Setup Menus in Admin Panel

  • LOGIN

  • No hay productos en el carrito.

Binomio al cubo: animación en LaTeX2e

Representación geométrica del cubo de un binomio.

Te comparto el código fuente de una diapositiva que elaboré usando LaTeX2e para explicar la representación geométrica del cubo de un binomio.

Te explico grosso modo el código fuente.

El documento es de la clase beamer. Empiezo cargando los paquetes que se requieren para generar la diapositiva (TikZ y tikz-3dplot). Indico las opciones de las diapositivas de la presentación en beamer y después indico información sobre el archivo en un comentario de varias líneas.

Para dar la impresión de que se trata de una animación, utilizo la instrucción \visible de beamer para que vayan apareciendo una a una las partes de la figura geométrica.
La primera parte que se muestra corresponde a el cubo de a. En esta parte también muestro los valores de a y de b en la representación geométrica usando la instrucción \pgfmathsetmacro{\a}{3.75}. De manera semejante para b. El valor de dx representa la separación entre los prismas rectangulares que se dibujan sucesivamente.
Después dibujo, una tras otra, las partes que corresponden a 3\,a^{2}b.
Luego se dibuja, una a una las tres partes que corresponden a 3\,ab^{2}. Finalmente, se muestra en la esquina superior frontal el cubo que representa a b^{3}.

A continuación se enlista el código fuente.

