pretty-math-equations-formatting.md

Pretty Math Equations Formatting | Start Chat

Make ChatGPT provide any mathematical formulas with LaTeX Equation formatting, thus rendering equations much more Elegantly. (it is possible to ask for the code to generate those equations in LaTeX yourself)

DO THIS ON CHAT GPT's WEBSITE ( https://chat.openai.com/chat ) FOR THE FORMATTING TO RENDER CORRECTLY!

Prompt

ra8Xwnf7V_U_sAIFF4Cu8

Welcome Message

Sure, I'll format all equations in my responses with LaTeX formatting and surround each equation with $$ as requested.

For example:

$$

\sum_{i=1}^n i = \frac{n(n+1)}{2}

$$

Conversation

ASSISTANT: Sure, I'll format all equations in my responses with LaTeX formatting and surround each equation with $$ as requested.

For example:

$$

\sum_{i=1}^n i = \frac{n(n+1)}{2}

$$ USER: what is the pythagorem theorem ASSISTANT: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be represented as:

$$

a^2 + b^2 = c^2

$$

where 'a' and 'b' are the lengths of the two shorter sides of the right triangle, and 'c' is the length of the hypotenuse. USER: what are the three rotation matrices? ASSISTANT: The three rotation matrices correspond to rotations about the x-axis, y-axis, and z-axis in three-dimensional space. They are:

1. Rotation about the x-axis:

$$

\begin{bmatrix}

1 & 0 & 0 \

0 & \cos(\theta) & -\sin(\theta) \

0 & \sin(\theta) & \cos(\theta)

\end{bmatrix}

$$

2. Rotation about the y-axis:

$$

\begin{bmatrix}

\cos(\theta) & 0 & \sin(\theta) \

0 & 1 & 0 \

-\sin(\theta) & 0 & \cos(\theta)

\end{bmatrix}

$$

3. Rotation about theThe three standard rotation matrices are:

4. Rotation about the x-axis by an angle $\theta$:

$$

\begin{bmatrix}

1 & 0 & 0 \\

0 & \cos \theta & - \sin \theta \\

0 & \sin \theta & \cos \theta 

\end{bmatrix}

$$

2. Rotation about the y-axis by an angle $\theta$:

$$

\begin{bmatrix}

\cos \theta & 0 & \sin \theta \\

0 & 1 & 0 \\

-\sin \theta & 0 & \cos \theta 

\end{bmatrix}

$$

3. Rotation about the z-axis by an angle $\theta$:

$$

\begin{bmatrix}

\cos \theta & -\sin \theta & 0 \\

\sin \theta & \cos \theta & 0 \\

0 & 0 & 1 

\end{bmatrix}

$$

In each matrix, $\cos \theta$ and $\sin \theta$ represent the cosine and sine of the angle $\theta$, respectively.