An overview of the functionality of GeoGebra
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- Carmel Palmer
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1 An overview of the functionality of GeoGebra Many of the geometric object can be created using the icon menus. The composite picture above shows the icons in the pictures. Most are clear enough to understand from the icon. The next page shows each menu along with the text descriptions that accompany the icons. GeoGebra also has more algebraic commands available from the input line. (The commands invoked by the icons each have text based versions.) I have organized some of those common courses in the pages that follow.
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3 GeoGebra Commands of interest for conic sections Conics - construction Conic[point A, point B, point C, point D, point E]: Conic section through five points A, B, C, D, and C. Note: No four of the points lie on one line. Circle[point M, number r]: Circle with midpoint M and radius r Circle[point M, segment s]: Circle with midpoint M and radius equal to Length[s] Circle[point M, point A]: Circle with midpoint M through point A Circle[point A, point B, point C]: Circle through three points A, B and C Ellipse[point F, point G, number a]: Ellipse with focal points F and G and principal axis length a. Note: Condition: 2a > Distance[F, G] Ellipse[point F, point G, segment s]: Ellipse with focal points F and G where the length of the principal axis equals the length of segment s (a = Length[s]). Hyperbola[point F, point G, number a]: Hyperbola with focal points F and G and principal axis length a. Note: Condition: 0 < 2a < Distance[F, G] Hyperbola[point F, point G, segment s]: Hyperbola with focal points F and G where the length of the principal axis equals the length of segment s (a = Length[s]) Parabola[point F, line g]: Parabola with focal point F and directrix g Conics Related information Asymptote[hyperbola h]: Both asymptotes of a hyperbola h Tangent[point A, conic c]: (All) tangents through point A to conic section c Tangent[line g, conic c]: (All) tangents to conic section c that are parallel to line g Directrix[parabola p]: Directrix of a parabola p Excentricity[conic c]: Excentricity of a conic section c FirstAxis[conic c]: Principal axis of a conic section c FirstAxisLength[conic c]: Length of a conic section c s principal axis SecondAxis[conic c]: Second axis of a conic section c SecondAxisLength[conic c]: Length of a conic section c's second axis Vertex[conic c]: (All) vertices of a conic section c Diameter[line g, conic c]: Diameter conjugate to line g relative to conic section c Diameter[vector v, conic c]: Diameter with direction vector v relative to conic section c
4 GeoGebra Commands of interest for college algebra/pre-calculus Polynomial investigation f(x) = x^3-3 x^2 + 1 R = Root[polynomial f]: All roots of polynomial f (as points) Asymptote[hyperbola h]: Both asymptotes of a hyperbola h Centroid[polygon poly]: Centroid of a polygon poly Circle[point M, number r]: Circle with midpoint M and radius r Circle[point M, segment s]: Circle with midpoint M and radius equal to Length[s] Circle[point M, point A]: Circle with midpoint M through point A Circle[point A, point B, point C]: Circle through three points A, B and C Direction[line g]: Direction vector of line g. Note: A line with equation ax + by = c has the direction vector (b, - a). Directrix[parabola p]: Directrix of a parabola p Ellipse[point F, point G, number a]: Ellipse with focal points F and G and principal axis length a. Note: Condition: 2a > Distance[F, G] Ellipse[point F, point G, segment s]: Ellipse with focal points F and G where the length of the principal axis equals the length of segment s (a = Length[s]). Excentricity[conic c]: Excentricity of a conic section c FirstAxis[conic c]: Principal axis of a conic section c FirstAxisLength[conic c]: Length of a conic section c s principal axis Hyperbola[point F, point G, number a]: Hyperbola with focal points F and G and principal axis length a. Note: Condition: 0 < 2a < Distance[F, G] Hyperbola[point F, point G, segment s]: Hyperbola with focal points F and G where the length of the principal axis equals the length of segment s (a = Length[s]) Div[number a, number b]: Integer quotient when number a is divided by number b Line[point A, point B]: Line through two points A and B Line[point A, line g]: Line through point A parallel to line g Line[point A, vector v]: Line through point A with direction vector v Mod[number a, number b]: Remainder when number a is divided by number b Parabola[point F, line g]: Parabola with focal point F and directrix g SecondAxis[conic c]: Second axis of a conic section c SecondAxisLength[conic c]: Length of a conic section c's second axis Vertex[conic c]: (All) vertices of a conic section c
5 GeoGebra Commands of interest for calculus Polynomial investigation f(x) = x^3-3 x^2 + 1 R = Root[polynomial f]: All roots of polynomial f (as points) E = Extremum[f] I = InflectionPoint[f] Derivative[f] Derivative[f, 2] Standard Calculus Derivative[function f]: Derivative of function f(x) Derivative[function f, number n]: n th derivative of function f(x) Root[function f, number a]: One root of function f with initial value a (Newton's method) Root[function f, number a, number b]: One root of function f on interval [a, b] (regula falsi) Tangent[number a, function f]: Tangent to function f(x) at x = a Tangent[point A, function f]: Tangent to function f(x) at x = x(a) TaylorPolynomial[function f, number a, number n] Curvature[point A, function f]: Curvature of function f in point A CurvatureVector[point A, function f]: Curvature vector of function f in point A OsculatingCircle[point A, function f]: Osculating circle of function f in point A Integral[function f]: Indefinite integral for function f(x) Integral[function f, number a, number b]: Definite integral of function f(x) from number a to b. Note: This command also draws the area between the function graph of f and the x-axis. Integral[function f, function g, number a, number b]: Definite integral of the difference of the functions f(x) - g(x) from number a to number b. Note: This command also draws the area between the function graphs of f and g. LowerSum[function f, number a, number b, number n]: Lower sum of function f on the interval [a, b] with n rectangles. Note: This command draws the rectangles of the lower sum too. UpperSum[function f, number a, number b, number n]: Upper sum of function f on the interval [a, b] with n rectangles. Note: This command draws the rectangles of the upper sum too. Derivative[curve c]: Tangent[point A, curve c]: Tangent to curve c in point A Curvature[point A, curve c]: Curvature of curve c in point A CurvatureVector[point A, curve c]: Curvature vector of curve c in point A OsculatingCircle[point A, curve c]: Osculating circle of curve c in point A
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