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%                            Michael Pokojovy                             % 
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figure(1);

set(gcf, 'PaperUnits', 'centimeters');
xSize = 16; ySize = 15;
xLeft = (21 - xSize)/2; yTop = (30 - ySize)/2;
set(gcf,'PaperPosition', [xLeft yTop xSize ySize]);
set(gcf,'Position',[0 0 xSize*50 ySize*50]);

hold on;

t = linspace(0, 2*pi, 200);

n     = [1, 3, 5, 10];
color = ['r', 'g', 'b', 'm'];

x = cos(t);
y = sin(t);
plot(x, y, 'k');

for i = 1:length(n)
    x = cos(t) + 1/n(i)*cos(n(i)*t);
    y = sin(t) + 1/n(i)*sin(n(i)*t);
    plot(x, y, color(i));
end

axis([-2 4 -2 4]);

hleg = legend('$\gamma(t) = (\cos(t), \sin(t))$', ...
              '$\gamma_{1}(t) = (\cos(t) + \cos(t), \sin(t) + \sin(t))$', ...
              '$\gamma_{3}(t) = (\cos(t) + \frac{1}{3} \cos(3t), \sin(t) + \frac{1}{3} \sin(3t))$', ...
              '$\gamma_{5}(t) = (\cos(t) + \frac{1}{5} \cos(5t), \sin(t) + \frac{1}{5} \sin(5t))$', ...
              '$\gamma_{10}(t) = (\cos(t) + \frac{1}{10} \cos(10t), \sin(t) + \frac{1}{10} \sin(10t))$');
          
set(hleg, 'interpreter', 'latex');
set(hleg, 'FontSize', 16);

xlabel('x_{1}');
ylabel('x_{2}');

t = title(['Folge von Wegen $(\gamma_{n})_{n}$ und deren $\mathcal{C}^{0}$-Grenzwert $\gamma$'], 'interpreter', 'latex');
set(t, 'FontSize', 16);