyperbola(Focus(F1),Focus(F2),(Pnt(M) or Real(a)))
incircle
incircle(A,B,C) draws the incircle of the ABC triangle.
incircle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx))
locus
locus(M,A) draws the locus of M (or locus(d,A) draws the envelope of d) when A:=element(C) (C is a curve). The example instructions below must be written in a geometric level on different lines.
locus(Pnt,Elem)
parabola
parabola(F,A)=focus F, top A (in the plane ABP) or (parabola(A,c) of equa. y=yA+c*(x-xA)^2 c=1/(2*p) and FA=p/2 geo2d) and parabola(P(x,y)) draws the conic if deg(P)=2.
parabola(Pnt(F)||Pnt(xA+i*yA),Pnt(A)||Real(c) ,
[Pnt(P)])
Transform
homothety
homothety(C,k,A)=point A1 such as vect(C,A1)=k*vect(C,A) i.e in 2-d it is the similarity center C, coeff abs(k) and angle arg(k).
homothety(Pnt(C),Real(k),Pnt(A))
inversion
inversion(C,k,A)=point A1 such as A1 on line(C,A) and mes_alg(CA1*CA)=k
inversion(Pnt(C),Real(k),Pnt(A))
isobarycenter((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx))
projection
projection(C,A) is the orthogonal projection of A on the curve C
projection(Curve,Pnt)
reflection
reflection(D,C) (or reflection(A,C))=symmetrical of C in the symmetry-line D (or sym-point A)
reflection((Pnt(A) or Line(D)),(Pnt(C) or Curve(C)))
rotation
rotation(B,a1,A)(resp rotation(d,a1,A)) is the transformation of A by rotation of center B (resp of axis d) and of angle a1.
rotation((Pnt(B) or Cplx or Dr3),Angle(a1),(Pnt(A) or Curve))
similarity
similarity(B,k,a1,A)=transformation of A in the similarity (center B or axis d, coeff k,angle a1) (or also
homothety(B,k*exp(i*a1),A)).
similarity(Pnt or Dr3,Real,Angle,Pnt)
translation
translation(B-A,C) (resp translation([a,b,c],C)) is the translation of C in the translation of vector AB (resp [a,b,c]).
translation(Vect, Pnt(C))