Department of Mathematics
Lecturer:
Samy Zafrany
Moodle Course Page
Please visit this page regularly for all administrative information:
homework assignments,
course adminstrator,
books and course materials,
exams and grading policy,
faculty and teaching assistants lists,
office hours,
study units,
etc.
Course Program
\(
r = \sin^{m_1}(m_0\phi) + \cos^{m_3}(m_2\phi) + \sin^{m_5}(m_4\theta) + \cos^{m_7}(m_6\theta) + \sin^{m_9}(m_8\theta) + \cos^{m_{11}}(m_{10}\theta) \\
\)
The parametric equations are:
\[
\begin{cases}
x &= r \sin(\phi) \cos(\theta) \\[0.5em]
y &= r \cos(\phi) \\[0.5em]
z &= r \sin(\phi) \sin(\theta)
\end{cases}
\]
Initial values of the twelve parameters are:
\(
\newcommand\T{\Rule{0pt}{1em}{.3em}}
\)
\[
\renewcommand{\arraystretch}{0.9}
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
m_0 & m_1 & m_2 & m_3 & m_4 & m_5 & m_6 & m_7 & m_8 & m_9 & m_{10} & m_{11} \\
\hline
4.0 & 3.0 & 2.0 & 3.0 & 6.0 & 2.0 & 6.0 & 4.0 & 8.0 & 4.0 & 6.0 & 8.0 \\
\hline
\end{array}
\]
The Python code for generating this movie can be obtained from here.
This is the classical Spherical Harmonics 3D surface with 8 static parameters
\(
r = \sin^{m_1}(m_0\phi) + \cos^{m_3}(m_2\phi) + \sin^{m_5}(m_4\theta) + \cos^{m_7}(m_6\theta) \\
\)
The parametric equations are:
\[
\begin{cases}
x &= r \sin(\phi) \cos(\theta) \\[0.5em]
y &= r \cos(\phi) \\[0.5em]
z &= r \sin(\phi) \sin(\theta)
\end{cases}
\]
Static values of the eight parameters are:
\(
\newcommand\T{\Rule{0pt}{1em}{.3em}}
\)
\[
\renewcommand{\arraystretch}{0.9}
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
m_0 & m_1 & m_2 & m_3 & m_4 & m_5 & m_6 & m_7 \\
\hline
4.0 & 3.0 & 2.0 & 3.0 & 6.0 & 2.0 & 6.0 & 4.0 \\
\hline
\end{array}
\]
The Python code for generating this movie can be obtained from here.
The Cartesian equation of the Conic Section surface is given by \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = \frac{z^2}{c^2} \]
The Cartesian equation of the Hyperoloid surface is given by \[ x^2 - y^2 - z^2 = 4 \] The tangent plane is \[ 3x - 2y - z - 4 = 0 \] The tangent point is \((3,2,1)\).
