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Symbolic view: Cmds menu Point

Im Dokument HP Prime Graphing Calculator User Guide (Seite 158-166)

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))

Numeric view: Cmds menu

Im Dokument HP Prime Graphing Calculator User Guide (Seite 158-166)