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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