# Math Girls Manga Math Online Tom Circle

Chapter 3 on Rotation is excellent ! He combines Analytic Geometry, Linear Algebra (Matrix) , and Physics (Rotation) into “one same thing” to show the beauty of Mathematics:

The following matrix represents a rotation \$latex rho (theta)\$ by an angle \$latex theta\$:

\$latex begin{pmatrix}
cos {theta} & -sin {theta}
sin {theta} & cos {theta}
end{pmatrix}
\$

Rotate by \$latex 2theta \$ will be:
\$latex begin{pmatrix}
cos {2theta} & -sin {2theta}
sin {2theta} & cos {2theta}
end{pmatrix}
\$

Which is equivalent to rotate 2 successive angle of \$latex theta \$:
\$latex rho (theta) .rho (theta) = rho^2 (theta) \$:

\$latex begin{pmatrix}
cos {theta} & -sin {theta}
sin {theta} & cos {theta}
end{pmatrix}^2
\$
= \$latex begin{pmatrix}
cos {theta} & -sin {theta}
sin {theta} & cos {theta}
end{pmatrix} \$ \$latex begin{pmatrix}
cos {theta} & -sin {theta}
sin {theta} & cos {theta}
end{pmatrix}\$
= \$latex begin{pmatrix}
cos ^2 {theta} – sin ^2 {theta…

View original post 46 more words ## Author: tomcircle

Math amateur

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