Lagrange_simple.svg
Size of this PNG preview of this SVG file:
512 × 450 pixels
.
Other resolutions:
273 × 240 pixels
|
546 × 480 pixels
|
874 × 768 pixels
|
1,165 × 1,024 pixels
|
2,330 × 2,048 pixels
.
Summary
Description Lagrange simple.svg |
English:
derivative of
https://en.wikipedia.org/wiki/File:Lagrange_simple.jpg
|
Date | |
Source | Own work based on: Lagrange simple.svg en:File:Lagrange simple.jpg |
Author |
Original:
Jacobmelgaard
Vector:
|
SVG development
InfoField
|
This
oversized
trigonometry was created with
Inkscape
.
This trigonometry uses
embedded
text that can be
easily translated
using a text editor.
|
Source Code
The graph was made in Matlab with the following source code
% Function data [X,Y] = meshgrid(-2:0.1:2, -2:0.1:2); Z = (X.^2).*Y; % Constraint data t = -pi:0.01:pi; xc = sqrt(3)*cos(t); yc = sqrt(3)*sin(t); zc = xc.^2 .* yc; % Plot graph and constraint figure(); surface = surfc(X,Y,Z); hold on; plot3(xc, yc, zc, 'k', 'LineWidth', 2); plot3(xc, yc ,-10*ones(1,length(t)), 'k', 'LineWidth', 1); set(gcf, 'Color', [1 1 1]); set(gcf, 'Position', [46 107 767 682]); % Axis labels text(0.2, -3, -10, 'x'); text(2.5, -.5, -10, 'y'); text(-2.4, -2, 0, 'z'); % Annotations of the max and min points % Point indicating max #1 plot3(sqrt(2), 1, 2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2), 1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',... 'String', '$$(\sqrt{2}, 1, 2)$$',... 'Position', [1.1 .1 2.1],... 'FontSize', 20); % Point indicating max #2 plot3(-sqrt(2), 1, 2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2), 1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',... 'String', '$$(-\sqrt{2}, 1, 2)$$',... 'Position', [-1.6 .1 2.1],... 'FontSize', 20); % Point indicating min #1 plot3(sqrt(2), -1, -2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2), -1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); plot3(0,1,-3,'kx') text('Interpreter', 'latex',... 'String', '$$(\sqrt{2}, -1, -2)$$',... 'Position', [.5 -.8 -1.4],... 'FontSize', 20); % Point indicating min #2 plot3(-sqrt(2), -1, -2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2), -1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',... 'String', '$$(-\sqrt{2}, -1, -2)$$',... 'Position', [-1.9 -.8 -1],... 'FontSize', 20); hold off; shading interp; view([25 18]); %plot2svg must be retrieved from http://www.zhinst.com/blogs/schwizer/ plot2svg;
Corresponding Mathematica code:
Block[{x, y, f = #^2 #2 &, g = #^2 + #2^2 &, c = 3}, sol = With[{max = MaxValue[{f[x, y], g[x, y] == c}, {x, y}]}, Solve[{f[x, y] == max, g[x, y] == c}, {x, y}, Reals] ]; Show[ Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, Mesh -> {{c}}, MeshFunctions -> g, PlotRange -> All, Boxed -> False, AspectRatio -> 1, PlotPoints -> 30, MeshStyle -> Cyan, PerformanceGoal -> "Quality", ColorFunction -> "DeepSeaColors"], Graphics3D[{Red, PointSize[Large], Point[{x, y, f[x, y]} /. sol]}] ] ]
Licensing
This file is licensed under the
Creative Commons
Attribution-Share Alike 3.0 Unported
license.
-
You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
-
Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.