% Filename: Cube-of-a-binomial.tex
%
% Description:
% A geometric representation of the cube of the binomial $a + b$ is shown.
% $(a + b)^3 = a^3 + 3 a^2 b + 3 a b^2 + b^3$.
%
% Author: Efraín Soto Apolinar.
% Date of creation: 05 / Feb / 2023
% Monterrey, N.L., Mexico.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Terms of use:
% Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
% https://creativecommons.org/licenses/by-nc-sa/4.0/
%
\documentclass[aspectratio=169]{beamer}
\usepackage{tikz}
\usepackage{tikz-3dplot}
%
\usetheme{Warsaw}
\useoutertheme{infolines} 
\usefonttheme{professionalfonts}
%
% About this slideshow
%
\author{Efra\'in Soto Apolinar}
\title[Binomio al cubo]{Binomio al cubo}
\subtitle{Aprende Matem\'aticas}
\institute{}
\date{}
%
%
%
\begin{document}
%
\section{Aprende Matem\'aticas}
\subsection{www.aprendematematicas.org.mx}
%
\begin{frame}[fragile]{}{} 
	%
	\begin{center}
	%
	\tdplotsetmaincoords{75}{120}
	%
	\begin{tikzpicture}[tdplot_main_coords]
	\pgfmathsetmacro{\a}{3.75}
	\pgfmathsetmacro{\b}{1.25}
	\pgfmathsetmacro{\dx}{0.35}
	\pgfmathsetmacro{\eje}{\a+\b+\dx}
	% Vertices of the rectangular prisms
	\coordinate (1) at (0,0,0);
	\coordinate (2) at (\a,0,0);
	\coordinate (3) at (\a,\a,0);
	\coordinate (4) at (0,\a,0);
	\coordinate (5) at (0,0,\a);
	\coordinate (6) at (\a,0,\a);
	\coordinate (7) at (\a,\a,\a);
	\coordinate (8) at (0,\a,\a);
	% 
	\coordinate (9) at (\a+\dx,0,0);
	\coordinate (10) at (\a+\b+\dx,0,0);
	\coordinate (11) at (\a+\b+\dx,\a,0);
	\coordinate (12) at (\a+\dx,\a,0);
	\coordinate (13) at (\a+\dx,0,\a);
	\coordinate (14) at (\a+\b+\dx,0,\a);
	\coordinate (15) at (\a+\b+\dx,\a,\a);
	\coordinate (16) at (\a+\dx,\a,\a);
	%
	\coordinate (17) at (0,\a+\dx,0);
	\coordinate (18) at (\a,\a+\dx,0);
	\coordinate (19) at (\a,\a+\b+\dx,0);
	\coordinate (20) at (0,\a+\b+\dx,0);
	\coordinate (21) at (0,\a+\dx,\a);
	\coordinate (22) at (\a,\a+\dx,\a);
	\coordinate (23) at (\a,\a+\b+\dx,\a);
	\coordinate (24) at (0,\a+\b+\dx,\a);
	%
	\coordinate (25) at (\a+\dx,\a+\dx,0);
	\coordinate (26) at (\a+\b+\dx,\a+\dx,0);
	\coordinate (27) at (\a+\b+\dx,\a+\b+\dx,0);
	\coordinate (28) at (\a+\dx,\a+\b+\dx,0);
	\coordinate (29) at (\a+\dx,\a+\dx,\a);
	\coordinate (30) at (\a+\b+\dx,\a+\dx,\a);
	\coordinate (31) at (\a+\b+\dx,\a+\b+\dx,\a);
	\coordinate (32) at (\a+\dx,\a+\b+\dx,\a);
	%
	\coordinate (33) at (0,0,\a+\dx);
	\coordinate (34) at (\a,0,\a+\dx);
	\coordinate (35) at (\a,\a,\a+\dx);
	\coordinate (36) at (0,\a,\a+\dx);
	\coordinate (37) at (0,0,\a+\b+\dx);
	\coordinate (38) at (\a,0,\a+\b+\dx);
	\coordinate (39) at (\a,\a,\a+\b+\dx);
	\coordinate (40) at (0,\a,\a+\b+\dx);
	% 
	\coordinate (41) at (\a+\dx,0,\a+\dx);
	\coordinate (42) at (\a+\b+\dx,0,\a+\dx);
	\coordinate (43) at (\a+\b+\dx,\a,\a+\dx);
	\coordinate (44) at (\a+\dx,\a,\a+\dx);
	\coordinate (45) at (\a+\dx,0,\a+\b+\dx);
	\coordinate (46) at (\a+\b+\dx,0,\a+\b+\dx);
	\coordinate (47) at (\a+\b+\dx,\a,\a+\b+\dx);
	\coordinate (48) at (\a+\dx,\a,\a+\b+\dx);
	%
	\coordinate (49) at (0,\a+\dx,\a+\dx);
	\coordinate (50) at (\a,\a+\dx,\a+\dx);
	\coordinate (51) at (\a,\a+\b+\dx,\a+\dx);
	\coordinate (52) at (0,\a+\b+\dx,\a+\dx);
	\coordinate (53) at (0,\a+\dx,\a+\b+\dx);
	\coordinate (54) at (\a,\a+\dx,\a+\b+\dx);
	\coordinate (55) at (\a,\a+\b+\dx,\a+\b+\dx);
	\coordinate (56) at (0,\a+\b+\dx,\a+\b+\dx);
	%
	\coordinate (57) at (\a+\dx,\a+\dx,\a+\dx);
	\coordinate (58) at (\a+\b+\dx,\a+\dx,\a+\dx);
	\coordinate (59) at (\a+\b+\dx,\a+\b+\dx,\a+\dx);
	\coordinate (60) at (\a+\dx,\a+\b+\dx,\a+\dx);
	\coordinate (61) at (\a+\dx,\a+\dx,\a+\b+\dx);
	\coordinate (62) at (\a+\b+\dx,\a+\dx,\a+\b+\dx);
	\coordinate (63) at (\a+\b+\dx,\a+\b+\dx,\a+\b+\dx);
	\coordinate (64) at (\a+\dx,\a+\b+\dx,\a+\b+\dx);
	% Indications for distances
	\draw[thick] (\a,0,0.05) -- (\a,0,-0.05) node [below] {\footnotesize$a$};
	\draw[thick] (0,\a,0.05) -- (0,\a,-0.05) node [below] {\footnotesize$a$};
	\draw[thick] (0,0.05,\a) -- (0,-0.05,\a) node [left] {\footnotesize$a$};
	%
	\visible<1-9>{
	% Indications for distances at the plane z = 0
	\draw[gray,dash dot dot]($(1)!-0.125!(20)$)--($(20)!-0.125!(1)$);
	\draw[gray,dash dot dot]($(1)!-0.125!(20)$)--($(20)!-0.125!(1)$);
	\draw[gray,dash dot dot]($(10)!-0.125!(27)$)--($(27)!-0.125!(10)$);
	\draw[gray,dash dot dot]($(1)!-0.125!(10)$)--($(10)!-0.125!(1)$);
	\draw[gray,dash dot dot]($(20)!-0.125!(27)$)--($(27)!-0.125!(20)$);
	\draw[gray,dash dot dot]($(2)!-0.125!(19)$)--($(19)!-0.125!(2)$);
	\draw[gray,dash dot dot]($(9)!-0.125!(28)$)--($(28)!-0.125!(9)$);
	\draw[gray,dash dot dot]($(4)!-0.125!(11)$)--($(11)!-0.125!(4)$);
	\draw[gray,dash dot dot]($(17)!-0.125!(26)$)--($(26)!-0.125!(17)$);
	\draw[gray,dash dot dot]($(1)!-0.125!(37)$)--($(37)!-0.0625!(1)$);
	% Indications for distances at the plane x = 0
	\draw[gray,dash dot dot]($(5)!-0.125!(24)$)--($(24)!-0.125!(5)$);
	\draw[gray,dash dot dot]($(33)!-0.125!(52)$)--($(52)!-0.125!(33)$);
	\draw[gray,dash dot dot]($(37)!-0.125!(56)$)--($(56)!-0.125!(37)$);
	\draw[gray,dash dot dot]($(2)!-0.125!(38)$)--($(38)!-0.125!(2)$);
	\draw[gray,dash dot dot]($(9)!-0.125!(45)$)--($(45)!-0.125!(9)$);
	\draw[gray,dash dot dot]($(10)!-0.125!(46)$)--($(46)!-0.125!(10)$);
	% Indications for distances at the plane x = \a
	\draw[gray,dash dot dot]($(5)!-0.125!(14)$)--($(14)!-0.125!(5)$);
	\draw[gray,dash dot dot]($(33)!-0.125!(42)$)--($(42)!-0.125!(33)$);
	\draw[gray,dash dot dot]($(4)!-0.125!(40)$)--($(40)!-0.125!(4)$);
	\draw[gray,dash dot dot]($(37)!-0.125!(46)$)--($(46)!-0.125!(37)$);
	\draw[gray,dash dot dot]($(17)!-0.125!(53)$)--($(53)!-0.125!(17)$);
	\draw[gray,dash dot dot]($(20)!-0.125!(56)$)--($(56)!-0.125!(20)$);
	}
	%
	\visible<2->{
	% Indications for distances (first part)
	\draw[thick,<->] (\a,\a+\b+\dx,-\dx) -- (0,\a+\b+\dx,-\dx) node[midway,fill=white] {\footnotesize$a$};
	\draw[gray] (\a,\a+\b+\dx,0) -- (\a,\a+\b+\dx,-2.0*\dx);
	\draw[gray] (0,\a+\b+\dx,0) -- (0,\a+\b+\dx,-2.0*\dx);
	\draw[thick,<->] (0,\a+\b+2.0*\dx,0) -- (0,\a+\b+2.0*\dx,\a) node[midway,fill=white] {\footnotesize$a$};
	\draw[gray] (0,\a+\b+\dx,\a) -- (0,\a+\b+3.0*\dx,\a);
	\draw[gray] (0,\a+\b+\dx,0) -- (0,\a+\b+3.0*\dx,0);
	\draw[thick,<->] (\a+\b+\dx,0,-\dx) -- (\a+\b+\dx,\a,-\dx) node[midway,fill=white] {\footnotesize$a$};
	\draw[gray] (\a+\b+\dx,0,0) -- (\a+\b+\dx,0,-2.0*\dx);
	\draw[gray] (\a+\b+\dx,\a,0) -- (\a+\b+\dx,\a,-2.0*\dx);
	\draw[thick,<->] (\a+\b+2.0*\dx,0,0) -- (\a+\b+2.0*\dx,0,\a) node[midway,fill=white] {\footnotesize$a$};
	\draw[gray] (\a+\b+\dx,0,\a) -- (\a+\b+3.0*\dx,0,\a);
	\draw[gray] (\a+\b+\dx,0,0) -- (\a+\b+3.0*\dx,0,0);
	}
	\visible<2->{
	% More indications for distances...
	\draw[thick,<->] (\a+\b+\dx,\a+\dx,-\dx) -- (\a+\b+\dx,\a+\b+\dx,-\dx) node[midway,fill=white] {\footnotesize$b$};
	\draw[gray] (\a+\b+\dx,\a+\b+\dx,0) -- (\a+\b+\dx,\a+\b+\dx,-2.0*\dx);
	\draw[gray] (\a+\b+\dx,\a+\dx,0) -- (\a+\b+\dx,\a+\dx,-2.0*\dx);
	\draw[thick,<->] (\a+\dx,\a+\b+\dx,-\dx) -- (\a+\b+\dx,\a+\b+\dx,-\dx) node[midway,fill=white] {\footnotesize$b$};
	\draw[gray] (\a+\dx,\a+\b+\dx,0) -- (\a+\dx,\a+\b+\dx,-2.0*\dx);
	\draw[thick,<->] (\a+\b+2.0*\dx,0,\a+\dx) -- (\a+\b+2.0*\dx,0,\a+\b+\dx) node[midway,fill=white] {\footnotesize$b$};
	\draw[gray] (\a+\b+\dx,0,\a+\dx) -- (\a+\b+3.0*\dx,0,\a+\dx);
	\draw[gray] (\a+\b+\dx,0,\a+\b+\dx) -- (\a+\b+3.0*\dx,0,\a+\b+\dx);
	\draw[thick,<->] (0,\a+\b+2.0*\dx,\a+\dx) -- (0,\a+\b+2.0*\dx,\a+\b+\dx) node[midway,fill=white] {\footnotesize$b$};
	\draw[gray] (0,\a+\b+\dx,\a+\dx) -- (0,\a+\b+3.0*\dx,\a+\dx);
