The Witch of Agnesi
The Witch of Agnesi is the curve that is described by the following equation:
The code to display the graph of these equations for a range of a in MatLab is :
% Exercise 1.8
% The Witch of Agnesi
%
% Jeff Thompson
%
clear;
steps = 2000; % Define the number of steps
range = 100 -(-100); % Define the abs of range
mesh = range/steps; % Define the mesh size
initialPosition = -100; % Define the starting position
hold all;
whitebg('white')
axis([-15 15 -15 15])
xlabel('x')
ylabel('y')
title('The Witch of Agnesi')
for a = 1:6
for i =1: steps+1
x(i)=initialPosition + (i-1)*mesh;
y(i)=(8*a^3)/(x(i)^2+4*a^2);
end
plot( x, y)
end
This produces the graph:
Three Leaved Rose
The Three Leaved Rose is the curve that is described by the following equation:
The code to display the graph of these equations where a=1 in MatLab is :
% Exercise 1.8
% Three-Leaved Rose
%
% Jeff Thompson
%
clear;
steps = 200; % Define the number of steps
range = 2*pi -(0); % Define the abs of range
mesh = range/steps; % Define the mesh size
initialPosition = 0; % Define the starting position
hold all;
whitebg('white')
axis([-5*pi 5*pi -5*pi 5*pi])
xlabel('theta')
ylabel('r')
title('Three-Leaved Rose')
a=10;
for i =1: steps+1
theta(i)=initialPosition + (i-1)*mesh;
r1(i)=a*sin(3*theta(i));
end
polar( theta, r1)
This produces the graph:
Strophoid
The Strophoid is the curve that is described by the following equation:
The code to display the graph of these equations where a=1 in MatLab is :
% Exercise 1.8
% Strophoid
%
% Jeff Thompson
%
clear;
steps = 200; % Define the number of steps
range = 2*pi -(0); % Define the abs of range
mesh = range/steps; % Define the mesh size
initialPosition = 0; % Define the starting position
hold all;
axis([-1 1 -1 1])
whitebg('white')
xlabel('theta')
ylabel('r')
title('The Strophoid')
a=1;
for i =1: steps+1
theta(i)=initialPosition + (i-1)*mesh;
r1(i)=a*cos(2*theta(i))*sec(theta(i));
end
polar( theta, r1)
This produces the graph:
The Arithmetic Spiral (Spiral of Archimedes)
The Arithmetic Spiralor Spiral of Archimedes is the curve that is described by the following equation:
The code to display the graph of these equations where a=1 in MatLab is :
% Exercise 1.8
% Spiral of Archimedes
%
% Jeff Thompson
%
clear;
steps = 1200; % Define the number of steps
range = 6*pi -(0); % Define the abs of range
mesh = range/steps; % Define the mesh size
initialPosition = 0; % Define the starting position
hold all;
whitebg('white')
axis([-5*pi 5*pi -5*pi 5*pi])
xlabel('theta')
ylabel('r')
title('The Spiral of Archimedes')
a=1;
for i =1: steps+1
theta(i)=initialPosition + (i-1)*mesh;
r1(i)=a*theta(i);
end
polar( theta, r1)
This produces the graph:
The Parabolic Spiral (Fermat’s Spiral)
The Fermat's Spiralor Parabolic Spiral is the curve that is described by the following equation:
The code to display the graph of these equations where a=1 in MatLab is :
% Exercise 1.8
% Parabolic Spiral
%
% Jeff Thompson
%
clear;
steps = 1000; % Define the number of steps
range = 5*pi -(-5*pi); % Define the abs of range
mesh = range/steps; % Define the mesh size
initialPosition = -5*pi; % Define the starting position
hold all;
whitebg('white')
axis([-5*pi 5*pi -5*pi 5*pi])
xlabel('theta')
ylabel('r')
title('The Parabolic Spiral')
a=.01;
k=100;
for i =1: steps+1
theta(i)=initialPosition + (i-1)*mesh;
r1(i)=real(a+sqrt(4*a*k*theta(i)));
r2(i)=real(a-sqrt(4*a*k*theta(i)));
end
polar( theta, r1)
polar( theta, r2)
This produces the graph:
