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3.1 Generating Theorem Environments Using Pandoc Fence Code Blocks

Bookdown has a lua filter called “latex-div.lua” which handles theorem environments for latex.

If $c$ denotes the length of the hypotenuse and $a$ and $b$ denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: $$a^2+b^2=c^2.$$

If $c$ denotes the length of the hypotenuse and $a$ and $b$ denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: $$a^2+b^2=c^2.$$

If $c$ denotes the length of the hypotenuse and $a$ and $b$ denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: $$a^2+b^2=c^2.$$

For any angle $\theta$, we have $${\sin }^2\theta +{\cos }^2\theta =1$$

For any angle $\theta$, we have $${\sin }^2\theta +{\cos }^2\theta =1$$

For any angle $\theta$, we have $${\sin }^2\theta +{\cos }^2\theta =1$$

By ??, we know that …. ??

Pandoc use ::: {#Id .Div_attributes} to start and ::: to end a Div block. Such a block can be converted to LaTeX environment using lua.

Let $f$ be a function differentiable over $(a,b)$. If $f^{\prime }\left(x\right)>0$ for any $x$ in $(a,b)$, then $f\left(a\right)<f\left(x\right)<f\left(b\right)$$ for any $x$ in $(a,b)$.

Find the hypotenuose for the right triangle whose legs are 4 and 3.

By ??, the hypothenuose is $$\sqrt{3^2+4^2}=5.$$

3.2 Practice

Simplify. Write with positive exponents.

1. $\left(3a^2{b}^3{c}^2\right)\left(4ab{c}^2\right)\left(2b^2{c}^3\right)$
2. $\frac{4y^3{z}^0}{x^2{y}^2}$
3. $(-2{)}^{-3}$