	\draw[gray] (0,\a+\b+\dx,\a+\b+\dx) -- (0,\a+\b+3.0*\dx,\a+\b+\dx);
	}
	% The geometric representation of the cube of the binomial
	%
	% First $a^3$
	%
	\visible<2->{
	\draw[red,thick,fill=cyan!35,opacity=0.5] (1) -- (2) -- (3) --(4) -- (1); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.5] (1) -- (4) -- (8) --(5) -- (1); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.5] (1) -- (2) -- (6) --(5) -- (1); % y = 0
	%
	\node at (0.5*\a,0.5*\a,0.5*\a) {$a^3$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.5] (5) -- (6) -- (7) --(8) -- (5); % z = \a
	\draw[red,thick,fill=cyan!35,opacity=0.5] (2) -- (3) -- (7) --(6) -- (2); % x = \a
	\draw[red,thick,fill=cyan!35,opacity=0.5] (4) -- (3) -- (7) --(8) -- (4); % y = \a
	}
	%
	\visible<3->{
	% Now: $a^2 b$ (front face)
	% Las paredes
	\draw[red,thick,fill=cyan!35,opacity=0.35] (9) -- (10) -- (11) --(12) -- (9); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (9) -- (12) -- (16) --(13) -- (9); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (9) -- (10) -- (14) --(13) -- (9); % y = 0
	%
	\node at (\a+0.5*\b+\dx,0.5*\a,0.5*\a) {$a^2b$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (13) -- (14) -- (15) --(16) -- (13); % z = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (10) -- (11) -- (15) --(14) -- (10); % x = \a + \b
	\draw[red,thick,fill=cyan!35,opacity=0.35] (12) -- (11) -- (15) --(16) -- (12); % y = \a
	}
	%
	\visible<4->{
	% +	+	+	+	+	+	+	+	+	+	+	+	+
	% Now: $a^2 b$ (face at the right)
	\draw[red,thick,fill=cyan!35,opacity=0.35] (17) -- (18) -- (19) --(20) -- (17); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (17) -- (20) -- (24) --(21) -- (17); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (17) -- (18) -- (22) --(21) -- (17); % y = \a
	%
	\node at (0.5*\a,\a+0.5*\b+\dx,0.5*\a) {$a^2b$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (21) -- (22) -- (23) --(24) -- (21); % z = \a 
	\draw[red,thick,fill=cyan!35,opacity=0.35] (18) -- (19) -- (23) --(22) -- (18); % x = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (20) -- (19) -- (23) --(24) -- (20); % y = \a + \b
	}
	%
	\visible<6->{
	% Now: $b^2 a$ (front corner)
	\draw[red,thick,fill=cyan!35,opacity=0.35] (25) -- (26) -- (27) --(28) -- (25); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (25) -- (28) -- (32) --(29) -- (25); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (25) -- (26) -- (30) --(29) -- (25); % y = \a
	%
	\node at (\a+0.5*\b+\dx,\a+0.5*\b+\dx,0.5*\a) {$ab^2$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (29) -- (30) -- (31) --(32) -- (29); % z = \a 
	\draw[red,thick,fill=cyan!35,opacity=0.35] (26) -- (27) -- (31) --(30) -- (26); % x = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (28) -- (27) -- (31) --(32) -- (28); % y = \a + \b
	}
	% 	+	+	+	+	+	+	+	+	+	+	+	+
	% Top layer
	% 	+	+	+	+	+	+	+	+	+	+	+	+
	\visible<5->{
	% First $a^2 b$ (Top cover)
	\draw[red,thick,fill=cyan!35,opacity=0.35] (33) -- (34) -- (35) --(36) -- (33); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (33) -- (36) -- (40) --(37) -- (33); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (33) -- (34) -- (38) --(37) -- (33); % y = 0
	%
	\node at (0.5*\a+\dx,0.5*\a+\dx,\a+0.5*\b+\dx) {$a^2b$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (37) -- (38) -- (39) --(40) -- (37); % z = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (34) -- (35) -- (39) --(38) -- (34); % x = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (36) -- (35) -- (39) --(40) -- (36); % y = \a
	}
	% Now: $a b^2$ (front part)
	\visible<7->{
	% Las paredes
	\draw[red,thick,fill=cyan!35,opacity=0.35] (41) -- (42) -- (43) --(44) -- (41); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (41) -- (44) -- (48) --(45) -- (41); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (41) -- (42) -- (46) --(45) -- (41); % y = 0
	%
	\node at (\a+0.5*\b+\dx,0.5*\a+\dx,\a+0.5*\b+\dx) {$ab^2$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (45) -- (46) -- (47) --(48) -- (45); % z = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (42) -- (43) -- (47) --(46) -- (42); % x = \a + \b
	\draw[red,thick,fill=cyan!35,opacity=0.35] (44) -- (43) -- (47) --(48) -- (44); % y = \a
	}
	%
	\visible<8->{
	% Now: $a^2 b$ (at the right)
	\draw[red,thick,fill=cyan!35,opacity=0.35] (49) -- (50) -- (51) --(52) -- (49); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (49) -- (52) -- (56) --(53) -- (49); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (49) -- (50) -- (54) --(53) -- (49); % y = \a
	%
	\node at (0.5*\a+\dx,\a+0.5*\b+\dx,\a+0.5*\b+\dx) {$ab^2$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (53) -- (54) -- (55) --(56) -- (53); % z = \a 
	\draw[red,thick,fill=cyan!35,opacity=0.35] (50) -- (51) -- (55) --(54) -- (50); % x = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (52) -- (51) -- (55) --(56) -- (52); % y = \a + \b
	}
	%
	\visible<9-10>{
	% Lastly, $b^3$ (little cube at the upper-front corner)
	\draw[red,thick,fill=cyan!35,opacity=0.35] (57) -- (58) -- (59) --(60) -- (57); % z = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (57) -- (60) -- (64) --(61) -- (57); % x = 0
	\draw[red,thick,fill=cyan!35,opacity=0.35] (57) -- (58) -- (62) --(61) -- (57); % y = \a
	%
	\node at (\a+0.5*\b+\dx,\a+0.5*\b+\dx,\a+0.5*\b+\dx) {$b^3$};
	%
	\draw[red,thick,fill=cyan!35,opacity=0.35] (61) -- (62) -- (63) --(64) -- (61); % z = \a 
	\draw[red,thick,fill=cyan!35,opacity=0.35] (58) -- (59) -- (63) --(62) -- (58); % x = \a
	\draw[red,thick,fill=cyan!35,opacity=0.35] (60) -- (59) -- (63) --(64) -- (60); % y = \a + \b
	}
	%
	\visible<6-9>{
	% Indications for distances at the plane x = \a + \dx
	\draw[gray,dash dot dot]($(13)!-0.125!(32)$)--($(32)!-0.125!(13)$);
	\draw[gray,dash dot dot]($(41)!-0.125!(60)$)--($(60)!-0.125!(41)$);
	\draw[gray,dash dot dot]($(45)!-0.125!(64)$)--($(64)!-0.125!(45)$);
	% Indications for distances at the plane x = \a + \dx + \b
	\draw[gray,dash dot dot]($(14)!-0.125!(31)$)--($(31)!-0.125!(14)$);
	\draw[gray,dash dot dot]($(42)!-0.125!(59)$)--($(59)!-0.125!(42)$);
	\draw[gray,dash dot dot]($(46)!-0.125!(63)$)--($(63)!-0.125!(46)$);
	% Indications for distances at the plane y = 0
	\draw[gray,dash dot dot]($(5)!-0.125!(14)$)--($(14)!-0.125!(5)$);
	\draw[gray,dash dot dot]($(33)!-0.125!(42)$)--($(42)!-0.125!(33)$);
	\draw[gray,dash dot dot]($(37)!-0.125!(46)$)--($(46)!-0.125!(37)$);
	% Indications for distances at the plane y = \a
	\draw[gray,dash dot dot]($(6)!-0.125!(23)$)--($(23)!-0.125!(6)$);
	\draw[gray,dash dot dot]($(34)!-0.125!(51)$)--($(51)!-0.125!(34)$);
	\draw[gray,dash dot dot]($(38)!-0.125!(55)$)--($(55)!-0.125!(38)$);
	% Indications for distances at the plane y = \a + \dx
	\draw[gray,dash dot dot]($(8)!-0.125!(15)$)--($(15)!-0.125!(8)$);
	\draw[gray,dash dot dot]($(36)!-0.125!(43)$)--($(43)!-0.125!(36)$);
	\draw[gray,dash dot dot]($(40)!-0.125!(47)$)--($(47)!-0.125!(40)$);
	% Indications for distances at the plane y = \a + \dx + \b
	\draw[gray,dash dot dot]($(24)!-0.125!(31)$)--($(31)!-0.125!(24)$);
	\draw[gray,dash dot dot]($(52)!-0.125!(59)$)--($(59)!-0.125!(52)$);
	\draw[gray,dash dot dot]($(56)!-0.125!(63)$)--($(63)!-0.125!(56)$);
	%
	\draw[gray,dash dot dot]($(53)!-0.125!(62)$)--($(62)!-0.125!(53)$);
	}	
	%
	\end{tikzpicture}
	%
	\end{center}
	%
	% Node indicating the algebraic representation of the cube of the binomial
	%
	\begin{tikzpicture}[remember picture,overlay]
		\node[below right,shift={(0.25,-0.5)}] at (current page.north west){$(a + b)^{3} = a^{3} + 3\,a^{2}b + 3\,ab^{2} + b^{3}$};
	\end{tikzpicture}
	%
\end{frame}
%
% That's all folks!
%
\end{document}

El resultado final se muestra a continuación.

Si aún no conoces LaTeX2e, te invito a aprenderlo con nuestro curso en línea gratuito, titulado LaTeX2e para principiantes.

marzo 20, 2023
Posts | Cursos
Efraín Soto Apolinar

El Prof. Efrain Soto Apolinar es autor de varios libros de matemáticas de bachillerato (álgebra, geometría plana, geometría analítica y funciones) y ha publicado un par de artículos científicos en el área de la educación matemática. El Prof. Soto es el fundador, titular e instructor del sitio web Aprende Matemáticas, donde ofrece cursos en línea sobre matemáticas, principalmente para los niveles bachillerato y universitario, así como cursos para la formación de profesores y profesores de matemáticas. Ha enseñado matemáticas desde el año 2002 en secundaria, bachillerato y en el nivel universitario. En este último caso, ha impartido cursos de matemáticas para estudiantes de ingeniería, cursos en modalidades regular y Honors, en Español al igual que en Inglés.

Website : https://www.aprendematematicas.org.mx/members/efrain-soto-apolinar/

0 responses on "Binomio al cubo: animación en LaTeX2e"

    Leave a Message

    Tu dirección de correo electrónico no será publicada. Los campos obligatorios están marcados con *

    Este sitio usa Akismet para reducir el spam. Aprende cómo se procesan los datos de tus comentarios.

    Accessibility by WAH
    X